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Why Does the Speed of Light Change How Time Works · Night Science Stories

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  Speaker 2: And welcome to the Sleepy Scientist. However the day has gone,
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  Speaker 2: I'm very grateful for the support. Now, this evening we're
• 1:55
  Speaker 2: looking at something that seems perfectly ordinary, right up until
• 1:59
  Speaker 2: you start thinking about it. Time. We all feel as
• 2:03
  Speaker 2: though we understand it. Seconds turn into minutes, minutes into hours,
• 2:08
  Speaker 2: and whatever we happen to be doing, it seems to
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  Speaker 2: tick along at exactly the same steady pace for everyone.
• 2:14
  Speaker 2: At least that's what most of us have always assumed.
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  Speaker 2: But light, of all things, has something rather surprising to
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  Speaker 2: say about that. It travels at nearly 300,000 kilometres every second.
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  Speaker 2: And the truly strange part isn't how fast it goes.
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  Speaker 2: It's that everyone who measures it gets exactly the same answer,
• 2:35
  Speaker 2: no matter how fast they themselves happen to be moving.
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  Speaker 2: For that to work, something else has to give. And
• 2:41
  Speaker 2: what gives is time. Two people can measure different amounts
• 2:45
  Speaker 2: of time between the same two events. A clock sent
• 2:48
  Speaker 2: off on a fast journey through space can come home
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  Speaker 2: having ticked away less time than one left sitting on Earth.
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  Speaker 2: Two observers can even disagree about whether faraway events happened
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  Speaker 2: at the same moment, and neither of them is wrong.
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  Speaker 2: Which leaves us with a rather peculiar question. Why should
• 3:05
  Speaker 2: something as ordinary as light have anything to do with
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  Speaker 2: how quickly time passes? So find a comfortable position, let
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  Speaker 2: the day slip into the background, and close your eyes
• 3:16
  Speaker 2: whenever you're ready. There's nothing you need to remember and
• 3:19
  Speaker 2: certainly no need to stay awake for the answer. Shall
• 3:23
  Speaker 2: we begin? Because time, it turns out, doesn't always pass
• 3:27
  Speaker 2: the way we imagine. And it all starts with a
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  Speaker 2: beam of light. Time seems like one of the few
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  Speaker 2: things in life that ought to be straightforward. A second passes,
• 3:37
  Speaker 2: followed by another second, and then another. Clocks move forwards,
• 3:42
  Speaker 2: birthdays arrive, and the world continues at what feels like
• 3:45
  Speaker 2: a perfectly steady pace. Whether you're sitting comfortably at home,
• 3:50
  Speaker 2: travelling along a railway, or looking out of an aeroplane window,
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  Speaker 2: there's no obvious reason to believe that time itself should
• 3:57
  Speaker 2: behave any differently. And yet, according to modern physics, it does.
• 4:03
  Speaker 2: The remarkable thing is that this strange behaviour of time
• 4:06
  Speaker 2: is connected to something that, at first, seems entirely unrelated.
• 4:11
  Speaker 2: The speed of light. Light travels through a vacuum at
• 4:15
  Speaker 2: exactly 299 million 792,458 metres per second. That's approximately 300,000
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  Speaker 2: kilometres every second. At that speed, light could travel around
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  Speaker 2: Earth's equator more than seven times in a single second.
• 4:35
  Speaker 2: A beam of light leaving the Moon takes approximately 1.3
• 4:38
  Speaker 2: seconds to reach us. And the sunlight falling through your
• 4:42
  Speaker 2: window began its journey roughly 8 minutes and 20 seconds
• 4:46
  Speaker 2: earlier travelling across nearly 150 million kilometres of space. These
• 4:52
  Speaker 2: are extraordinary distances, crossed in remarkably little time. But the
• 4:57
  Speaker 2: most important thing about light isn't simply how quickly it travels.
• 5:02
  Speaker 2: It's that its speed through a vacuum is the same
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  Speaker 2: for every observer moving at a constant velocity, regardless of
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  Speaker 2: how quickly those observers are travelling relative to one another.
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  Speaker 2: And this creates a rather interesting problem. Imagine sitting inside
• 5:17
  Speaker 2: a train that's travelling smoothly along a straight railway line.
• 5:21
  Speaker 2: You throw a ball towards the front of the carriage.
• 5:24
  Speaker 2: From your perspective, the ball moves forwards at an ordinary speed,
• 5:28
  Speaker 2: but someone standing beside the track sees something slightly different.
• 5:32
  Speaker 2: To that observer, the ball's forward velocity includes the movement
• 5:36
  Speaker 2: of the train itself. Both descriptions make perfect sense. Now
• 5:41
  Speaker 2: imagine replacing the ball with a beam of light. you
• 5:44
  Speaker 2: might expect the same principle to apply. Perhaps someone travelling
• 5:48
  Speaker 2: towards the beam would measure it moving faster, while someone
• 5:51
  Speaker 2: travelling in the same direction would measure it moving more slowly.
• 5:55
  Speaker 2: But that isn't what happens. Both observers, when measuring the
• 5:59
  Speaker 2: light locally with their own clocks and measuring instruments, obtain
• 6:03
  Speaker 2: exactly the same speed in a vacuum. It doesn't matter
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  Speaker 2: whether they're standing beside the railway or travelling aboard the train.
• 6:10
  Speaker 2: The speed of light remains unchanged. This was one of
• 6:14
  Speaker 2: the central insights behind Albert Einstein's special theory of relativity,
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  Speaker 2: published in 1905. And it forced physicists to reconsider something
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  Speaker 2: they had previously taken almost entirely for granted. The nature
• 6:30
  Speaker 2: of time. In ordinary life, we tend to imagine that
• 6:34
  Speaker 2: the universe possesses one enormous invisible clock, ticking away at
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  Speaker 2: exactly the same rate everywhere. Under this assumption, Two people
• 6:44
  Speaker 2: might disagree about how fast an object is moving, or
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  Speaker 2: how far it has travelled, but they should always agree
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  Speaker 2: about the amount of time that has passed between the
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  Speaker 2: same two events. Einstein showed that this assumption cannot be
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  Speaker 2: maintained alongside the constant speed of light. If different observers
• 7:02
  Speaker 2: are to agree on the speed of light, they cannot
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  Speaker 2: always agree on measurements of distance and time. The measurements
• 7:08
  Speaker 2: themselves must depend upon the observer's state of motion. And
• 7:12
  Speaker 2: this is where time becomes considerably more interesting. Imagine two
• 7:17
  Speaker 2: identical clocks. One remains on Earth, while the other travels
• 7:21
  Speaker 2: aboard a spacecraft moving at an enormous speed. Both clocks
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  Speaker 2: are perfectly accurate. Neither has been damaged, and neither has
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  Speaker 2: developed some peculiar mechanical fault. Yet, when the clocks are
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  Speaker 2: eventually brought together again, they can display different amounts of
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  Speaker 2: elapsed time. The clock that travelled along the particular high-speed
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  Speaker 2: journey may have recorded less time than the clock that
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  Speaker 2: remained behind. This phenomenon is known as time dilation. It
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  Speaker 2: isn't an illusion caused by the way light reaches our eyes,
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  Speaker 2: nor does it mean that the travelling clock was somehow
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  Speaker 2: prevented from working properly. The difference is real, and importantly
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  Speaker 2: the person travelling with that clock would never notice anything
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  Speaker 2: unusual about the passage of their own time. Their watch
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  Speaker 2: would tick normally. their heart would beat normally. Their thoughts
• 8:14
  Speaker 2: and conversations would continue at their familiar pace. A minute
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  Speaker 2: would still feel like a minute. This distinction matters because
• 8:23
  Speaker 2: relativity doesn't suggest that people can somehow feel their personal
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  Speaker 2: experience of time becoming slower. Instead, it describes how different
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  Speaker 2: observers measure elapsed time, particularly when they follow different paths
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  Speaker 2: through what physicists call spacetime. Spacetime is the combined structure
• 8:42
  Speaker 2: of space and time, in which an event is identified
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  Speaker 2: not only by where it happens, but also by when
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  Speaker 2: it happens. An observer's journey through spacetime determines the time
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  Speaker 2: accumulated by a clock travelling alongside them. Physicists call this
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  Speaker 2: measured elapsed time proper time. Another observer, moving differently, may
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  Speaker 2: assign a different time interval to those same events using
• 9:06
  Speaker 2: the clocks and coordinates of their own reference frames. Neither
• 9:10
  Speaker 2: measurement needs to be incorrect. They're simply describing the events
• 9:14
  Speaker 2: from different perspectives within the same physical universe. There is
• 9:19
  Speaker 2: another distinction worth making. When sunlight takes a little over
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  Speaker 2: eight minutes to reach Earth, that delay doesn't mean time
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  Speaker 2: is running more slowly on the Sun. It simply means
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  Speaker 2: that light requires time to cross the distance between us.
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  Speaker 2: Light travel time and relativistic time dilation are different phenomena.
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  Speaker 2: Even though both involve the finite speed of light, the
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  Speaker 2: deeper connection lies in the way space and time are related.
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  Speaker 2: Light doesn't travel around the universe, somehow interfering with clocks
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  Speaker 2: and making them change speed. Instead, the fact that light
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  Speaker 2: possesses an invariant speed tells us something fundamental about the
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  Speaker 2: geometry of space-time itself. Distance and duration are not completely
• 10:04
  Speaker 2: independent properties of reality. They are connected in a way
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  Speaker 2: that everyday experience rarely allows us to notice. At the
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  Speaker 2: modest speeds of ordinary life, these differences are so incredibly
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  Speaker 2: small that we can comfortably ignore them A person walking
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  Speaker 2: to the shops doesn't need to worry about returning home
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  Speaker 2: noticeably younger than somebody who stayed behind, which is probably
• 10:27
  Speaker 2: just as well, because buying a loaf of bread would
• 10:30
  Speaker 2: become a rather complicated affair. But the underlying physics is
• 10:35
  Speaker 2: still there. Every clock follows its own path through spacetime,
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  Speaker 2: and the amount of time it measures belongs to that path.
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  Speaker 2: What makes this especially remarkable is that none of it
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  Speaker 2: depends on how we happen to perceive time, The effect
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  Speaker 2: exists whether we're watching the clocks, ignoring them, or fast asleep.
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  Speaker 2: Time is a measurable part of the physical universe, and
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  Speaker 2: its behaviour is inseparably connected to the universal speed of light.
• 11:04
  Speaker 2: Something we experience as perfectly ordinary turns out to have
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  Speaker 2: a rather extraordinary structure, and perhaps the strangest part is
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  Speaker 2: that every one of us experiences our own passing seconds
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  Speaker 2: as entirely normal. even though the universe doesn't require everyone
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  Speaker 2: else's seconds to fit into one universal clock. For much
• 11:23
  Speaker 2: of human history, the speed of light was something nobody
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  Speaker 2: could measure, and many people weren't entirely convinced that it
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  Speaker 2: needed measuring at all. After all, light appears to arrive
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  Speaker 2: almost immediately. When you open the curtains in the morning,
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  Speaker 2: the room becomes illuminated without any noticeable delay. When a
• 11:42
  Speaker 2: candle is lit, its surroundings brighten at once. And when
• 11:47
  Speaker 2: you look towards a distant hill, there is nothing about
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  Speaker 2: the experience that suggests the light reaching your eyes has
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  Speaker 2: spent any measurable amount of time travelling. It was therefore
• 11:57
  Speaker 2: quite reasonable for early thinkers to wonder whether light might
• 12:01
  Speaker 2: move instantaneously. Perhaps it simply appeared wherever it was needed,
• 12:06
  Speaker 2: without requiring any time to cross the intervening distance. The
• 12:10
  Speaker 2: problem was that light travels so extraordinarily quickly that The
• 12:15
  Speaker 2: distinguishing between instantaneous movement and merely enormous speed was almost
• 12:20
  Speaker 2: impossible with the instruments available. Even across several kilometres the
• 12:25
  Speaker 2: delay is measured in tiny fractions of a second, and
• 12:29
  Speaker 2: in the 17th century measuring such an interval presented a
• 12:33
  Speaker 2: considerable challenge. The Italian scientist Galileo Galilei was among those
• 12:38
  Speaker 2: who attempted to investigate the question experimentally. He proposed a
• 12:42
  Speaker 2: remarkably straightforward arrangement involving two observers, each carrying a lantern
• 12:47
  Speaker 2: fitted with a cover. The observers would stand some distance apart,
• 12:52
  Speaker 2: perhaps on neighbouring hills. One would uncover their lantern, sending
• 12:56
  Speaker 2: a flash towards the other. As soon as the second
• 13:00
  Speaker 2: observer saw the light, they would uncover their own lantern
• 13:03
  Speaker 2: in response. The first observer would then measure the interval
• 13:07
  Speaker 2: between revealing their light and seeing the returning signal. If
• 13:11
  Speaker 2: light required time to travel, perhaps the delay would become
• 13:15
  Speaker 2: noticeable as the observers moved farther apart. It was a
• 13:19
  Speaker 2: sensible idea. Unfortunately, human reaction times were enormously longer than
• 13:24
  Speaker 2: the light travel times involved. Across a distance of one kilometre,
• 13:29
  Speaker 2: light takes only about three millionths of a second to
• 13:32
  Speaker 2: complete a one-way journey. No person operating a lantern by
• 13:36
  Speaker 2: hand could reliably distinguish such a tiny interval. Galileo could
• 13:41
  Speaker 2: not establish a measurable speed, although his investigation helped make
• 13:45
  Speaker 2: the question an experimental one. The decisive evidence would eventually
• 13:49
  Speaker 2: come from somewhere much farther away. Jupiter. In 1676, the
• 13:55
  Speaker 2: Danish astronomer Ola Rømer was studying the movements of Io,
• 13:59
  Speaker 2: one of Jupiter's largest moons. Io completes an orbit around
• 14:03
  Speaker 2: Jupiter in approximately one day and 18 hours. During its journey,
• 14:08
  Speaker 2: the Moon regularly passes into Jupiter's shadow, temporarily disappearing from
• 14:13
  Speaker 2: view before emerging again. These eclipses provided astronomers with something
• 14:18
  Speaker 2: resembling a natural astronomical clock. By observing repeated appearances and disappearances,
• 14:25
  Speaker 2: they could calculate when future events ought to occur. But
• 14:29
  Speaker 2: Riemer noticed something peculiar. The observed eclipse times did not
• 14:34
  Speaker 2: always agree with the predictions. When Earth and Jupiter were
• 14:38
  Speaker 2: moving farther apart, the eclipses appeared progressively later than expected.
• 14:43
  Speaker 2: When the distance between the planets was decreasing, the apparent
• 14:46
  Speaker 2: timing shifted in the opposite direction. The Moon itself was
• 14:51
  Speaker 2: not simply changing its orbital behaviour to accommodate observers on Earth. Instead,
• 14:56
  Speaker 2: ROMA recognised that the changing distance between the planets affected
• 15:01
  Speaker 2: how long the light took to reach us. When Earth
• 15:04
  Speaker 2: was farther away, the light had additional distance to travel.
• 15:08
  Speaker 2: And additional distance required additional time. Over successive observations, those
• 15:13
  Speaker 2: small differences accumulated into delays large enough to measure. This
• 15:18
  Speaker 2: was a remarkable discovery. It suggested that light did not
• 15:22
  Speaker 2: arrive instantaneously, but travelled at a finite speed. Roma's measurements
• 15:28
  Speaker 2: were not precise enough to establish the modern value, partly
• 15:31
  Speaker 2: because the astronomical distances involved were not yet known accurately. Nevertheless,
• 15:36
  Speaker 2: the essential principle had been demonstrated. Light takes time to travel.
• 15:42
  Speaker 2: For the first time, astronomers had convincing evidence that even
• 15:46
  Speaker 2: something travelling at an almost unimaginable speed obeyed a measurable
• 15:50
  Speaker 2: relationship between distance and duration. Nearly two centuries later, scientists
• 15:56
  Speaker 2: succeeded in bringing the problem back down to Earth. In 1849,
• 16:01
  Speaker 2: the French physicist Hippolyte Fizeau devised an experiment using a
• 16:06
  Speaker 2: rapidly rotating toothed wheel. He directed a beam of light
• 16:10
  Speaker 2: through a gap between the wheel's teeth towards a distant
• 16:13
  Speaker 2: mirror positioned several kilometres away. The light reflected from the
• 16:18
  Speaker 2: mirror and travelled back towards the wheel. But while it
• 16:21
  Speaker 2: was away, the wheel continued rotating. At certain rotational speeds,
• 16:27
  Speaker 2: a tooth moved into the position previously occupied by the gap,
• 16:31
  Speaker 2: blocking the returning light. By knowing the wheel's rotation rate
• 16:35
  Speaker 2: and the distance travelled by the beam, Vizot could estimate
• 16:39
  Speaker 2: how much time had passed. It was an ingenious method.
• 16:43
  Speaker 2: Instead of relying on human reaction times, he used the
• 16:47
  Speaker 2: predictable movement of machinery to measure an interval far too
• 16:51
  Speaker 2: brief for anyone to perceive. His result came impressively close
• 16:55
  Speaker 2: to the speed accepted today. The French physicist Léon Foucault
• 17:00
  Speaker 2: later developed a different technique involving a rotating mirror. By
• 17:04
  Speaker 2: observing the tiny change in direction of reflected light while
• 17:08
  Speaker 2: the mirror turned, he could obtain an increasingly accurate estimate
• 17:12
  Speaker 2: of its travel time. The American physicist Albert Abraham Michelson
• 17:17
  Speaker 2: subsequently refined rotating mirror measurements carrying out experiments that achieved
• 17:23
  Speaker 2: still greater precision. Meanwhile, another important development was changing how
• 17:28
  Speaker 2: scientists understood light itself. During the 19th century, the Scottish
• 17:33
  Speaker 2: physicist James Clerk Maxwell developed equations describing the relationship between
• 17:39
  Speaker 2: electricity and magnetism. His mathematical work showed that disturbances in
• 17:44
  Speaker 2: electromagnetic fields could propagate as waves through empty space. Remarkably,
• 17:50
  Speaker 2: the predicted speed of those waves agreed with measurements of
• 17:53
  Speaker 2: the speed of light. This supported the understanding that visible
• 17:57
  Speaker 2: light is a form of electromagnetic radiation. The same fundamental
• 18:02
  Speaker 2: phenomenon also includes radio waves, microwaves, infrared radiation, ultraviolet radiation,
• 18:09
  Speaker 2: X-rays and gamma rays. They differ in frequency and wavelength,
• 18:13
  Speaker 2: but all propagate through a vacuum at the same fundamental speed. Today,
• 18:18
  Speaker 2: that speed has an exact defined value. In 1983, the
• 18:23
  Speaker 2: international scientific community adopted a definition of the metre based
• 18:28
  Speaker 2: on the distance light travels through a vacuum during a
• 18:30
  Speaker 2: precisely specified fraction of a second. The International Bureau of
• 18:35
  Speaker 2: Weights and Measures helps maintain the international system of measurement
• 18:39
  Speaker 2: standards underlying this definition. Consequently, the speed of light in
• 18:44
  Speaker 2: a vacuum is now fixed at exactly 299,792,458 metres per second.
• 18:55
  Speaker 2: This exactness comes from the way the metre is defined,
• 18:59
  Speaker 2: not from an experiment that somehow eliminated every possible measurement uncertainty.
• 19:05
  Speaker 2: And the discovery that light takes time to travel has
• 19:08
  Speaker 2: given astronomy one of its most beautiful characteristics. Looking into
• 19:13
  Speaker 2: space also means looking into the past. We see the
• 19:17
  Speaker 2: moon as it was a little over a second ago,
• 19:19
  Speaker 2: the sun as it was several minutes ago, and distant
• 19:23
  Speaker 2: galaxies as they existed millions or billions of years earlier.
• 19:27
  Speaker 2: The greater the distance, the longer the light has spent
• 19:30
  Speaker 2: travelling towards us. But this ordinary delay is different from
• 19:34
  Speaker 2: relativistic time dilation. Light travel time describes how long a
• 19:39
  Speaker 2: signal takes to cross a distance. Time dilation describes how
• 19:43
  Speaker 2: different observers or clocks can measure different elapsed times because
• 19:47
  Speaker 2: of their motion or gravitational circumstances. The two ideas are connected,
• 19:53
  Speaker 2: but they are not interchangeable. And that distinction reveals something
• 19:57
  Speaker 2: especially important. Discovering that light has a finite speed was
• 20:02
  Speaker 2: already a remarkable achievement. Discovering that its speed is invariant,
• 20:07
  Speaker 2: regardless of the motion of the observer, revealed something far
• 20:11
  Speaker 2: more surprising. The measurements of space and time themselves cannot
• 20:15
  Speaker 2: be the same for everyone. What began with lanterns, distant
• 20:19
  Speaker 2: moons and spinning wheels eventually helped overturn the familiar idea
• 20:24
  Speaker 2: of a single universal clock. All because light, despite its
• 20:28
  Speaker 2: extraordinary speed, takes time to get anywhere. Imagine standing on
• 20:33
  Speaker 2: a railway platform watching a train pass through the station.
• 20:36
  Speaker 2: The train is travelling at 60 kilometres per hour. Inside
• 20:40
  Speaker 2: one of its carriages, a passenger walks towards the front
• 20:43
  Speaker 2: at 5km per hour, measured relative to the train. From
• 20:47
  Speaker 2: the passenger's perspective, they're simply walking at an ordinary pace.
• 20:51
  Speaker 2: But from the platform, their movement combines with the movement
• 20:54
  Speaker 2: of the train itself. They're travelling forwards at approximately 65km
• 20:59
  Speaker 2: per hour. If they turn around and walk towards the
• 21:02
  Speaker 2: rear of the carriage, their speed relative to the platform
• 21:06
  Speaker 2: becomes approximately 55km per hour. This is the familiar principle
• 21:12
  Speaker 2: of adding and subtracting velocities. It works beautifully for the
• 21:17
  Speaker 2: movements we encounter in everyday life. And for centuries physicists
• 21:21
  Speaker 2: naturally assumed that light should behave in much the same way.
• 21:25
  Speaker 2: If a source of light were moving towards you, perhaps
• 21:29
  Speaker 2: the light would travel towards you a little faster. If
• 21:31
  Speaker 2: you were travelling away from the source, perhaps you would
• 21:34
  Speaker 2: measure a slightly lower speed. It seems perfectly reasonable. Unfortunately,
• 21:40
  Speaker 2: light doesn't follow that expectation. To understand why, it's helpful
• 21:46
  Speaker 2: to return to the 19th century, when scientists were discovering
• 21:49
  Speaker 2: something remarkable about electricity and magnetism. The Scottish physicist James
• 21:55
  Speaker 2: Clerk Maxwell developed a set of equations describing how electric
• 21:59
  Speaker 2: and magnetic fields behave. Among their most important consequences was
• 22:04
  Speaker 2: the prediction that changing electric and magnetic fields could propagate
• 22:08
  Speaker 2: through space as electromagnetic waves, and those waves possessed a
• 22:13
  Speaker 2: characteristic speed. When Maxwell calculated that speed using the known
• 22:18
  Speaker 2: electromagnetic properties of a vacuum, the result was remarkably close
• 22:23
  Speaker 2: to the experimentally measured speed of light. This suggested that
• 22:27
  Speaker 2: light itself was an electromagnetic wave. It was an extraordinary
• 22:32
  Speaker 2: unification of phenomena that had previously seemed quite separate. but
• 22:37
  Speaker 2: it also raised a difficult question. A wave usually travels
• 22:41
  Speaker 2: through something. Sound waves travel through air, water or another material.
• 22:47
  Speaker 2: Ocean waves involve the movement of water. Vibrations along a
• 22:51
  Speaker 2: string require the string itself. So what was light travelling through?
• 22:56
  Speaker 2: Many 19th century physicists proposed the existence of an invisible
• 23:00
  Speaker 2: substance called the luminiferous ether. The ether was imagined as
• 23:05
  Speaker 2: a medium filling space, allowing light waves to propagate even
• 23:09
  Speaker 2: where there was no ordinary matter. If such a medium existed,
• 23:13
  Speaker 2: it seemed reasonable to expect that light would have a
• 23:16
  Speaker 2: particular speed relative to it. And because Earth travels around
• 23:20
  Speaker 2: the Sun, our planet ought to move through the aether.
• 23:24
  Speaker 2: This movement might produce an effect resembling a gentle wind,
• 23:28
  Speaker 2: except that the supposed wind would be detectable through measurements
• 23:32
  Speaker 2: of light rather than the movement of air. The idea
• 23:36
  Speaker 2: was known as the Aether Wind. In 1887, two American physicists,
• 23:42
  Speaker 2: Albert Abraham Michelson and Edward Williams Morley, carried out an
• 23:46
  Speaker 2: experiment designed to investigate this possibility. Their apparatus used a
• 23:51
  Speaker 2: device called an interferometer. A beam of light was divided
• 23:55
  Speaker 2: into two beams travelling along perpendicular paths. Mirrors reflected the
• 24:00
  Speaker 2: beams back towards one another, where they were recombined. When
• 24:05
  Speaker 2: light waves overlap, they produce patterns of reinforcement and cancellation
• 24:09
  Speaker 2: known as interference fringes. If Earth's movement through the aether
• 24:13
  Speaker 2: changed the relative travel times along the two paths, rotating
• 24:17
  Speaker 2: the apparatus should alter the interference pattern. The expected changes
• 24:21
  Speaker 2: were extremely small, but the experiment was designed to detect them,
• 24:26
  Speaker 2: and the result was puzzling. Michelson and Morley did not
• 24:30
  Speaker 2: observe the anticipated shift corresponding to Earth's motion through a
• 24:33
  Speaker 2: stationary aether. The experiment did not, by itself, establish every
• 24:39
  Speaker 2: principle of modern relativity. But it placed an important constraint
• 24:43
  Speaker 2: on conventional aether theories. Something about the existing understanding of
• 24:48
  Speaker 2: light and motion needed reconsidering. Several physicists developed mathematical explanations.
• 24:54
  Speaker 2: The Irish physicist George Francis Fitzgerald suggested that objects moving
• 24:59
  Speaker 2: through the aether might contract slightly along their direction of motion.
• 25:04
  Speaker 2: The Dutch physicist Hendrik Antoon Lawrence developed related ideas and
• 25:09
  Speaker 2: mathematical transformations describing how measurements could change between moving systems.
• 25:15
  Speaker 2: These transformations could account for results that were otherwise difficult
• 25:19
  Speaker 2: to reconcile with the expected aether wind. But the underlying
• 25:23
  Speaker 2: interpretation still involved an assumed preferred state of rest associated
• 25:28
  Speaker 2: with the aether. Then, in 1905, Albert Einstein proposed a
• 25:33
  Speaker 2: different way of understanding the problem. His special theory of
• 25:37
  Speaker 2: relativity began with two fundamental principles. The first was the
• 25:42
  Speaker 2: principle of relativity. The laws of physics are the same
• 25:45
  Speaker 2: in every inertial reference frame, meaning every frame moving at
• 25:50
  Speaker 2: a constant velocity without rotation or acceleration. No experiment performed
• 25:56
  Speaker 2: entirely within such a frame can reveal some absolute state
• 25:59
  Speaker 2: of uniform motion. The second principle concerned light. The speed
• 26:05
  Speaker 2: of light in a vacuum is the same for every
• 26:08
  Speaker 2: inertial observer, regardless of the motion of the light source.
• 26:13
  Speaker 2: This was a profound departure from ordinary expectations. Consider a
• 26:17
  Speaker 2: spacecraft travelling away from Earth at half the speed of light.
• 26:22
  Speaker 2: An astronaut aboard the spacecraft switches on a lamp directing
• 26:26
  Speaker 2: its beam forwards. Someone on Earth measures that light travelling
• 26:30
  Speaker 2: through a vacuum at approximately 300,000 km per second. What
• 26:35
  Speaker 2: does the astronaut measure? Exactly the same speed. Not one
• 26:40
  Speaker 2: and a half times the speed of light, and not
• 26:43
  Speaker 2: half the speed of light. The astronaut obtains the same
• 26:47
  Speaker 2: fundamental value as the observer on Earth. Even if the
• 26:51
  Speaker 2: spacecraft travels at 99% of the speed of light, the
• 26:55
  Speaker 2: result remains unchanged. This doesn't mean the observers necessarily see
• 27:00
  Speaker 2: identical colours or frequencies. Relative motion can produce a relativistic
• 27:05
  Speaker 2: Doppler shift, changing the observed frequency of the light. But
• 27:10
  Speaker 2: its measured vacuum speed remains the same. There is also
• 27:14
  Speaker 2: an important distinction between measuring speed and simply watching a
• 27:17
  Speaker 2: distant object. An observer must establish distances and times using
• 27:22
  Speaker 2: measuring instruments and synchronised clocks within their own reference frames.
• 27:27
  Speaker 2: The arrival times of light signals alone can be misleading,
• 27:30
  Speaker 2: because those signals themselves require time to travel. Once the
• 27:34
  Speaker 2: measurements are defined correctly, the extraordinary result remains. Every inertial
• 27:40
  Speaker 2: observer measures the same speed of light in a vacuum,
• 27:43
  Speaker 2: and this presents an unavoidable consequence. If two observers moving
• 27:47
  Speaker 2: relative to one another cannot disagree about light speed, they
• 27:51
  Speaker 2: cannot always use the same measurements of distance and duration.
• 27:55
  Speaker 2: Their clocks and rulers must be related in a way
• 27:57
  Speaker 2: that differs from the ordinary addition of velocities. The Lorentz
• 28:02
  Speaker 2: transformations provide those relationships. What appears to be an unchanging
• 28:07
  Speaker 2: speed is possible because measurements of space and time depend
• 28:10
  Speaker 2: upon relative motion. Light isn't somehow adjusting its behaviour to
• 28:14
  Speaker 2: accommodate whoever happens to be watching. Rather, the structure of
• 28:18
  Speaker 2: space-time ensures that its speed is invariant. And this is
• 28:22
  Speaker 2: what makes the discovery so remarkable. The speed of light
• 28:26
  Speaker 2: is not simply an impressive number, describing how quickly something moves.
• 28:31
  Speaker 2: It is a fundamental feature of the universe, connecting the
• 28:34
  Speaker 2: way we measure distances with the way we measure time.
• 28:37
  Speaker 2: A person aboard a spacecraft and someone standing on Earth
• 28:41
  Speaker 2: can disagree about how much time has passed, yet agree
• 28:44
  Speaker 2: completely about the speed of a passing beam of light.
• 28:48
  Speaker 2: Neither observer needs to be wrong. The remarkable consistency of
• 28:52
  Speaker 2: light is precisely what allows their different measurements of space
• 28:56
  Speaker 2: and time to fit together. And what once seemed like
• 29:00
  Speaker 2: a rather inconvenient property of electromagnetic waves turns out to
• 29:04
  Speaker 2: be one of the deepest organising principles of physical reality.
• 29:08
  Speaker 2: One of the most extraordinary discoveries in physics can be
• 29:11
  Speaker 2: understood using something as simple as two mirrors and a
• 29:14
  Speaker 2: beam of light. There's no need for an enormous telescope,
• 29:18
  Speaker 2: a particle accelerator, or any particularly complicated machinery. Just two
• 29:24
  Speaker 2: mirrors facing one another with a little empty space between
• 29:27
  Speaker 2: them and from this remarkably simple arrangement we can discover
• 29:32
  Speaker 2: why time doesn't always pass at the same rate for everyone.
• 29:36
  Speaker 2: Imagine building a rather unusual clock. Instead of using swinging pendulums,
• 29:41
  Speaker 2: turning gears or vibrating crystals, this clock measures time by
• 29:45
  Speaker 2: bouncing a pulse of light between two perfectly reflecting mirrors.
• 29:50
  Speaker 2: One mirror sits directly above the other, separated by a
• 29:53
  Speaker 2: fixed distance. A pulse of light leaves the lower mirror,
• 29:57
  Speaker 2: travels upwards, reflects from the upper mirror, and returns to
• 30:01
  Speaker 2: where it began. Each completed journey represents one tick of
• 30:06
  Speaker 2: the clock. Because the mirrors remain the same distance apart,
• 30:10
  Speaker 2: and because light travels through a vacuum at a constant speed,
• 30:13
  Speaker 2: every journey takes exactly the same amount of time. The
• 30:17
  Speaker 2: clock therefore provides a perfectly regular way of measuring the
• 30:21
  Speaker 2: passage of time. For simplicity, imagine the mirrors are separated
• 30:24
  Speaker 2: by one and a half metres. Light travels upwards across
• 30:28
  Speaker 2: that distance, then returns along the same path. The complete
• 30:32
  Speaker 2: journey covers three metres. At the speed of light, this
• 30:35
  Speaker 2: takes approximately ten billionths of a second. An extraordinarily short interval, certainly,
• 30:41
  Speaker 2: but a perfectly measurable one in principle. Now imagine placing
• 30:45
  Speaker 2: this clock inside a spacecraft. An astronaut sits beside it,
• 30:51
  Speaker 2: watching the pulse of a light bounce between the mirrors.
• 30:54
  Speaker 2: From the astronaut's perspective, everything is perfectly ordinary. The spacecraft
• 30:59
  Speaker 2: is at rest relative to them. The mirrors remain stationary,
• 31:03
  Speaker 2: and the light travels directly upwards and downwards. The clock
• 31:07
  Speaker 2: ticks regularly. Nothing about the astronaut's surroundings suggests that time
• 31:12
  Speaker 2: is behaving unusually. But now consider somebody watching the spacecraft
• 31:17
  Speaker 2: pass by at an enormous speed. Perhaps the spacecraft is
• 31:22
  Speaker 2: travelling horizontally at 80% of the speed of light. To
• 31:26
  Speaker 2: this second observer, the mirrors are moving sideways while the
• 31:29
  Speaker 2: light travels between them, and this changes something rather important,
• 31:34
  Speaker 2: the path taken by the light. When the pulse leaves
• 31:38
  Speaker 2: the lower mirror, the upper mirror is positioned directly above it,
• 31:42
  Speaker 2: but by the time the light reaches the upper mirror,
• 31:44
  Speaker 2: the spacecraft has moved forwards. The light must therefore travel
• 31:48
  Speaker 2: diagonally upwards to meet the moving mirror. After reflecting, it
• 31:52
  Speaker 2: travels diagonally downwards towards the lower mirror, which has continued
• 31:56
  Speaker 2: moving forwards. From the outside observer's perspective, the light follows
• 32:00
  Speaker 2: a zigzag path through space. And that path is longer
• 32:04
  Speaker 2: than the simple vertical journey measured by the astronaut. This
• 32:09
  Speaker 2: creates a fascinating problem. Both observers must measure exactly the
• 32:13
  Speaker 2: same speed of light through the vacuum. The astronaut sees
• 32:16
  Speaker 2: the light travelling vertically between two stationary mirrors. The outside
• 32:21
  Speaker 2: observer calculates that the light travels a longer diagonal distance,
• 32:25
  Speaker 2: yet neither observer can obtain a different value for light speed.
• 32:29
  Speaker 2: So how can the light travel farther without travelling faster?
• 32:33
  Speaker 2: The answer is that the observers must measure different amounts
• 32:36
  Speaker 2: of time. For the outside observer, the light takes longer
• 32:39
  Speaker 2: to complete its journey between the moving mirrors, and because
• 32:43
  Speaker 2: each completed journey represents one tick of the clock, the
• 32:46
  Speaker 2: outside observer concludes that the moving clock is ticking more slowly.
• 32:51
  Speaker 2: This is the essential idea behind time dilation. The extraordinary
• 32:55
  Speaker 2: part is that nothing has happened to the clock itself.
• 32:58
  Speaker 2: Its mirrors haven't moved farther apart in its own reference frame.
• 33:03
  Speaker 2: The light hasn't lost energy in some way that makes
• 33:05
  Speaker 2: it travel more slowly. And the astronaut hasn't experienced any
• 33:09
  Speaker 2: strange interruption in the normal passage of time. The difference
• 33:13
  Speaker 2: arises because the two observers measure the same physical process
• 33:17
  Speaker 2: from different reference frames. For a spacecraft travelling at 80%
• 33:22
  Speaker 2: of the speed of light, the difference is substantial. The
• 33:26
  Speaker 2: outside observer calculates that approximately 1.67 seconds pass in their
• 33:31
  Speaker 2: reference frame for every second, accumulated by the moving clock. Meanwhile,
• 33:37
  Speaker 2: the astronaut continues to measure one perfectly ordinary second at
• 33:41
  Speaker 2: a time. This difference can be calculated using the mathematics
• 33:45
  Speaker 2: of special relativity. particularly the relationship known as the Lorentz factor.
• 33:51
  Speaker 2: But the important insight doesn't require complicated mathematics. It follows
• 33:55
  Speaker 2: from the geometry of the light's journey, and the requirement
• 33:59
  Speaker 2: that its speed remains unchanged. Now, there's a rather reasonable
• 34:03
  Speaker 2: question we might ask. What if the clock didn't use light?
• 34:07
  Speaker 2: Suppose the astronaut replaced it with an ordinary mechanical clock,
• 34:11
  Speaker 2: one containing carefully manufactured gears and a moving second hand.
• 34:16
  Speaker 2: Would that clock also run slowly when measured from outside
• 34:19
  Speaker 2: the spacecraft? Yes. And the same would be true of
• 34:23
  Speaker 2: an atomic clock, which measures time using the extremely regular
• 34:27
  Speaker 2: behaviour of atoms. The principle of relativity requires all properly
• 34:32
  Speaker 2: functioning clocks travelling together to measure the same elapsed time. Otherwise,
• 34:37
  Speaker 2: an astronaut could compare different clocks inside a smoothly moving spacecraft.
• 34:41
  Speaker 2: and discover their motion relative to some supposedly absolute state
• 34:45
  Speaker 2: of rest. That would contradict the fundamental principles of special relativity.
• 34:51
  Speaker 2: So the effect isn't confined to light bouncing between mirrors.
• 34:55
  Speaker 2: Every physical process aboard the spacecraft follows the same relationship.
• 35:00
  Speaker 2: The astronauts' heartbeat, the chemical reactions inside their body, and
• 35:05
  Speaker 2: the movements of the spacecraft's instruments all proceed normally according
• 35:09
  Speaker 2: to clocks travelling alongside them. from the outside observer's reference frame,
• 35:15
  Speaker 2: those processes take longer. And there's another subtle point. Neither
• 35:21
  Speaker 2: observer is entitled to claim that their own reference frame
• 35:23
  Speaker 2: represents the one true state of rest. If both are
• 35:27
  Speaker 2: moving inertially, each can describe the other's moving clock as
• 35:31
  Speaker 2: ticking more slowly, using measurements defined within their respective frames.
• 35:37
  Speaker 2: This isn't a contradiction. because the observers also differ in
• 35:40
  Speaker 2: how they assign times to events occurring at separated locations.
• 35:45
  Speaker 2: The full relationship between their measurements includes both time dilation
• 35:50
  Speaker 2: and the relativity of simultaneity. The light clock reveals an
• 35:54
  Speaker 2: important part of that relationship with extraordinary simplicity. Two observers
• 35:59
  Speaker 2: can disagree about how much time passes between the ticks
• 36:02
  Speaker 2: of a moving clock, while agreeing completely about the speed
• 36:06
  Speaker 2: of the light inside it. The difference isn't caused by
• 36:10
  Speaker 2: faulty measurements or imperfect instruments. It is built into the
• 36:13
  Speaker 2: way space and time fit together. What we normally imagine
• 36:17
  Speaker 2: as two separate things, distance and duration, turn out to
• 36:21
  Speaker 2: be connected. And all it takes to uncover that connection
• 36:24
  Speaker 2: is a pulse of light, two mirrors, and the surprising
• 36:28
  Speaker 2: fact that the speed of light refuses to change. A
• 36:32
  Speaker 2: clock is supposed to be something we can trust, whether
• 36:35
  Speaker 2: it's an old-fashioned grandfather clock, a wristwatch, or an extraordinarily
• 36:39
  Speaker 2: precise atomic clock, its purpose is to measure the passage
• 36:43
  Speaker 2: of time as reliably as possible. And when two accurate
• 36:47
  Speaker 2: clocks are placed beside one another, we naturally expect them
• 36:51
  Speaker 2: to agree. But one of the most remarkable consequences of
• 36:55
  Speaker 2: Einstein's special relativity is that two perfectly functioning clocks can
• 37:01
  Speaker 2: measure different amounts of elapsed time without either one being inaccurate.
• 37:06
  Speaker 2: All that's required is for them to follow different paths
• 37:08
  Speaker 2: through spacetime. The phenomenon responsible for this is called time dilation.
• 37:15
  Speaker 2: In its simplest form, time dilation describes how a clock
• 37:18
  Speaker 2: moving relative to an observer measures less elapsed time between
• 37:22
  Speaker 2: two events on that clock's journey than the interval assigned
• 37:26
  Speaker 2: to those events in the observer's inertial reference frame. The
• 37:30
  Speaker 2: difference isn't a mechanical problem. or some strange interference affecting
• 37:34
  Speaker 2: the clock's internal workings, it's a fundamental feature of how
• 37:38
  Speaker 2: time is measured. To understand it more precisely, physicists distinguish
• 37:43
  Speaker 2: between two important quantities. The first is called proper time.
• 37:49
  Speaker 2: Proper time is the elapsed time measured by a clock
• 37:51
  Speaker 2: travelling along a particular path through spacetime. Imagine an astronaut
• 37:56
  Speaker 2: sitting inside a spacecraft with a clock attached to the
• 37:59
  Speaker 2: wall beside them. The clock begins measuring time when the
• 38:03
  Speaker 2: astronaut presses a button and stops when they press it again.
• 38:07
  Speaker 2: Because both events occur at the clock's location in its
• 38:10
  Speaker 2: own reference frame, the interval recorded by that clock is
• 38:14
  Speaker 2: the proper time between those events. The second quantity is
• 38:17
  Speaker 2: coordinate time. This is the time interval assigned to events
• 38:21
  Speaker 2: using the clocks and coordinate system of a particular reference frame.
• 38:26
  Speaker 2: An observer on Earth Watching the spacecraft travel past at
• 38:30
  Speaker 2: a constant velocity can assign their own time coordinates to
• 38:34
  Speaker 2: the astronaut's two button presses, and the interval they calculate
• 38:38
  Speaker 2: can be longer than the time recorded aboard the spacecraft.
• 38:42
  Speaker 2: The relationship between these measurements can be described mathematically. An
• 38:46
  Speaker 2: important quantity used in that calculation is called the Lorentz factor,
• 38:51
  Speaker 2: named after the Dutch physicist Hendrik Antoon Lorentz. The Lorentz
• 38:55
  Speaker 2: factor tells us how strongly relativistic effects depend on the
• 38:59
  Speaker 2: relative speed between two inertial reference frames. Its mathematical definition
• 39:04
  Speaker 2: is the Lorentz factor equals one divided by the square
• 39:07
  Speaker 2: root of one minus the square of the relative speed
• 39:10
  Speaker 2: divided by the square of the speed of light. That
• 39:13
  Speaker 2: might sound rather complicated when spoken aloud, but the behaviour
• 39:17
  Speaker 2: it describes is surprisingly straightforward. At low speeds, the Lorentz
• 39:22
  Speaker 2: factor is extremely close to one, As the relative speed
• 39:26
  Speaker 2: increases the factor becomes larger and as that speed approaches
• 39:29
  Speaker 2: the speed of light, the factor grows dramatically. This explains
• 39:35
  Speaker 2: why time dilation is almost impossible to notice during ordinary life.
• 39:40
  Speaker 2: Consider someone travelling in a car at 100km per hour.
• 39:44
  Speaker 2: Compared with the speed of light, that's an extraordinarily small velocity.
• 39:50
  Speaker 2: The resulting difference between the driver's elapsed time and the
• 39:53
  Speaker 2: coordinate time assigned by an observer standing beside the road
• 39:57
  Speaker 2: is so tiny that an ordinary clock could never reveal it.
• 40:01
  Speaker 2: Even the speeds reached by commercial aircraft produce differences measured
• 40:06
  Speaker 2: in extremely small fractions of a second. The effect exists,
• 40:11
  Speaker 2: but is almost completely hidden beneath the familiar rhythms of
• 40:14
  Speaker 2: everyday life. Now imagine a spacecraft travelling at 80% of
• 40:19
  Speaker 2: the speed of light. At that velocity, the Lorentz factor
• 40:23
  Speaker 2: is approximately 1.67. This means that for every 1.67 seconds
• 40:29
  Speaker 2: measured in Earth's chosen inertial reference frame, approximately one second
• 40:34
  Speaker 2: passes aboard the spacecraft. In other words, the moving clock
• 40:38
  Speaker 2: accumulates about 60% as much elapsed time as clocks stationary
• 40:42
  Speaker 2: in the Earth-based frame over the corresponding interval. If 10
• 40:46
  Speaker 2: years pass according to that external coordinate system, the astronaut's
• 40:51
  Speaker 2: clock records approximately 6 years. It's an extraordinary difference. And
• 40:56
  Speaker 2: the effect becomes even more pronounced at higher velocities. Suppose
• 41:00
  Speaker 2: the spacecraft accelerates until it is travelling at 99% of
• 41:04
  Speaker 2: the speed of light. The Lorentz factor is now approximately 7.1.
• 41:08
  Speaker 2: For every 7.1 seconds assigned by the external observer, the
• 41:14
  Speaker 2: spacecraft clock accumulates approximately one second, or, over a much
• 41:20
  Speaker 2: longer interval, approximately 14% as much time passes aboard the spacecraft.
• 41:26
  Speaker 2: A journey that takes a little over seven years, according
• 41:29
  Speaker 2: to Earth's reference frame, could therefore involve only about one
• 41:32
  Speaker 2: year of lapse time for the astronaut, assuming the spacecraft
• 41:36
  Speaker 2: maintains that speed throughout the interval being considered. Yet the
• 41:41
  Speaker 2: astronaut would experience nothing unusual. Their heartbeat wouldn't suddenly become sluggish.
• 41:47
  Speaker 2: Their thoughts wouldn't stretch into slow motion. A cup of
• 41:50
  Speaker 2: tea wouldn't take seven times longer to cool according to
• 41:54
  Speaker 2: the clock beside them. Everything aboard the spacecraft would continue
• 41:58
  Speaker 2: behaving normally. That's because every physical process travelling with the
• 42:02
  Speaker 2: astronaut is governed by the same local measurement of time.
• 42:07
  Speaker 2: The astronaut isn't somehow living in a world where their
• 42:09
  Speaker 2: own seconds have become longer. Their seconds remain perfectly ordinary.
• 42:15
  Speaker 2: It's the comparison between different reference frames that produces the difference.
• 42:19
  Speaker 2: And there is another fascinating detail. Suppose the astronaut looks
• 42:24
  Speaker 2: back towards Earth, while both the spacecraft and the planet
• 42:27
  Speaker 2: are moving at a constant velocity relative to one another.
• 42:31
  Speaker 2: From the astronaut's inertial reference frame, Earth is the object
• 42:36
  Speaker 2: moving away. The astronaut can therefore calculate that clocks on
• 42:40
  Speaker 2: Earth are running more slowly than their own. This is
• 42:43
  Speaker 2: known as the reciprocity of time dilation. Each inertial observer
• 42:47
  Speaker 2: can describe the other's moving clock as ticking more slowly.
• 42:51
  Speaker 2: At first, that sounds contradictory. Surely both clocks cannot be
• 42:56
  Speaker 2: slower than each other. But the apparent contradiction disappears once
• 43:00
  Speaker 2: we recognise that the observers are using different reference frames,
• 43:04
  Speaker 2: with different definitions of which distant events occur simultaneously. They're
• 43:09
  Speaker 2: not comparing the same sets of distant events when assigning
• 43:13
  Speaker 2: clock readings at a particular moment. Their measurements are related
• 43:17
  Speaker 2: consistently by the Lorentz transformations. There's also an important difference
• 43:22
  Speaker 2: between calculating the rate of a distant clock and actually
• 43:25
  Speaker 2: seeing its light signals arrive. If a spacecraft is moving away,
• 43:30
  Speaker 2: successive flashes from its clock take progressively longer to reach
• 43:34
  Speaker 2: an observer on Earth. This can make the clock appear
• 43:37
  Speaker 2: to tick even more slowly than the time dilation calculation
• 43:41
  Speaker 2: alone predicts. The additional effect is associated with the relativistic
• 43:45
  Speaker 2: Doppler shift. Conversely, a clock approaching an observer can appear
• 43:50
  Speaker 2: to tick faster because successive signals have progressively less distance
• 43:55
  Speaker 2: to travel. Neither appearance directly represents the clock's underlying time
• 44:00
  Speaker 2: dilation factor. Physicists account for signal travel times and relative
• 44:05
  Speaker 2: motion when comparing clock rates, and once those effects are
• 44:09
  Speaker 2: properly distinguished, the conclusion remains beautifully consistent. There is no
• 44:15
  Speaker 2: single universal clock against which every other clock must be judged.
• 44:20
  Speaker 2: Each physical clock measures the proper time accumulated along its
• 44:24
  Speaker 2: own journey through spacetime. Different observers can assign different intervals
• 44:29
  Speaker 2: to that journey, but the mathematical relationships between their measurements
• 44:34
  Speaker 2: are precise and predictable. Time dilation doesn't mean that time
• 44:39
  Speaker 2: has somehow become unreliable. It means that time is more
• 44:42
  Speaker 2: closely connected to motion than our ordinary experience suggests. And
• 44:47
  Speaker 2: perhaps the most remarkable part is how perfectly normal everything
• 44:51
  Speaker 2: remains for the people actually experiencing it. No matter how
• 44:55
  Speaker 2: quickly you're travelling, your own clock continues to measure your
• 44:58
  Speaker 2: own passing seconds. It's only when we compare those seconds
• 45:02
  Speaker 2: with the measurements of another observer that the extraordinary flexibility
• 45:06
  Speaker 2: of time becomes apparent. There is something wonderfully reassuring about
• 45:11
  Speaker 2: the idea of the present moment. Whatever you happen to
• 45:14
  Speaker 2: be doing right now, it seems reasonable to imagine that
• 45:18
  Speaker 2: the rest of the universe is experiencing its own version
• 45:22
  Speaker 2: of the same instant. Somewhere, a star is shining. Somewhere else,
• 45:28
  Speaker 2: a planet is turning. And here on Earth, countless people
• 45:33
  Speaker 2: are going about their lives, all apparently sharing one enormous,
• 45:37
  Speaker 2: invisible moment called now. We might disagree about what time
• 45:42
  Speaker 2: it is in different countries, of course, but that's simply
• 45:45
  Speaker 2: a matter of how we've chosen to organise our clocks. Surely,
• 45:49
  Speaker 2: beneath those different time zones, there must be one universal
• 45:53
  Speaker 2: present moment that everyone can agree upon. According to Albert
• 45:58
  Speaker 2: Einstein's special relativity, however, things are rather more complicated. Two
• 46:03
  Speaker 2: events that happen at exactly the same time for one
• 46:06
  Speaker 2: observer may occur at different times for another observer moving
• 46:10
  Speaker 2: relative to the first. This phenomenon is known as the
• 46:14
  Speaker 2: relativity of simultaneity, and it reveals something rather extraordinary about
• 46:19
  Speaker 2: the nature of time. To understand it, imagine a long
• 46:23
  Speaker 2: train travelling smoothly along a straight railway track. The train
• 46:27
  Speaker 2: is moving at a constant velocity, with its passengers sitting
• 46:31
  Speaker 2: comfortably inside. Beside the railway, an observer stands on a platform.
• 46:36
  Speaker 2: At one particular moment, the midpoint of the train passes
• 46:40
  Speaker 2: directly in front of the observer, and at precisely that instant,
• 46:45
  Speaker 2: something rather dramatic happens. Two bolts of lightning strike the railway.
• 46:50
  Speaker 2: One strikes beside the front of the train, while the
• 46:53
  Speaker 2: other strikes beside the rear. The strikes occur at equal
• 46:57
  Speaker 2: distances from the observer standing on the platforms. And, according
• 47:01
  Speaker 2: to clocks synchronised along the railway, both strikes happen at
• 47:05
  Speaker 2: exactly the same time. The observer sees the two flashes
• 47:09
  Speaker 2: arrive simultaneously, because the light has travelled equal distances through
• 47:13
  Speaker 2: the platform's reference frame, and because its speed is the
• 47:17
  Speaker 2: same in both directions, the observer concludes that the lightning
• 47:20
  Speaker 2: strikes were simultaneous. So far, everything seems straightforward. But now
• 47:26
  Speaker 2: consider a passenger sitting at the exact midpoint of the train.
• 47:30
  Speaker 2: When the lightning strikes, this passenger is passing the observer
• 47:34
  Speaker 2: on the platform. However, the train continues moving forwards while
• 47:39
  Speaker 2: the light from the two strikes travels towards the passenger.
• 47:42
  Speaker 2: And this makes a rather important difference. The passenger is
• 47:46
  Speaker 2: moving towards the light coming from the front of the train.
• 47:50
  Speaker 2: At the same time, they're moving away from the light
• 47:52
  Speaker 2: travelling forwards from the rear. Consequently, the flash from the
• 47:56
  Speaker 2: front reaches the passenger before the flash from the rear.
• 48:00
  Speaker 2: the passenger receives the two signals at different times. Now,
• 48:05
  Speaker 2: it would be tempting to explain this simply by saying
• 48:07
  Speaker 2: that the passenger moved towards one flash and away from
• 48:11
  Speaker 2: the other. And from the platform's reference frame, that explanation
• 48:15
  Speaker 2: is perfectly correct. But the passenger is also entitled to
• 48:20
  Speaker 2: describe the events using the train's own reference frame. Within
• 48:23
  Speaker 2: that frame, the train is stationary and the railway is
• 48:27
  Speaker 2: moving backwards. The passenger occupies the midpoint between the train's ends,
• 48:32
  Speaker 2: and light still travels at the same speed in both directions.
• 48:36
  Speaker 2: If the lightning strikes had occurred simultaneously according to clocks
• 48:39
  Speaker 2: synchronised aboard the train, their light would have reached the
• 48:43
  Speaker 2: passenger together. But it didn't. The flash from the front
• 48:48
  Speaker 2: arrived first. After accounting for the light's travel time within
• 48:52
  Speaker 2: the train's reference frame, the passenger concludes that the front
• 48:55
  Speaker 2: lightning strike happened earlier than the rear strike. The two
• 49:00
  Speaker 2: observers therefore disagree about whether the events occurred simultaneously, and remarkably,
• 49:06
  Speaker 2: neither observer has made a mistake. The disagreement isn't caused
• 49:10
  Speaker 2: by poor eyesight, faulty clocks, or a misunderstanding about how
• 49:15
  Speaker 2: quickly light travels. It's a genuine difference in the time coordinates.
• 49:20
  Speaker 2: assigned to the two events. This is the relativity of simultaneity,
• 49:24
  Speaker 2: and it raises an important question. How do we actually
• 49:28
  Speaker 2: decide whether two distant events happen at the same time?
• 49:32
  Speaker 2: After all, we cannot simply look at them and trust
• 49:34
  Speaker 2: that the light arrives without delay. Light takes time to travel.
• 49:39
  Speaker 2: so seeing two events together doesn't necessarily mean they occurred together.
• 49:44
  Speaker 2: Einstein addressed this problem through a procedure for synchronising clocks.
• 49:49
  Speaker 2: Imagine two clocks positioned at opposite ends of a long laboratory.
• 49:53
  Speaker 2: An observer beside the first clock sends a light signal
• 49:56
  Speaker 2: towards the second. The signal reaches the distant clock is
• 50:00
  Speaker 2: reflected and eventually returns to its starting point. By recording
• 50:05
  Speaker 2: the departure and return times, the observer can determine the
• 50:09
  Speaker 2: midpoint of the round-trip interval. In Einstein's standard synchronisation procedure,
• 50:15
  Speaker 2: the distant reflection event is assigned that midpoint time, using
• 50:19
  Speaker 2: the convention that light travels equally quickly in both directions
• 50:23
  Speaker 2: within the inertial reference frame. The clocks can then be
• 50:27
  Speaker 2: coordinated so that events occurring at different locations can be
• 50:31
  Speaker 2: assigned consistent times. This gives physicists a precise operational meaning
• 50:36
  Speaker 2: for simultaneity. But clocks synchronised in one inertial reference frame
• 50:42
  Speaker 2: will not generally be synchronised according to another frame moving
• 50:45
  Speaker 2: relative to the first, and that is the crucial detail.
• 50:49
  Speaker 2: Different inertial observers use different arrangements of distant simultaneous events.
• 50:54
  Speaker 2: This also helps explain something that initially seems contradictory about
• 50:58
  Speaker 2: time dilation. An observer on Earth can describe a moving
• 51:02
  Speaker 2: spacecraft's clock as ticking more slowly. Meanwhile, an astronaut aboard
• 51:07
  Speaker 2: the spacecraft can describe Earth's clocks as ticking more slowly.
• 51:11
  Speaker 2: How can both descriptions be correct? Because the observers disagree
• 51:15
  Speaker 2: about which distant clock readings should be compared at the
• 51:18
  Speaker 2: same moment. Their definitions of simultaneity are different. Once those
• 51:23
  Speaker 2: differences are included, the measurements agree perfectly with the Lorentz
• 51:27
  Speaker 2: transformations of special relativity. There is no mathematical contradiction, and
• 51:33
  Speaker 2: there is no need to identify one observer as possessing
• 51:36
  Speaker 2: the correct universal time. This doesn't mean that the order
• 51:40
  Speaker 2: of every event becomes uncertain. If one event can physically
• 51:44
  Speaker 2: influence another through a signal travelling at or below the
• 51:47
  Speaker 2: speed of light, all inertial observers agree upon their causal ordering.
• 51:53
  Speaker 2: A cause cannot simply become its own effect because someone
• 51:56
  Speaker 2: happens to move differently. The disagreement about temporal order concerns
• 52:02
  Speaker 2: events separated in such a way that no light speed
• 52:06
  Speaker 2: or slower signal could travel between them. Physicists describe these
• 52:10
  Speaker 2: as space-like separated events. Their ordering can depend upon the
• 52:15
  Speaker 2: observer's reference frame. But the proper time measured by a
• 52:19
  Speaker 2: clock between events along its own journey remains a well-defined
• 52:23
  Speaker 2: physical quantity. The absence of a universal present therefore doesn't
• 52:28
  Speaker 2: mean that time is arbitrary. It means that nature has
• 52:31
  Speaker 2: a more intricate system of relationships than the one suggested
• 52:35
  Speaker 2: by everyday experience. Here on Earth, the differences are usually
• 52:39
  Speaker 2: far too small to notice. We can comfortably agree that
• 52:43
  Speaker 2: two distant clocks show the same time without worrying about
• 52:46
  Speaker 2: our movements, through the supermarket or along a railway platform.
• 52:52
  Speaker 2: But at velocities approaching the speed of light, those differences
• 52:56
  Speaker 2: become impossible to ignore. And the result is a rather
• 52:59
  Speaker 2: beautiful change in how we understand the universe. There is
• 53:03
  Speaker 2: no single invisible clock whose present moment stretches across all
• 53:08
  Speaker 2: of space. Different observers can divide space-time into moments of past,
• 53:13
  Speaker 2: present and future in different ways. Yet the underlying events
• 53:18
  Speaker 2: remain real, the laws of physics remain consistent. and the
• 53:22
  Speaker 2: relationships between measurements can be calculated precisely. What changes is
• 53:27
  Speaker 2: not the existence of reality, but the way time is
• 53:30
  Speaker 2: assigned to events occurring in different places. And all of
• 53:34
  Speaker 2: this follows from the extraordinary fact that light travels at
• 53:38
  Speaker 2: the same speed for every inertial observer. Even something as
• 53:42
  Speaker 2: familiar as the word now turns out to have a
• 53:44
  Speaker 2: little more depth than we might have imagined. If time
• 53:48
  Speaker 2: can change depending on how an observer moves, it seems
• 53:51
  Speaker 2: reasonable to wonder whether space might behave differently as well.
• 53:56
  Speaker 2: After all, distance and time are closely connected whenever we
• 53:59
  Speaker 2: describe motion. We measure how far something travels, how long
• 54:03
  Speaker 2: the journey takes, and from those measurements calculate its speed.
• 54:08
  Speaker 2: But special relativity reveals that these quantities are not quite
• 54:12
  Speaker 2: as independent as everyday experience suggests. When observers moving relative
• 54:17
  Speaker 2: to one another disagree about the passage of time, They
• 54:20
  Speaker 2: can also disagree about the lengths of objects and the
• 54:23
  Speaker 2: distances between places, and once again, neither observer needs to
• 54:27
  Speaker 2: be mistaken. This extraordinary effect is known as length contraction,
• 54:32
  Speaker 2: or more specifically, Lorentz contraction. It describes how an object's
• 54:37
  Speaker 2: measured length along its direction of motion becomes shorter in
• 54:41
  Speaker 2: a reference frame where that object is moving. To understand
• 54:45
  Speaker 2: what this means, imagine a spacecraft resting inside an enormous hangar.
• 54:50
  Speaker 2: The spacecraft is exactly 100 metres long, measured from its
• 54:55
  Speaker 2: nose to its tail. Engineers can walk alongside it with
• 54:58
  Speaker 2: measuring equipment, carefully determine the positions of both ends and
• 55:03
  Speaker 2: agree upon its length. The measurement is perfectly ordinary. Now
• 55:07
  Speaker 2: imagine that the spacecraft leaves the hangar and accelerates through
• 55:11
  Speaker 2: space until it reaches 80% of the speed of light
• 55:14
  Speaker 2: relative to Earth. An astronaut travelling aboard the spacecraft decides
• 55:18
  Speaker 2: to measure its length again. they obtain exactly the same
• 55:22
  Speaker 2: result– 100 metres. Nothing has happened to the spacecraft's structure
• 55:27
  Speaker 2: merely because it is now moving uniformly relative to Earth.
• 55:32
  Speaker 2: Its walls haven't been compressed, its engines haven't become shorter,
• 55:36
  Speaker 2: and the astronaut hasn't suddenly found themselves squeezed into a
• 55:39
  Speaker 2: smaller cabin. From their own perspective, everything remains exactly as
• 55:44
  Speaker 2: it should. But an observer on Earth measures something different.
• 55:48
  Speaker 2: According to the observer's reference frame, the spacecraft is no
• 55:51
  Speaker 2: longer 100 metres long. Its measured length along the direction
• 55:55
  Speaker 2: of travel is only 60 metres. That's a reduction of 40%,
• 56:00
  Speaker 2: and remarkably both measurements are correct. The reason lies in
• 56:04
  Speaker 2: the same mathematics that explains time dilation. The Lorentz factor,
• 56:09
  Speaker 2: which describes how measurements change between inertial reference frames, also
• 56:13
  Speaker 2: determines the amount of length contraction. For an object travelling
• 56:17
  Speaker 2: at 80% of the speed of light, the Lorentz factor
• 56:20
  Speaker 2: is approximately 1.67. The relationship can be expressed quite simply.
• 56:26
  Speaker 2: The length measured along the direction of motion equals the
• 56:29
  Speaker 2: object's rest length divided by the Lorentz factor. A spacecraft
• 56:33
  Speaker 2: measuring 100 metres in its own rest frame therefore measures
• 56:37
  Speaker 2: approximately 60 metres in a reference frame where it travels
• 56:41
  Speaker 2: at 80% of the speed of light. but there's an
• 56:44
  Speaker 2: important detail hidden inside this calculation. What does it actually
• 56:49
  Speaker 2: mean to measure the length of something that's moving? Imagine
• 56:52
  Speaker 2: trying to measure a passing train. You could determine where
• 56:55
  Speaker 2: its front is at one moment, then measure where its
• 56:58
  Speaker 2: rear is several seconds later. But during those seconds, the
• 57:02
  Speaker 2: train would have moved. You wouldn't be measuring the positions
• 57:05
  Speaker 2: of its two ends at the same time. To obtain
• 57:07
  Speaker 2: the train's length in your reference frame, you need to
• 57:10
  Speaker 2: determine the positions of the front and rear simultaneously. The
• 57:14
  Speaker 2: same principle applies to a spacecraft. An observer measuring its
• 57:18
  Speaker 2: length must establish where both ends are at the same instant,
• 57:22
  Speaker 2: according to clocks synchronised in their own reference frame. And
• 57:26
  Speaker 2: this is where the relativity of simultaneity becomes essential. Two
• 57:30
  Speaker 2: observers moving relative to one another do not necessarily agree
• 57:34
  Speaker 2: about which distant events happen simultaneously. Consequently, their measurements of
• 57:39
  Speaker 2: an object's length involve different pairs of events at its
• 57:42
  Speaker 2: front and rear, They aren't simply disagreeing over an identical measurement.
• 57:47
  Speaker 2: They're measuring spatial separation according to different definitions of simultaneity.
• 57:53
  Speaker 2: This is why Lorentz contraction cannot be separated from the
• 57:56
  Speaker 2: unusual behaviour of time. The two effects are connected through
• 58:00
  Speaker 2: the geometry of spacetime. There's another detail worth appreciating. Length
• 58:05
  Speaker 2: contraction only affects dimensions parallel to the direction of relative motion.
• 58:11
  Speaker 2: If the spacecraft travels forwards, Its measured length from nose
• 58:15
  Speaker 2: to tail becomes shorter in Earth's reference frame, but its
• 58:19
  Speaker 2: width and height, measured perpendicular to the direction of travel,
• 58:24
  Speaker 2: remain unchanged under the corresponding Lorentz transformation. And none of
• 58:28
  Speaker 2: this requires the spacecraft to undergo physical compression. An astronaut
• 58:33
  Speaker 2: aboard it continues to measure the same familiar dimensions. The
• 58:37
  Speaker 2: underlying mathematical relationships are called the Lorentz transformations. developed through
• 58:42
  Speaker 2: the work of Hendrik Antun Lorentz and incorporated into Albert
• 58:46
  Speaker 2: Einstein's special relativity. These equations connect measurements of position and
• 58:51
  Speaker 2: time made in different inertial reference frames. In classical physics,
• 58:56
  Speaker 2: observers moving relative to one another could assign different spatial
• 59:00
  Speaker 2: coordinates to events while retaining one shared universal time. The
• 59:05
  Speaker 2: Lorentz transformations replace that assumption. They mix spatial and and
• 59:10
  Speaker 2: temporal coordinates while preserving the invariant speed of light and
• 59:13
  Speaker 2: the spacetime interval between events. What one observer measures as
• 59:18
  Speaker 2: a particular combination of distance and duration can therefore differ
• 59:22
  Speaker 2: from another observer's measurements. The importance of this becomes especially
• 59:27
  Speaker 2: clear when considering journeys between stars, Imagine a spacecraft travelling
• 59:32
  Speaker 2: from Earth towards Proxima Centauri, the nearest star to the Sun,
• 59:36
  Speaker 2: approximately 4.24 light-years away. Suppose the spacecraft travels at a
• 59:42
  Speaker 2: constant 80% of the speed of light for almost the
• 59:45
  Speaker 2: entire journey, with acceleration and deceleration neglected for simplicity. According
• 59:52
  Speaker 2: to Earth's reference frame, the journey takes approximately 5.3 years
• 59:57
  Speaker 2: That's because the spacecraft must cross a distance of 4.24
• 1:00:00
  Speaker 2: light years while travelling at four-fifths of the speed of light.
• 1:00:04
  Speaker 2: But the astronauts aboard experience a different duration. Their clocks
• 1:00:08
  Speaker 2: accumulate approximately 3.2 years during the journey. How can they
• 1:00:13
  Speaker 2: reach the star in so much less time without exceeding
• 1:00:16
  Speaker 2: the speed of light? Because the distance they measure is different.
• 1:00:20
  Speaker 2: In the spacecraft's inertial reference frame, the separation between Earth
• 1:00:24
  Speaker 2: and Proxima Centauri along the direction of travel is contracted
• 1:00:27
  Speaker 2: to approximately 2.54 light years. The star is moving towards
• 1:00:32
  Speaker 2: the spacecraft at 80% of the speed of light in
• 1:00:35
  Speaker 2: this description. It therefore takes approximately 3.2 years to arrive.
• 1:00:40
  Speaker 2: The shorter measure distance and shorter elapsed time agree perfectly.
• 1:00:44
  Speaker 2: Neither observer calculates that the spacecraft has travelled faster than light,
• 1:00:49
  Speaker 2: and neither has made an incorrect measurement. The difference arises
• 1:00:53
  Speaker 2: because space and time are being measured within different reference frames.
• 1:00:57
  Speaker 2: This also explains why length contraction isn't merely something an
• 1:01:01
  Speaker 2: observer would necessarily see by looking through a window. The
• 1:01:05
  Speaker 2: visual appearance of a fast-moving object depends upon when light
• 1:01:08
  Speaker 2: from its different surfaces reaches the observer. Those light travel
• 1:01:12
  Speaker 2: delays can produce optical distortions that are distinct from the
• 1:01:16
  Speaker 2: length calculated using simultaneous position measurements. Relativistic contraction is a
• 1:01:22
  Speaker 2: statement about measured spatial geometry, not simply the appearance of
• 1:01:26
  Speaker 2: a photograph, and just as moving observers can each calculate
• 1:01:29
  Speaker 2: that the other's clock is running slowly, they can each
• 1:01:32
  Speaker 2: measure the other's objects as contracted along the direction of
• 1:01:35
  Speaker 2: relative motion. Their measurements remain consistent. because they use different
• 1:01:40
  Speaker 2: definitions of distant simultaneous events. What makes all of this
• 1:01:45
  Speaker 2: remarkable is that time dilation, length contraction and the relativity
• 1:01:50
  Speaker 2: of simultaneity are not three unrelated peculiarities. They are different
• 1:01:55
  Speaker 2: consequences of the same underlying structure. The speed of light
• 1:01:59
  Speaker 2: remains invariant and the measurements of space and time adjust
• 1:02:03
  Speaker 2: according to precise mathematical relationships. The universe doesn't provide one
• 1:02:08
  Speaker 2: absolute measurement of distance, or one universal measure of elapsed
• 1:02:12
  Speaker 2: time for every observer. Instead, it provides a consistent space-time
• 1:02:17
  Speaker 2: geometry within which different observers can make different, equally valid measurements.
• 1:02:23
  Speaker 2: And so a spacecraft that is 100 metres long can
• 1:02:26
  Speaker 2: also be 60 metres long, depending upon the reference frame
• 1:02:29
  Speaker 2: in which its length is measured. A journey lasting more
• 1:02:33
  Speaker 2: than five years can involve little more than three years
• 1:02:36
  Speaker 2: aboard the spacecraft. Nothing has to break, stretch, or malfunction.
• 1:02:42
  Speaker 2: Space and time simply turn out to be connected far
• 1:02:45
  Speaker 2: more deeply than our everyday experience would ever lead us
• 1:02:48
  Speaker 2: to suspect. There is a rather beautiful idea in physics
• 1:02:51
  Speaker 2: that changes the way we think about the universe. Space
• 1:02:54
  Speaker 2: and time, which seem like two completely separate things, are
• 1:02:58
  Speaker 2: actually parts of one connected structure. We usually imagine space
• 1:03:02
  Speaker 2: as the place where things happen, and time as something
• 1:03:05
  Speaker 2: that passes while those things are happening. A planet moves
• 1:03:09
  Speaker 2: through space. A clock measures the time it takes to
• 1:03:12
  Speaker 2: complete its journey. But according to modern physics, this separation
• 1:03:17
  Speaker 2: isn't quite correct. Space and time belong together, and the
• 1:03:21
  Speaker 2: name physicists give to their combined structure is spacetime. The
• 1:03:25
  Speaker 2: idea became especially clear through the work of the German
• 1:03:28
  Speaker 2: mathematician Hermann Minkowski. In 1908, Minkowski presented a geometric interpretation
• 1:03:35
  Speaker 2: of Albert Einstein's special relativity, showing that the theory could
• 1:03:39
  Speaker 2: be understood by treating space and time as dimensions of
• 1:03:42
  Speaker 2: a single four-dimensional framework. It was an important development. Rather
• 1:03:48
  Speaker 2: than thinking of time as an independent clock ticking somewhere
• 1:03:51
  Speaker 2: outside the universe, physicists could describe events as positions within
• 1:03:55
  Speaker 2: spacetime itself. To understand what this means, imagine something very simple.
• 1:04:01
  Speaker 2: A small lamp flashes in an otherwise empty room. We
• 1:04:05
  Speaker 2: might describe the event by saying that the flash occurred
• 1:04:08
  Speaker 2: near the centre of the room, but that description is incomplete.
• 1:04:11
  Speaker 2: We also need to know when the flash happened. Perhaps
• 1:04:14
  Speaker 2: it occurred at precisely midnight. Together, the location and the
• 1:04:19
  Speaker 2: time identify one particular event, and in physics, an event
• 1:04:23
  Speaker 2: is simply something occurring at a particular place and moment.
• 1:04:27
  Speaker 2: To specify that event completely, we need four coordinates. Three
• 1:04:31
  Speaker 2: describe its position in space, one describes its position in time.
• 1:04:35
  Speaker 2: These four coordinates identify the event within spacetime. Different observers
• 1:04:40
  Speaker 2: may assign different numerical coordinates to the same event, particularly
• 1:04:44
  Speaker 2: if they're moving relative to one another. But the event
• 1:04:47
  Speaker 2: itself remains the same. The lamp either flashed or it didn't.
• 1:04:52
  Speaker 2: Relativity changes how observers describe the event, not whether it occurred.
• 1:04:56
  Speaker 2: Now imagine following the lamp through time. Perhaps it remains
• 1:05:00
  Speaker 2: sitting on a table for several hours. Its position in
• 1:05:03
  Speaker 2: the room doesn't change, but its time coordinate continues advancing.
• 1:05:07
  Speaker 2: In a diagram showing position horizontally and time vertically, the
• 1:05:11
  Speaker 2: lamp would trace a vertical line. Physicists call this a
• 1:05:15
  Speaker 2: world line. A world line represents the succession of events
• 1:05:18
  Speaker 2: associated with an object throughout its existence. If the lamp
• 1:05:22
  Speaker 2: were carried across the room, its world line would become tilted,
• 1:05:26
  Speaker 2: reflecting its changing spatial position as time passes. A spacecraft
• 1:05:32
  Speaker 2: travelling through the solar system follows a world line too.
• 1:05:35
  Speaker 2: So does Earth as it orbits the Sun. And so
• 1:05:38
  Speaker 2: does every person, although our journeys are generally rather less
• 1:05:42
  Speaker 2: dramatic than those of spacecraft. Even sitting perfectly still, you're
• 1:05:47
  Speaker 2: following a world line through spacetime. The interesting part is
• 1:05:51
  Speaker 2: that different world lines can connect the same two events.
• 1:05:54
  Speaker 2: Two people might leave the same location, travel along different routes,
• 1:05:59
  Speaker 2: and eventually meet again. Their paths through space would be different.
• 1:06:03
  Speaker 2: And according to relativity, the amount of time accumulated along
• 1:06:07
  Speaker 2: their journeys can be different as well. To understand why,
• 1:06:11
  Speaker 2: we need another important idea, the space-time interval. In ordinary geometry,
• 1:06:16
  Speaker 2: the distance between two points can be calculated from their
• 1:06:19
  Speaker 2: spatial separation. But space-time geometry includes time as well. The
• 1:06:25
  Speaker 2: space-time interval combines differences in position and time into one
• 1:06:29
  Speaker 2: mathematical quantity. Using a common sign convention, its defining relationship
• 1:06:35
  Speaker 2: can be expressed as follows. The spacetime interval squared equals
• 1:06:39
  Speaker 2: the speed of light squared multiplied by the time separation
• 1:06:42
  Speaker 2: squared minus the square of the spatial separation. The spatial
• 1:06:46
  Speaker 2: separation here means the ordinary three-dimensional distance between the two events,
• 1:06:51
  Speaker 2: calculated within the chosen reference frames. What's remarkable is that
• 1:06:55
  Speaker 2: different inertial observers agree on the spacetime interval, even when
• 1:06:59
  Speaker 2: they disagree about the individual distances and time intervals used
• 1:07:03
  Speaker 2: to calculate it. The Lorentz transformations preserve this quantity. This
• 1:07:08
  Speaker 2: is one of the deepest features of special relativity. Space
• 1:07:12
  Speaker 2: and time measurements can change between observers while the underlying
• 1:07:15
  Speaker 2: spacetime geometry remains consistent, and the speed of light provides
• 1:07:20
  Speaker 2: the connection between the spatial and temporal parts of that geometry.
• 1:07:25
  Speaker 2: It tells us which separations through spacetime are possible for
• 1:07:28
  Speaker 2: light and which are possible for objects possessing mass. This
• 1:07:32
  Speaker 2: leads to three important categories. The first is called a
• 1:07:36
  Speaker 2: time-like separation. Two events have a time-like separation when an
• 1:07:40
  Speaker 2: object travelling more slowly than light could move from one
• 1:07:43
  Speaker 2: event to the other. A person leaving home and arriving
• 1:07:47
  Speaker 2: at work later follows a time-like path. The second category
• 1:07:51
  Speaker 2: is a light-like separation. This occurs when two events can
• 1:07:55
  Speaker 2: be connected by a light signal travelling through a vacuum.
• 1:07:59
  Speaker 2: For such events the space-time interval is zero. The third
• 1:08:02
  Speaker 2: category is a space-like separation. Two events are space-like separated
• 1:08:07
  Speaker 2: when the distance between them is too great for even
• 1:08:10
  Speaker 2: light to travel from one to the other during the
• 1:08:13
  Speaker 2: time separating them. Neither event can causally influence the other
• 1:08:17
  Speaker 2: through an ordinary light speed or slower signal. These categories
• 1:08:22
  Speaker 2: reveal something profound about the structure of the universe. Every
• 1:08:26
  Speaker 2: event has a collection of other events that it can
• 1:08:28
  Speaker 2: potentially influence, and another collection that could have influenced it.
• 1:08:33
  Speaker 2: The boundaries of these regions are known as light cones.
• 1:08:36
  Speaker 2: Imagine a single flash of light expanding outward from a
• 1:08:40
  Speaker 2: point in empty space. As time passes, the expanding sphere
• 1:08:44
  Speaker 2: becomes larger. If we represent time vertically in two spatial
• 1:08:48
  Speaker 2: dimensions horizontally, The expanding light forms the surface of a cone.
• 1:08:52
  Speaker 2: This is the future light cone. It marks the boundary
• 1:08:55
  Speaker 2: of events that a light signal leaving the original event
• 1:08:58
  Speaker 2: could reach. A corresponding past light cone identifies the events
• 1:09:03
  Speaker 2: from which light could have arrived at the original location.
• 1:09:06
  Speaker 2: Events inside these cones can have time-like relationships with the
• 1:09:10
  Speaker 2: original event. Events outside them are space-like separated. Light therefore
• 1:09:15
  Speaker 2: defines the boundaries of possible causal influence. And within those boundaries,
• 1:09:20
  Speaker 2: objects follow their own worldlines, accumulating time along the way.
• 1:09:25
  Speaker 2: This accumulated time is called proper time. For a clock
• 1:09:29
  Speaker 2: following a time-like worldline, proper time is the duration actually
• 1:09:33
  Speaker 2: measured by that clock. In flat spacetime, the proper time
• 1:09:37
  Speaker 2: between two events can be understood geometrically through the length
• 1:09:41
  Speaker 2: of the time-like worldline connecting them, using the appropriate spacetime metric.
• 1:09:46
  Speaker 2: Unlike ordinary spatial geometry, however, the straight inertial path between
• 1:09:51
  Speaker 2: two time-like separated events accumulates the greatest proper time among
• 1:09:56
  Speaker 2: time-like paths connecting those events. A traveller following a different
• 1:10:01
  Speaker 2: route can therefore experience less elapsed time, and that is
• 1:10:04
  Speaker 2: an extraordinary conclusion. Time is not simply an external quantity
• 1:10:09
  Speaker 2: shared equally by every possible journey. It's connected to the
• 1:10:13
  Speaker 2: path an object follows through space-time. Two observers may begin together,
• 1:10:18
  Speaker 2: travel along different world lines, and reunite with their clocks
• 1:10:22
  Speaker 2: showing different amounts of elapsed time. Neither clock needs to
• 1:10:25
  Speaker 2: be inaccurate. Each has measured the proper time along its
• 1:10:28
  Speaker 2: own path. Minkowski's geometric description allows us to understand these
• 1:10:34
  Speaker 2: differences as properties of spacetime itself. The same structure explains
• 1:10:39
  Speaker 2: why observers disagree about simultaneity, why moving clocks can measure
• 1:10:44
  Speaker 2: different intervals, and why the speed of light remains invariant.
• 1:10:49
  Speaker 2: What initially seems like a collection of strange and unrelated
• 1:10:52
  Speaker 2: effects becomes part of one remarkably consistent picture. Space and
• 1:10:58
  Speaker 2: time are not separate backgrounds against which the universe unfolds.
• 1:11:02
  Speaker 2: They form a connected framework in which every event has
• 1:11:05
  Speaker 2: a place, every physical object traces a path, and the
• 1:11:09
  Speaker 2: speed of light defines the boundaries of possible causal relationships
• 1:11:13
  Speaker 2: And even though our everyday experience makes time feel like
• 1:11:16
  Speaker 2: one universal rhythm, the geometry of space-time reveals something considerably
• 1:11:21
  Speaker 2: more interesting. Every clock measures its own journey through the universe,
• 1:11:26
  Speaker 2: and the passage of time is woven into the structure
• 1:11:29
  Speaker 2: of that journey itself. Imagine two people who have been
• 1:11:32
  Speaker 2: together since the very beginning of their lives. They were
• 1:11:35
  Speaker 2: born on the same day, grew up together, and have
• 1:11:38
  Speaker 2: always been exactly the same age. but one day they
• 1:11:41
  Speaker 2: decide to take very different journeys. One remains on Earth,
• 1:11:45
  Speaker 2: enjoying a fairly ordinary existence. The other boards a spacecraft
• 1:11:49
  Speaker 2: and travels into the depths of space at a speed
• 1:11:52
  Speaker 2: approaching that of light. Years later, the spacecraft returns. The
• 1:11:57
  Speaker 2: two are reunited, standing beside one another once again. And
• 1:12:02
  Speaker 2: something extraordinary has happened. They are no longer the same age.
• 1:12:06
  Speaker 2: The person who travelled through space is younger than the
• 1:12:09
  Speaker 2: person who remained on Earth. Not because they discovered some
• 1:12:13
  Speaker 2: remarkable treatment for ageing, or because the conditions aboard the
• 1:12:16
  Speaker 2: spacecraft somehow preserved their body. They have simply experienced less time.
• 1:12:21
  Speaker 2: This famous scenario is known as the Twin Paradox, one
• 1:12:25
  Speaker 2: of the most fascinating consequences of Albert Einstein's special theory
• 1:12:29
  Speaker 2: of relativity. And despite its name, the result is not
• 1:12:33
  Speaker 2: actually a paradox. It is a perfectly consistent consequence of
• 1:12:38
  Speaker 2: the way time behaves in spacetime. To understand how it works,
• 1:12:42
  Speaker 2: imagine two identical twins, both 20 years old. One twin
• 1:12:46
  Speaker 2: remains on Earth, while the other prepares for a journey
• 1:12:49
  Speaker 2: aboard an extraordinarily powerful spacecraft. For simplicity, we'll imagine that
• 1:12:55
  Speaker 2: the spacecraft can accelerate very rapidly, travel at a constant
• 1:12:59
  Speaker 2: speed for most of its journey, and turn around in
• 1:13:02
  Speaker 2: a relatively short interval. We'll also ignore the small complications
• 1:13:06
  Speaker 2: introduced by Earth's gravity and orbital motion, The spacecraft travels
• 1:13:11
  Speaker 2: away from Earth at 80% of the speed of light.
• 1:13:14
  Speaker 2: At this velocity the effects of special relativity are substantial.
• 1:13:19
  Speaker 2: According to clocks in Earth's reference frame, the spacecraft spends
• 1:13:23
  Speaker 2: five years travelling away from the planet. It reaches a
• 1:13:26
  Speaker 2: point approximately four light years from Earth, turns around and
• 1:13:30
  Speaker 2: spends another five years returning at the same speed. The
• 1:13:34
  Speaker 2: entire journey therefore takes approximately ten years according to the
• 1:13:37
  Speaker 2: Earth-based twin. By the time the spacecraft returns that twin
• 1:13:41
  Speaker 2: has celebrated their 30th birthday. But aboard the spacecraft the
• 1:13:46
  Speaker 2: situation is different. At 80% of the speed of light
• 1:13:50
  Speaker 2: the Lorentz factor is approximately 1.67. This means the travelling
• 1:13:55
  Speaker 2: twin accumulates only about 60% as much time during each
• 1:13:59
  Speaker 2: constant speed portion of the journey as the corresponding interval
• 1:14:03
  Speaker 2: measured in Earth's frame. Instead of experiencing 10 years, the
• 1:14:07
  Speaker 2: astronaut experiences approximately 6. And when the twins finally meet again,
• 1:14:12
  Speaker 2: one is 30 years old. The other is only 26.
• 1:14:16
  Speaker 2: Four years have passed for one twin without passing for
• 1:14:19
  Speaker 2: the other. It sounds rather like something from a science
• 1:14:22
  Speaker 2: fiction story. But the underlying physics is entirely real. The
• 1:14:27
  Speaker 2: difference arises because the twins have followed different paths through space-time.
• 1:14:31
  Speaker 2: Physicists call these paths world-lines. Each twin carries a clock
• 1:14:36
  Speaker 2: along their own worldline, and that clock measures the proper
• 1:14:39
  Speaker 2: time accumulated during the journey. The Earth-based twin follows one
• 1:14:43
  Speaker 2: path between departure and reunion. The travelling twin follows another.
• 1:14:48
  Speaker 2: And those different paths can have different amounts of proper
• 1:14:51
  Speaker 2: time associated with them. But there's an interesting complication. During
• 1:14:56
  Speaker 2: the outward journey, the astronaut sees Earth moving away. According
• 1:15:00
  Speaker 2: to the principle of relativity, the astronaut is entitled to
• 1:15:03
  Speaker 2: consider themselves stationary within their own inertial reference frame. From
• 1:15:08
  Speaker 2: that perspective, it's the Earth-based twin whose clock is moving.
• 1:15:12
  Speaker 2: And moving clocks run slowly, so the astronaut can calculate
• 1:15:16
  Speaker 2: that their sibling's clock is ticking more slowly than their own. Meanwhile,
• 1:15:20
  Speaker 2: the twin on Earth calculates exactly the opposite. Each regards
• 1:15:24
  Speaker 2: the other's clock as running slowly. How, then, can they
• 1:15:28
  Speaker 2: eventually agree that the travelling twin has aged less? The
• 1:15:32
  Speaker 2: answer lies in an important difference between their complete journeys.
• 1:15:36
  Speaker 2: The Earth-based twin remains approximately within the same inertial reference
• 1:15:40
  Speaker 2: frame throughout the experiment. The travelling twin does not. In
• 1:15:45
  Speaker 2: order to return home, the spacecraft must change direction. It
• 1:15:49
  Speaker 2: slows down, turns around, and accelerates back towards Earth. During
• 1:15:53
  Speaker 2: this manoeuvre, the travelling twin changes from one inertial reference
• 1:15:57
  Speaker 2: frame to another, and this change has an important consequence
• 1:16:00
  Speaker 2: for how they assign times to distant events. Because simultaneity
• 1:16:05
  Speaker 2: is relative, the astronauts' outgoing and incoming reference frames disagree
• 1:16:10
  Speaker 2: about which events on Earth are happening at the same
• 1:16:12
  Speaker 2: time as the turnaround. In the simplified journey, immediately before
• 1:16:17
  Speaker 2: turning around, The outgoing reference frame assigns a time of
• 1:16:20
  Speaker 2: approximately 1.8 years after departure to the distant Earth event
• 1:16:24
  Speaker 2: simultaneous with the turnaround. Immediately after adopting the incoming reference frame,
• 1:16:29
  Speaker 2: that assignment becomes approximately 8.2 years after departure. Earth hasn't
• 1:16:35
  Speaker 2: suddenly experienced a physical leap forwards in time. The difference
• 1:16:38
  Speaker 2: reflects a change in which distant Earth event the astronaut's
• 1:16:42
  Speaker 2: reference frame regards as simultaneous with the turnaround. This is
• 1:16:46
  Speaker 2: the crucial piece that resolves the apparent contradiction. The travelling
• 1:16:50
  Speaker 2: twin can describe Earth's moving clocks as running slowly during
• 1:16:54
  Speaker 2: both constant speed portions of the journey, while still calculating
• 1:16:58
  Speaker 2: that more time has accumulated on Earth by the reunion,
• 1:17:01
  Speaker 2: and the result agrees precisely with the calculation made by
• 1:17:04
  Speaker 2: the twin who remained behind. It's also important to understand
• 1:17:08
  Speaker 2: the role of acceleration. The spacecraft must change its velocity
• 1:17:13
  Speaker 2: to complete the conventional outward and return journey. But acceleration
• 1:17:17
  Speaker 2: isn't some special substance that directly removes years from the
• 1:17:21
  Speaker 2: astronaut's life. The accumulated difference in time depends upon the
• 1:17:25
  Speaker 2: complete path through space-time. Even if the turnaround happens extremely rapidly,
• 1:17:30
  Speaker 2: contributing very little elapsed time to the journey, the age
• 1:17:34
  Speaker 2: difference remains substantial. Throughout the entire experience, both twins feel
• 1:17:39
  Speaker 2: perfectly normal. The astronaut's heartbeat continues at its familiar pace.
• 1:17:44
  Speaker 2: Their biological processes proceed normally, and their clock measures ordinary seconds.
• 1:17:49
  Speaker 2: Back on Earth, the other twin experiences exactly the same
• 1:17:53
  Speaker 2: sense of time passing naturally. Neither person feels their own
• 1:17:57
  Speaker 2: life moving unusually quickly or slowly. The difference only becomes
• 1:18:01
  Speaker 2: undeniable when they meet again. At that moment, the twins
• 1:18:05
  Speaker 2: can place their clocks beside one another and compare them directly.
• 1:18:09
  Speaker 2: There are no distant signals to correct for, no disagreements
• 1:18:12
  Speaker 2: about simultaneity, and no uncertainty about which event is being measured.
• 1:18:17
  Speaker 2: They are standing together at the same location. And their
• 1:18:21
  Speaker 2: clocks genuinely disagree. This is what makes the twin paradox
• 1:18:25
  Speaker 2: such a powerful illustration of relativity. It shows that elapsed
• 1:18:29
  Speaker 2: time is not a universal quantity assigned equally to every
• 1:18:33
  Speaker 2: possible journey. It belongs to the particular path an object
• 1:18:37
  Speaker 2: follows through spacetime. The same principle applies to people, spacecraft, atoms,
• 1:18:43
  Speaker 2: and every other physical system capable of accumulating proper time.
• 1:18:47
  Speaker 2: And perhaps the most remarkable part is that neither twin
• 1:18:50
  Speaker 2: has done anything extraordinary to the passage of time itself.
• 1:18:54
  Speaker 2: They have simply travelled differently. One spent ten years following
• 1:18:58
  Speaker 2: a relatively stationary path through Earth's reference frame. The other
• 1:19:02
  Speaker 2: travelled enormous distances at a substantial fraction of the speed
• 1:19:05
  Speaker 2: of light and accumulated only six years. Both journeys are
• 1:19:10
  Speaker 2: perfectly consistent with the laws of physics. The universe doesn't
• 1:19:14
  Speaker 2: require every clock to agree after following different paths. It
• 1:19:18
  Speaker 2: only requires each clock to measure its own elapsed time consistently.
• 1:19:22
  Speaker 2: And so two people who began their lives at exactly
• 1:19:25
  Speaker 2: the same age can meet again years later, having experienced
• 1:19:28
  Speaker 2: genuinely different amounts of time. Not because one escaped time,
• 1:19:33
  Speaker 2: but because time itself is inseparable from the journey taken
• 1:19:36
  Speaker 2: through space-time. there is something rather extraordinary about travelling close
• 1:19:41
  Speaker 2: to the speed of light. The faster you move relative
• 1:19:44
  Speaker 2: to another observer, the greater the difference between the amount
• 1:19:48
  Speaker 2: of time you experience and the amount they measure. And
• 1:19:51
  Speaker 2: as your speed approaches the speed of light, that difference
• 1:19:55
  Speaker 2: becomes increasingly dramatic. A journey that takes decades according to
• 1:20:00
  Speaker 2: clocks on Earth might involve only a few years, or
• 1:20:04
  Speaker 2: even a few months for someone aboard a sufficiently fast spacecraft.
• 1:20:08
  Speaker 2: The remarkable part is that nobody involved would notice their
• 1:20:11
  Speaker 2: own time behaving unusually. Their clocks would continue ticking normally,
• 1:20:16
  Speaker 2: their thoughts would proceed at their familiar pace, and every
• 1:20:20
  Speaker 2: passing second would feel exactly as it always had. Yet
• 1:20:24
  Speaker 2: the amounts of time accumulated along their different journeys could
• 1:20:27
  Speaker 2: be enormously different. The mathematical relationship responsible for this is
• 1:20:33
  Speaker 2: described by the Lorentz Factor. At ordinary speeds, the Lorentz
• 1:20:37
  Speaker 2: factor is almost exactly one, but as relative velocity increases
• 1:20:42
  Speaker 2: towards the speed of light, the factor grows larger, describing
• 1:20:46
  Speaker 2: progressively stronger time dilation. Consider a spacecraft travelling at half
• 1:20:51
  Speaker 2: the speed of light. That is approximately 150,000 kilometres every second.
• 1:20:58
  Speaker 2: At this velocity, the Lorentz factor is approximately 1.15, If
• 1:21:04
  Speaker 2: 10 years pass according to clocks in Earth's reference frame,
• 1:21:07
  Speaker 2: approximately 8.7 years pass aboard the spacecraft. The difference is
• 1:21:13
  Speaker 2: already substantial. But suppose we increase the spacecraft's speed to
• 1:21:17
  Speaker 2: 80% of the speed of the light. The Lorentz factor
• 1:21:21
  Speaker 2: becomes approximately 1.67. Now, during 10 years measured in Earth's frame,
• 1:21:27
  Speaker 2: the spacecraft accumulates only 6 years. 4 years separate the
• 1:21:32
  Speaker 2: two measurements. increase the speed again, this time to 99%
• 1:21:37
  Speaker 2: of the speed of light. The Lorentz factor rises to
• 1:21:41
  Speaker 2: approximately 7.1. During 10 years of Earth time, the spacecraft
• 1:21:46
  Speaker 2: experiences only about 1.4 years, and if the spacecraft reaches 99.9%
• 1:21:53
  Speaker 2: of the speed of light, the difference becomes even more remarkable.
• 1:21:58
  Speaker 2: The Lorentz factor is now approximately 22.4. For every 22.4
• 1:22:04
  Speaker 2: seconds measured in Earth's reference frame, only one second passes
• 1:22:08
  Speaker 2: aboard the spacecraft. Ten years of Earth time would correspond
• 1:22:12
  Speaker 2: to approximately five and a half months for the traveller.
• 1:22:15
  Speaker 2: These comparisons assume uniform motion during the intervals being measured
• 1:22:20
  Speaker 2: with the clocks related through the same inertial reference frames.
• 1:22:24
  Speaker 2: The enormous differences reveal how dramatically measurements of time can
• 1:22:28
  Speaker 2: change as relative speed approaches the universal limit. but they
• 1:22:33
  Speaker 2: also raise an interesting question. Why not simply continue accelerating?
• 1:22:39
  Speaker 2: If travelling at 99.9% of the speed of light produces
• 1:22:44
  Speaker 2: such extraordinary effects, perhaps travelling at exactly the speed of
• 1:22:48
  Speaker 2: light would make the journey even shorter. Unfortunately, nature places
• 1:22:54
  Speaker 2: a rather firm restriction on that possibility. An object possessing
• 1:22:58
  Speaker 2: mass cannot be accelerated to the speed of light. and
• 1:23:02
  Speaker 2: the reason involves energy. In ordinary circumstances, increasing an object's
• 1:23:07
  Speaker 2: speed requires supplying additional kinetic energy. A car accelerates because
• 1:23:12
  Speaker 2: its engine transfers energy into its motion. A spacecraft accelerates
• 1:23:17
  Speaker 2: because its propulsion system provides energy and momentum. At low speeds,
• 1:23:23
  Speaker 2: the familiar equations of classical mechanics describe these changes extremely well.
• 1:23:29
  Speaker 2: But as an object's velocity approaches the speed of light,
• 1:23:32
  Speaker 2: The relationship between energy and speed becomes increasingly different. Special
• 1:23:37
  Speaker 2: relativity describes the total energy of a freely moving massive
• 1:23:41
  Speaker 2: object through a relationship involving its mass, the speed of light,
• 1:23:46
  Speaker 2: and the Lorentz factor. The total relativistic energy equals the
• 1:23:51
  Speaker 2: Lorentz factor multiplied by the object's rest mass and multiplied
• 1:23:56
  Speaker 2: by the square of the speed of light. The kinetic
• 1:23:59
  Speaker 2: energy is the additional energy associated with motion beyond the
• 1:24:03
  Speaker 2: object's rest energy. As the Lorentz factor grows, the amount
• 1:24:07
  Speaker 2: of energy required to produce further increases in speed grows dramatically,
• 1:24:12
  Speaker 2: and as the object's speed approaches the speed of light,
• 1:24:16
  Speaker 2: the Lorentz factor increases without bound. Reaching the speed of
• 1:24:20
  Speaker 2: light would therefore require an infinite amount of energy for
• 1:24:23
  Speaker 2: an object with non-zero rest mass. No finite propulsion system
• 1:24:29
  Speaker 2: could provide that. Even an unimaginably advanced spacecraft would remain
• 1:24:33
  Speaker 2: below the speed of light, regardless of how closely it approached.
• 1:24:38
  Speaker 2: There is an important distinction here between massive objects and
• 1:24:41
  Speaker 2: particles without rest mass. Photons, the particles associated with electromagnetic radiation,
• 1:24:49
  Speaker 2: have zero rest mass. When freely propagating through a vacuum,
• 1:24:53
  Speaker 2: they travel at the speed of a light. They do
• 1:24:56
  Speaker 2: not need to be accelerated from rest to reach that speed,
• 1:25:00
  Speaker 2: because a photon has no valid rest frame. Massive objects,
• 1:25:04
  Speaker 2: by contrast, follow time-like paths through spacetime and cannot reach
• 1:25:08
  Speaker 2: the light speed limit. Yet even without reaching that limit,
• 1:25:12
  Speaker 2: relativistic travel offers some extraordinary possibilities. Imagine a spacecraft travelling
• 1:25:19
  Speaker 2: towards a star 10 light years away, measured in Earth's
• 1:25:22
  Speaker 2: reference frame. At 99.9% of the speed of light, the
• 1:25:27
  Speaker 2: journey would take just over 10 years according to Earth-based clocks.
• 1:25:32
  Speaker 2: But the astronauts would experience only about five and a
• 1:25:35
  Speaker 2: half months of travel. How could they reach a destination
• 1:25:38
  Speaker 2: 10 light-years away in less than half a year without
• 1:25:41
  Speaker 2: travelling faster than light? The answer involves length contraction. In
• 1:25:47
  Speaker 2: the spacecraft's reference frame, the distance between Earth and the
• 1:25:50
  Speaker 2: destination is contracted along the direction of motion. Instead of
• 1:25:55
  Speaker 2: 10 light years, the astronauts measure approximately 0.45 light years.
• 1:26:02
  Speaker 2: The destination approaches them at 99.9% of the speed of light,
• 1:26:07
  Speaker 2: and crossing that shorter distance takes approximately five and a
• 1:26:10
  Speaker 2: half months. Both descriptions agree perfectly. The spacecraft never exceeds
• 1:26:16
  Speaker 2: the speed of light. Space and time are simply measured
• 1:26:19
  Speaker 2: differently in the two reference frames. Of course, there's a
• 1:26:23
  Speaker 2: considerable difference between a journey that's mathematically possible and one
• 1:26:28
  Speaker 2: that human beings could realistically undertake. Accelerating a spacecraft to
• 1:26:33
  Speaker 2: such an enormous velocity would require extraordinary amounts of energy.
• 1:26:38
  Speaker 2: Its passengers would also need to survive the acceleration and
• 1:26:42
  Speaker 2: eventual deceleration. An interstellar space, although extraordinarily empty, isn't completely
• 1:26:49
  Speaker 2: devoid of matter. Hydrogen atoms, tiny dust grains and other
• 1:26:53
  Speaker 2: particles would strike a rapidly moving spacecraft with tremendous relative energies.
• 1:26:59
  Speaker 2: Even radiation arriving from the direction of travel would become
• 1:27:03
  Speaker 2: increasingly blue-shifted, potentially creating additional hazards. Protecting a spacecraft and
• 1:27:09
  Speaker 2: its occupants would present immense engineering challenges. The simplified journey
• 1:27:15
  Speaker 2: also ignores the time and distance required to accelerate and
• 1:27:19
  Speaker 2: slow down. both of which would matter enormously in practice. Nevertheless,
• 1:27:24
  Speaker 2: the underlying physics remains fascinating. Relativity allows travellers to experience
• 1:27:30
  Speaker 2: dramatically less elapsed time than people remaining on Earth, without
• 1:27:34
  Speaker 2: requiring any violation of the universal speed limit. The closer
• 1:27:39
  Speaker 2: their velocity approaches that limit, the greater the possible difference becomes,
• 1:27:44
  Speaker 2: and throughout the entire experience their own seconds continue passing normally.
• 1:27:50
  Speaker 2: A clock aboard the spacecraft never announces that time has slowed.
• 1:27:55
  Speaker 2: It simply measures the proper time associated with its journey.
• 1:27:59
  Speaker 2: What changes is the relationship between that time and the
• 1:28:02
  Speaker 2: measurements made elsewhere. The speed of light, therefore, represents something
• 1:28:07
  Speaker 2: more profound than the fastest speed a spacecraft might hope
• 1:28:11
  Speaker 2: to achieve. It defines the structure within which motion, distance,
• 1:28:15
  Speaker 2: energy and time are connected. And although the universe won't
• 1:28:19
  Speaker 2: allow a massive object to reach that speed, approaching it
• 1:28:23
  Speaker 2: reveals just how flexible the passage of time can be.
• 1:28:27
  Speaker 2: It's one thing to imagine a spacecraft travelling close to
• 1:28:29
  Speaker 2: the speed of light, with its passengers ageing more slowly
• 1:28:33
  Speaker 2: than the people they leave behind, but it's quite another
• 1:28:36
  Speaker 2: to demonstrate that this really happens. After all, thought experiments
• 1:28:41
  Speaker 2: are wonderfully useful in physics, but the universe has a
• 1:28:44
  Speaker 2: rather important habit of demanding evidence, and fortunately the strange
• 1:28:48
  Speaker 2: relationship between motion and time is something scientists have been
• 1:28:52
  Speaker 2: able to measure. Not just once, but repeatedly, using particles,
• 1:28:57
  Speaker 2: atomic clocks, aircraft and some extraordinarily precise equipment. Perhaps the
• 1:29:02
  Speaker 2: most surprising evidence begins high above our heads, where invisible
• 1:29:06
  Speaker 2: particles are constantly arriving from space. Earth is continually bombarded
• 1:29:11
  Speaker 2: by cosmic rays. These are high-energy particles, mostly protons and
• 1:29:16
  Speaker 2: atomic nuclei, travelling through space at enormous speeds. When they
• 1:29:22
  Speaker 2: encounter molecules in the upper atmosphere, they can produce showers
• 1:29:25
  Speaker 2: of secondary particles. Among these are particles called muons. A
• 1:29:29
  Speaker 2: muon is an elementary particle closely related to the electron,
• 1:29:33
  Speaker 2: although it is approximately 207 times more massive. Unlike electrons, however,
• 1:29:39
  Speaker 2: muons are unstable. They eventually decay into other particles through
• 1:29:43
  Speaker 2: a process governed by the weak nuclear interaction, and their
• 1:29:47
  Speaker 2: average lifetime is remarkably short. When measured in the muon's
• 1:29:52
  Speaker 2: own rest frame, its mean lifetime is approximately 2.2 microseconds.
• 1:29:57
  Speaker 2: A microsecond is one millionth of a second. So even
• 1:30:02
  Speaker 2: by the standards of particle physics, a muon doesn't tend
• 1:30:05
  Speaker 2: to remain around for very long. Now, imagine a muon
• 1:30:08
  Speaker 2: created 15 kilometres above Earth's surface. It's travelling downwards at
• 1:30:13
  Speaker 2: a speed extremely close to the speed of light, without
• 1:30:18
  Speaker 2: relativistic time dilation. its short lifetime would present a considerable problem.
• 1:30:23
  Speaker 2: Even light itself travels only about 660 metres during 2.2 microseconds.
• 1:30:30
  Speaker 2: And because a muon possesses mass, it cannot travel quite
• 1:30:33
  Speaker 2: as quickly as light. If its lifetime was simply 2.2
• 1:30:37
  Speaker 2: microseconds in Earth's reference frame, most mons produced high in
• 1:30:41
  Speaker 2: the atmosphere would decay long before reaching the ground. Yet
• 1:30:45
  Speaker 2: enormous numbers of mons do reach Earth's surface. In fact,
• 1:30:49
  Speaker 2: morns produced by cosmic rays are passing through our surroundings,
• 1:30:53
  Speaker 2: and occasionally through our bodies, all the time. We don't
• 1:30:57
  Speaker 2: notice them, and the overwhelming majority cause us no concern.
• 1:31:02
  Speaker 2: But their presence provides an extraordinary demonstration of relativity. From
• 1:31:06
  Speaker 2: Earth's reference frame, the muons are travelling at tremendous speeds,
• 1:31:11
  Speaker 2: and because of time dilation, their average lifetime measured in
• 1:31:14
  Speaker 2: that frame is substantially longer than than the lifetime measured
• 1:31:18
  Speaker 2: in their own rest frame, a muon travelling sufficiently close
• 1:31:21
  Speaker 2: to the speed of light can survive, on average, for
• 1:31:25
  Speaker 2: many tens of microseconds according to clocks on Earth. That
• 1:31:29
  Speaker 2: gives it enough time to cover a much greater distance
• 1:31:31
  Speaker 2: through the atmosphere. This doesn't mean every muon survives for
• 1:31:35
  Speaker 2: exactly the same duration. Particle decay is a probabilistic process.
• 1:31:41
  Speaker 2: Some muons decay almost immediately, while others survive considerably longer
• 1:31:46
  Speaker 2: than the average. but when scientists examine large numbers of muons,
• 1:31:50
  Speaker 2: the distribution of their decay times agrees with the predictions
• 1:31:54
  Speaker 2: of special relativity. There's also a beautiful alternative way of
• 1:31:58
  Speaker 2: describing the same phenomenon. Imagine considering the journey from the
• 1:32:02
  Speaker 2: muon's perspective, using the inertial reference frame in which it
• 1:32:06
  Speaker 2: is momentarily at rest. The muon's own average lifetime remains
• 1:32:10
  Speaker 2: approximately 2.2 microseconds, but the atmosphere is moving towards it
• 1:32:15
  Speaker 2: at enormous speed, And because of Lorentz contraction, the thickness
• 1:32:20
  Speaker 2: of the atmosphere along the direction of motion is reduced
• 1:32:23
  Speaker 2: in that reference frame. The muon therefore has a much
• 1:32:26
  Speaker 2: shorter distance to cross. From Earth's perspective, the muon survives
• 1:32:31
  Speaker 2: longer because of time dilation. From the muon's perspective, the
• 1:32:35
  Speaker 2: atmosphere is shorter because of length contraction. Both descriptions predict
• 1:32:39
  Speaker 2: the same physical outcome, and both follow from the same
• 1:32:43
  Speaker 2: underlying structure of spacetime. Scientists have also tested this effect
• 1:32:48
  Speaker 2: under much more controlled conditions. At the European Organisation for
• 1:32:52
  Speaker 2: Nuclear Research, commonly known as CERN, researchers have used particle
• 1:32:57
  Speaker 2: accelerators to investigate how unstable particles behave at relativistic speeds.
• 1:33:02
  Speaker 2: One particularly important experiment was reported in 1977. The researchers
• 1:33:08
  Speaker 2: used a large muon storage ring, in which magnetic fields
• 1:33:12
  Speaker 2: guided high-energy muons around a circular path. The muons travelled
• 1:33:17
  Speaker 2: at approximately 99.4% of the speed of light. At that velocity,
• 1:33:22
  Speaker 2: their Lorentz factor was approximately 29.3. Special relativity therefore predicted
• 1:33:28
  Speaker 2: that their average lifetime measured in the laboratory should be
• 1:33:32
  Speaker 2: roughly 29 times longer than their proper lifetime. Instead of
• 1:33:36
  Speaker 2: surviving for an average of approximately 2.2 microseconds, the muons
• 1:33:40
  Speaker 2: should survive for around 64 microseconds. and that's remarkably close
• 1:33:45
  Speaker 2: to what the researchers measured. The observed average lifetimes were
• 1:33:49
  Speaker 2: approximately 64.4 microseconds, depending slightly on the particle sample and measurement.
• 1:33:56
  Speaker 2: The results agreed closely with the predictions of relativistic time dilation.
• 1:34:01
  Speaker 2: This was especially significant because the Myuns were travelling around
• 1:34:04
  Speaker 2: a circular path. Their direction was continually changing. Yet the
• 1:34:09
  Speaker 2: relationship between their speed accumulated proper time. and laboratory time
• 1:34:15
  Speaker 2: remained consistent with relativity. It provided powerful experimental evidence that
• 1:34:20
  Speaker 2: the difference in elapsed time was a genuine physical effect,
• 1:34:25
  Speaker 2: but perhaps an even more familiar demonstration involved something considerably
• 1:34:30
  Speaker 2: larger than an elementary particle, an aeroplane. In 1971, The
• 1:34:36
  Speaker 2: physicists Joseph Hafele and Richard Keating carried out an experiment
• 1:34:41
  Speaker 2: using highly accurate cesium atomic clocks. They placed four clocks
• 1:34:46
  Speaker 2: aboard commercial aircraft and flew them around the world. One
• 1:34:50
  Speaker 2: journey travelled eastwards, another travelled westwards. The clocks were then
• 1:34:55
  Speaker 2: compared with precision time standards, maintained by the United States
• 1:34:59
  Speaker 2: Naval Observatory. The experiment involved two different relativistic effects. The
• 1:35:05
  Speaker 2: first was time dilation caused by motion. The second was
• 1:35:10
  Speaker 2: gravitational time dilation, because clocks at aircraft altitude experience a
• 1:35:15
  Speaker 2: different gravitational environment from clocks on Earth's surface. Earth's rotation
• 1:35:20
  Speaker 2: also mattered. An aircraft travelling eastwards generally moves faster relative
• 1:35:26
  Speaker 2: to a suitable non-rotating reference frame, centred on Earth than
• 1:35:30
  Speaker 2: one travelling westwards. As a result, the combined relativistic effects
• 1:35:34
  Speaker 2: were different for the two journeys, and when the clocks returned,
• 1:35:38
  Speaker 2: they no longer agreed perfectly with the reference clocks on
• 1:35:41
  Speaker 2: the ground. The eastward clocks had lost approximately 59 nanoseconds.
• 1:35:47
  Speaker 2: The westward clocks had gained approximately 273 nanoseconds. A nanosecond
• 1:35:53
  Speaker 2: is one billionth of a second. These were incredibly small differences,
• 1:35:58
  Speaker 2: but they were measurable, and importantly, they were consistent. within
• 1:36:02
  Speaker 2: the experimental uncertainties, with the predictions calculated from the aircraft's
• 1:36:07
  Speaker 2: movements and gravitational circumstances, the clocks had not simply become
• 1:36:12
  Speaker 2: unreliable because they were taken on an unusually long flight.
• 1:36:17
  Speaker 2: Their accumulated differences reflected the physical paths they had followed,
• 1:36:21
  Speaker 2: and that is the important distinction. Relativistic time dilation isn't
• 1:36:26
  Speaker 2: merely a question of how a moving clock appears when
• 1:36:29
  Speaker 2: viewed from somewhere else. Light travel delays, the Doppler effect,
• 1:36:34
  Speaker 2: and imperfect observations can all influence what someone sees. But
• 1:36:39
  Speaker 2: these experiments examined actual measurements of elapsed time. The moons
• 1:36:44
  Speaker 2: decayed according to lifetimes predicted by relativity. The atomic clocks
• 1:36:49
  Speaker 2: accumulated different readings after travelling around Earth, and those differences
• 1:36:54
  Speaker 2: could be measured directly, without relying upon somebody watching a
• 1:36:57
  Speaker 2: distant moving clock through a telescope. more than a century
• 1:37:01
  Speaker 2: after Einstein developed special relativity, its predictions have become an
• 1:37:06
  Speaker 2: established part of experimental physics. The differences are often tiny,
• 1:37:11
  Speaker 2: and detecting them can require extraordinary precision. But the principle
• 1:37:16
  Speaker 2: is unmistakable. Two clocks following different journeys through spacetime do
• 1:37:20
  Speaker 2: not necessarily accumulate the same amount of time, and whether
• 1:37:24
  Speaker 2: those clocks are built from atoms, carried aboard aircraft or
• 1:37:28
  Speaker 2: represented by the natural decay of particles, The same physical
• 1:37:32
  Speaker 2: relationships apply. Time dilation is not simply a curious mathematical possibility.
• 1:37:38
  Speaker 2: It is something the universe actually does, and all around us,
• 1:37:42
  Speaker 2: from the atmosphere above our heads to the delicate workings
• 1:37:45
  Speaker 2: of laboratory instruments, nature provides evidence that time is not
• 1:37:49
  Speaker 2: quite as universal as it once seemed. There is a
• 1:37:52
  Speaker 2: rather fascinating statement that often appears in discussions about Einstein's
• 1:37:56
  Speaker 2: theory of relativity. Time stops for light. it's an extraordinary idea.
• 1:38:03
  Speaker 2: A beam of light might travel across the entire observable universe,
• 1:38:08
  Speaker 2: passing through space for billions of years, and yet somehow
• 1:38:12
  Speaker 2: experience no passage of time at all. At least, that's
• 1:38:16
  Speaker 2: how the idea is frequently described. But while there's an
• 1:38:20
  Speaker 2: important piece of genuine physics behind this statement, the complete
• 1:38:24
  Speaker 2: explanation is a little more subtle, and understanding why reveals
• 1:38:28
  Speaker 2: something remarkable about the relationship between light and space-time. Light
• 1:38:33
  Speaker 2: is made up of particles called photons. Photons are the
• 1:38:37
  Speaker 2: elementary particles associated with electromagnetic radiation, which includes visible light,
• 1:38:43
  Speaker 2: radio waves, microwaves, and x-rays. Unlike electrons, protons, and many
• 1:38:50
  Speaker 2: other particles, photons have no rest mass, and when they
• 1:38:54
  Speaker 2: propagate freely through a vacuum, they travel at exactly the
• 1:38:58
  Speaker 2: speed of light. They don't gradually accelerate towards that speed,
• 1:39:03
  Speaker 2: nor do they begin their journey at rest before somehow
• 1:39:06
  Speaker 2: gathering momentum. A freely propagating photon in a vacuum travels
• 1:39:12
  Speaker 2: at the invariant speed of light, and this gives photons
• 1:39:15
  Speaker 2: a rather unusual place within the geometry of spacetime. Massive
• 1:39:20
  Speaker 2: objects such as people, planets and spacecraft follow what physicists
• 1:39:25
  Speaker 2: call time-like world lines. These are paths through space-time along
• 1:39:30
  Speaker 2: which an ordinary physical clock can travel, measuring the elapsed
• 1:39:34
  Speaker 2: time associated with its journey. That elapsed time is called
• 1:39:38
  Speaker 2: proper time. If you sit comfortably in a chair for
• 1:39:42
  Speaker 2: an hour, the clock beside you measures approximately one hour
• 1:39:45
  Speaker 2: of proper time. If you travel aboard a spacecraft, your
• 1:39:49
  Speaker 2: clock measures the proper time accumulated along your particular journey.
• 1:39:53
  Speaker 2: But photons follow a different kind of path. Their paths
• 1:39:57
  Speaker 2: through spacetime are called light-like world lines, or null world lines,
• 1:40:02
  Speaker 2: and the mathematical properties of these paths are rather extraordinary.
• 1:40:06
  Speaker 2: For a light-like path, the spacetime interval between neighbouring events
• 1:40:10
  Speaker 2: is zero. In the geometry of special relativity, this means
• 1:40:14
  Speaker 2: that the proper time interval along an ideal, light-like path,
• 1:40:19
  Speaker 2: is also zero. That statement is mathematically precise, and it's
• 1:40:25
  Speaker 2: the origin of the familiar claim that time stops for light.
• 1:40:29
  Speaker 2: But we need to be careful about what it actually means.
• 1:40:32
  Speaker 2: Consider a photon leaving the surface of the sun. It
• 1:40:36
  Speaker 2: travels across approximately 150 million kilometres of space before reaching Earth.
• 1:40:43
  Speaker 2: According to clocks in a reference frame approximately at rest
• 1:40:46
  Speaker 2: with the Sun and Earth, the journey takes around 8
• 1:40:49
  Speaker 2: minutes and 20 seconds. During those minutes, countless physical processes
• 1:40:54
  Speaker 2: continue taking place. Earth rotates slightly, clouds move across the atmosphere,
• 1:41:00
  Speaker 2: and people go about their ordinary lives. The light genuinely
• 1:41:04
  Speaker 2: requires time to cross the distance. Now imagine light arriving
• 1:41:09
  Speaker 2: from a star 1,000 light years away. According to a
• 1:41:13
  Speaker 2: suitable astronomical reference frame, that light has spent approximately 1,000
• 1:41:18
  Speaker 2: years travelling towards us. Civilisations may have risen and disappeared
• 1:41:23
  Speaker 2: during its journey. Entire generations of people could have lived
• 1:41:27
  Speaker 2: their lives before the light finally reached a telescope on Earth.
• 1:41:31
  Speaker 2: And yet, in the idealised description of light travelling through spacetime,
• 1:41:35
  Speaker 2: the proper time interval along its light-like worldline remains zero.
• 1:41:40
  Speaker 2: How can both statements be true? because they describe different
• 1:41:43
  Speaker 2: mathematical quantities. The thousand years represent a coordinate time interval
• 1:41:49
  Speaker 2: measured within a particular reference frame. The zero interval describes
• 1:41:53
  Speaker 2: the invariant spacetime geometry of the light-like path itself. There
• 1:41:58
  Speaker 2: is no contradiction between them. But this brings us to
• 1:42:02
  Speaker 2: a particularly important distinction. We cannot simply imagine sitting beside
• 1:42:07
  Speaker 2: a photon and asking what the journey looks like from
• 1:42:10
  Speaker 2: its perspective. in special relativity, a photon does not possess
• 1:42:15
  Speaker 2: a valid inertial rest frame. An inertial reference frame is
• 1:42:20
  Speaker 2: one in which an observer can be considered at rest,
• 1:42:23
  Speaker 2: while measuring distances, durations, and the speeds of objects moving
• 1:42:27
  Speaker 2: around them. For a massive observer, we can describe such
• 1:42:31
  Speaker 2: a frame. Even if someone is travelling at an enormous
• 1:42:34
  Speaker 2: fraction of the speed of light, there's always an inertial
• 1:42:38
  Speaker 2: frame in which they are stationary. But photons are different.
• 1:42:42
  Speaker 2: No physically valid Lorentz transformation allows us to move into
• 1:42:46
  Speaker 2: a reference frame travelling alongside a photon at the speed
• 1:42:49
  Speaker 2: of light. The mathematical transformations connecting ordinary inertial frames become
• 1:42:55
  Speaker 2: singular in that limit, so there is no legitimate photon
• 1:42:59
  Speaker 2: rest frame from which we can describe the universe, and
• 1:43:02
  Speaker 2: this means that expressions such as seeing the universe from
• 1:43:06
  Speaker 2: a photon's perspective need to be treated very carefully. They're
• 1:43:10
  Speaker 2: sometimes useful as poetic descriptions, but they aren't literal statements
• 1:43:15
  Speaker 2: about observations a photon could make. A photon doesn't carry
• 1:43:19
  Speaker 2: a functioning clock that records zero seconds while the rest
• 1:43:22
  Speaker 2: of the universe ages. Nor does relativity establish that a
• 1:43:26
  Speaker 2: photon sees its entire journey compressed into one frozen instant.
• 1:43:32
  Speaker 2: The theory simply tells us that light-like paths have zero
• 1:43:36
  Speaker 2: proper time interval. while photons themselves cannot be assigned ordinary
• 1:43:41
  Speaker 2: inertial rest frames. This distinction also prevents us from making
• 1:43:46
  Speaker 2: unsupported claims about what photons might experience. Questions about awareness, perception,
• 1:43:52
  Speaker 2: or subjective experience are not answered by the mathematical properties
• 1:43:56
  Speaker 2: of a null worldline. Photons are elementary particles, and physics
• 1:44:01
  Speaker 2: does not attribute consciousness or an internal sense of time
• 1:44:05
  Speaker 2: to them. The absence of proper time along a light-like
• 1:44:09
  Speaker 2: path is a geometric statement, not a description of what
• 1:44:12
  Speaker 2: it feels like to be light. There is another interesting question.
• 1:44:17
  Speaker 2: What happens if a massive observer travels faster and faster,
• 1:44:21
  Speaker 2: approaching the speed of light? As their velocity increases relative
• 1:44:27
  Speaker 2: to a chosen inertial frame, the time dilation becomes increasingly large.
• 1:44:33
  Speaker 2: A traveller moving at 99.9% of the speed of light
• 1:44:37
  Speaker 2: accumulates much less time than stationary clocks in that frame
• 1:44:41
  Speaker 2: over the corresponding interval. At even greater speeds, the difference
• 1:44:46
  Speaker 2: becomes more dramatic. But no matter how closely the traveller
• 1:44:50
  Speaker 2: approaches light speed, they remain below it. Their worldline remains time-like.
• 1:44:56
  Speaker 2: They continue possessing a valid rest frame, and their own
• 1:44:59
  Speaker 2: clock continues measuring ordinary proper time. Reaching the speed of
• 1:45:04
  Speaker 2: light would require an object with non-zero rest mass to
• 1:45:07
  Speaker 2: acquire an unbounded amount of energy, so the traveller can
• 1:45:11
  Speaker 2: never simply become equivalent to a photon by accelerating. The
• 1:45:15
  Speaker 2: distinction between timelike and lightlike paths remains fundamental, and that
• 1:45:20
  Speaker 2: distinction tells us something important about the speed of light itself.
• 1:45:24
  Speaker 2: It isn't merely the speed at which a particular kind
• 1:45:27
  Speaker 2: of particle happens to move. It's the invariant speed defining
• 1:45:31
  Speaker 2: the boundary between the world lines available to massive objects,
• 1:45:35
  Speaker 2: and those followed by freely propagating massless radiation. Light travels
• 1:45:40
  Speaker 2: along the null directions of spacetime. Massive observers travel within
• 1:45:45
  Speaker 2: those boundaries, accumulating proper time along their journeys. And the
• 1:45:50
  Speaker 2: geometry connecting these possibilities is what gives special relativity its
• 1:45:54
  Speaker 2: remarkable consistency. So, Does time exist for a particle of light?
• 1:46:01
  Speaker 2: The most accurate answer is that the ordinary idea of
• 1:46:04
  Speaker 2: time passing for an observer cannot be applied directly to
• 1:46:08
  Speaker 2: a photon. A photon has no valid rest frame, and
• 1:46:12
  Speaker 2: its light-like path has zero proper time interval. But that
• 1:46:16
  Speaker 2: doesn't mean its journey takes no time according to clocks
• 1:46:19
  Speaker 2: elsewhere in the universe. Sunlight still takes several minutes to
• 1:46:23
  Speaker 2: reach Earth. Starlight still crosses enormous distances over centuries, millennia,
• 1:46:30
  Speaker 2: or billions of years. And astronomers can measure those travel
• 1:46:34
  Speaker 2: times without any difficulty. What makes light extraordinary is not
• 1:46:39
  Speaker 2: that it somehow escapes the existence of time. It's that
• 1:46:42
  Speaker 2: its path through spacetime differs fundamentally from the paths followed
• 1:46:47
  Speaker 2: by objects possessing mass. And through that difference, we discover
• 1:46:52
  Speaker 2: just how deeply the nature of time is connected to
• 1:46:55
  Speaker 2: the speed of light. Gravity is something we encounter every day,
• 1:46:59
  Speaker 2: usually without giving it much thought. It keeps our feet
• 1:47:03
  Speaker 2: on the ground, holds the oceans against Earth's surface, and
• 1:47:06
  Speaker 2: ensures that objects released from our hands fall towards the floor.
• 1:47:12
  Speaker 2: But gravity does something considerably more surprising as well. It
• 1:47:16
  Speaker 2: changes the rate at which time passes. A clock resting
• 1:47:19
  Speaker 2: at the top of a mountain measures time at a
• 1:47:22
  Speaker 2: slightly different rate from an identical clock sitting beside the sea.
• 1:47:26
  Speaker 2: Both clocks can be perfectly accurate. Neither needs to move
• 1:47:30
  Speaker 2: at anything approaching the speed of light. And yet, when
• 1:47:33
  Speaker 2: their readings are compared carefully, a measurable difference appears. This
• 1:47:37
  Speaker 2: remarkable phenomenon is known as gravitational time dilation, and it
• 1:47:42
  Speaker 2: reveals that the relationship between light, space and time extends
• 1:47:47
  Speaker 2: far beyond objects travelling at enormous velocities. In 1915, Albert
• 1:47:53
  Speaker 2: Einstein completed the central field equations of his general theory
• 1:47:57
  Speaker 2: of relativity. His earlier theory, special relativity, had explained how
• 1:48:02
  Speaker 2: measurements of space and time depend upon relative motion. General
• 1:48:07
  Speaker 2: relativity extended that understanding to include gravity. Instead of describing
• 1:48:12
  Speaker 2: gravity simply as an invisible force pulling objects towards one another,
• 1:48:17
  Speaker 2: Einstein developed a theory in which matter and energy influence
• 1:48:20
  Speaker 2: the geometry of spacetime. Objects moving freely under gravity follow
• 1:48:25
  Speaker 2: paths determined by that geometry. And because time forms part
• 1:48:30
  Speaker 2: of spacetime, gravity also affects the elapsed time measured by clocks.
• 1:48:36
  Speaker 2: One of the central ideas leading Einstein towards this understanding
• 1:48:39
  Speaker 2: was the equivalence principle. Imagine standing inside a completely enclosed lift.
• 1:48:45
  Speaker 2: You cannot see outside and you have no way of
• 1:48:48
  Speaker 2: knowing where the lift happens to be. If it is
• 1:48:51
  Speaker 2: resting on Earth, you feel the familiar pressure of the
• 1:48:54
  Speaker 2: floor supporting your weight. Now imagine the lift floating far
• 1:48:58
  Speaker 2: away from planets and stars, somewhere in deep space. If
• 1:49:02
  Speaker 2: a powerful engine accelerates it upwards, you once again feel
• 1:49:07
  Speaker 2: pressed against the floor. Under suitable conditions, the two situations
• 1:49:11
  Speaker 2: can produce locally indistinguishable effects. The equivalence principle expresses the
• 1:49:16
  Speaker 2: close relationship between gravitational environments and accelerated reference frames. More precisely,
• 1:49:24
  Speaker 2: the effects of gravity in a sufficiently small region can
• 1:49:27
  Speaker 2: be related to those experienced in an accelerating laboratory, and
• 1:49:31
  Speaker 2: this connection has an extraordinary implication for time. Consider a
• 1:49:36
  Speaker 2: beam of light travelling vertically through an accelerating spacecraft. While
• 1:49:41
  Speaker 2: the light is moving, the spacecraft's velocity changes. The observer
• 1:49:46
  Speaker 2: receiving the light therefore measures a different frequency from the
• 1:49:49
  Speaker 2: one associated with its emission. Einstein recognised that a corresponding
• 1:49:54
  Speaker 2: effect should occur when light travels between different heights in
• 1:49:57
  Speaker 2: a gravitational field. This is gravitational redshift. Light travelling upwards,
• 1:50:03
  Speaker 2: away from Earth's surface is measured by a stationary observer
• 1:50:07
  Speaker 2: at the higher altitude to have a slightly lower frequency
• 1:50:10
  Speaker 2: than it had when emitted below. Light travelling downwards towards
• 1:50:15
  Speaker 2: a lower altitude is measured to have a correspondingly higher frequency.
• 1:50:20
  Speaker 2: These frequency changes are connected to the way clocks tick
• 1:50:23
  Speaker 2: at different gravitational heights. After all, frequency measures how many
• 1:50:28
  Speaker 2: cycles occur during a given interval of time. If otherwise
• 1:50:32
  Speaker 2: identical atomic clocks operate at different rates, the frequencies associated
• 1:50:36
  Speaker 2: with their atomic transitions also differ when compared using a
• 1:50:40
  Speaker 2: common reference. And this means that gravity affects timekeeping itself.
• 1:50:45
  Speaker 2: Imagine placing two extraordinarily accurate atomic clocks at different heights
• 1:50:50
  Speaker 2: above Earth. One sits in a laboratory beside the sea.
• 1:50:54
  Speaker 2: The other rests on a mountain, 1,000 metres higher. Because
• 1:50:59
  Speaker 2: the higher clock is farther from Earth's centre, it occupies
• 1:51:02
  Speaker 2: a slightly different gravitational potential. According to general relativity, the
• 1:51:08
  Speaker 2: clock on the mountain accumulates time a little faster than
• 1:51:11
  Speaker 2: the clock at sea level when their relative motion and
• 1:51:14
  Speaker 2: other relevant effects are accounted for. The difference is tiny.
• 1:51:19
  Speaker 2: For a height difference of approximately 1,000 metres, the gravitational
• 1:51:24
  Speaker 2: contribution is roughly 9 nanoseconds per day. A nanosecond is
• 1:51:29
  Speaker 2: one billionth of a second. So the difference would be
• 1:51:32
  Speaker 2: completely invisible to ordinary clocks, and certainly to anyone simply
• 1:51:37
  Speaker 2: going about their daily routine. But sufficiently precise atomic clocks
• 1:51:41
  Speaker 2: can detect effects of this kind, and the result is remarkable.
• 1:51:46
  Speaker 2: Two people living at different altitudes can accumulate slightly different
• 1:51:50
  Speaker 2: amounts of time, even when neither is travelling at an
• 1:51:53
  Speaker 2: extraordinary speed. The person at the higher altitude experiences no
• 1:51:58
  Speaker 2: unusual sensation. Their heartbeat remains normal, their thoughts proceed at
• 1:52:03
  Speaker 2: their familiar pace, and their clock continues measuring perfectly ordinary seconds.
• 1:52:09
  Speaker 2: The difference only becomes apparent when measurements from the two
• 1:52:13
  Speaker 2: locations are compared. The effect was tested through an ingenious
• 1:52:17
  Speaker 2: experiment carried out at Harvard University. In 1959, the physicists
• 1:52:23
  Speaker 2: Robert Pound and Glenn Rebke used gamma rays to investigate
• 1:52:27
  Speaker 2: the gravitational frequency shift predicted by Einstein's theory. Their experiment
• 1:52:33
  Speaker 2: involved transmitting gamma radiation through a vertical distance of approximately 22.5
• 1:52:39
  Speaker 2: metres inside a university building. Gamma rays are a form
• 1:52:44
  Speaker 2: of electromagnetic radiation, just like visible light, although they possess
• 1:52:49
  Speaker 2: much higher frequencies and photon energies. The researchers used a
• 1:52:54
  Speaker 2: particularly precise nuclear phenomenon known as the Musbauer effect, which
• 1:52:59
  Speaker 2: allowed them to detect extremely small differences in gamma-ray energy.
• 1:53:04
  Speaker 2: As the radiation travelled between different gravitational heights, general relativity
• 1:53:09
  Speaker 2: predicted a minute change in the frequency measured by observers
• 1:53:13
  Speaker 2: at those locations. The expected difference was extraordinarily small, that
• 1:53:18
  Speaker 2: the experiment was sensitive enough to investigate it. The results,
• 1:53:23
  Speaker 2: reported in 1960, supported the predicted gravitational redshift and became
• 1:53:28
  Speaker 2: an important experimental confirmation of general relativity. There is, however,
• 1:53:33
  Speaker 2: a subtle distinction worth appreciating. The gravitational change in measured
• 1:53:38
  Speaker 2: light frequency does not mean that light simply slows down
• 1:53:42
  Speaker 2: as it travels upwards. According to general relativity, every freely
• 1:53:47
  Speaker 2: falling observer making a sufficiently local measurement in a vacuum
• 1:53:52
  Speaker 2: obtains the same fundamental speed of light, approximately 300,000 km
• 1:53:57
  Speaker 2: per second. That local invariance remains essential. When physicists describe
• 1:54:03
  Speaker 2: light travelling across larger regions of curved spacetime, they may
• 1:54:07
  Speaker 2: use coordinates in which its calculated coordinate speed varies. But
• 1:54:12
  Speaker 2: coordinate speed depends upon how distances and times are labelled.
• 1:54:16
  Speaker 2: it should not be confused with the speed measured locally
• 1:54:19
  Speaker 2: by an observer using appropriate instruments. Gravity changes the geometry
• 1:54:24
  Speaker 2: connecting events, rather than simply imposing a mechanical resistance upon
• 1:54:29
  Speaker 2: passing light. And within that geometry, clocks following different world
• 1:54:34
  Speaker 2: lines can accumulate different amounts of proper time. This is
• 1:54:38
  Speaker 2: why gravitational time dilation and the time dilation associated with
• 1:54:43
  Speaker 2: relative motion are closely related, but not identical. Special relativity
• 1:54:48
  Speaker 2: describes the differences between clock measurements associated with motion in
• 1:54:53
  Speaker 2: flat spacetime. General relativity allows us to examine clocks in
• 1:54:58
  Speaker 2: gravitational environments where spacetime curvature matters. When comparing clocks near Earth,
• 1:55:05
  Speaker 2: both effects may need to be considered. A clock can
• 1:55:08
  Speaker 2: be influenced by its motion, its gravitational environment, and the
• 1:55:12
  Speaker 2: particular path it follows between two events. None of this
• 1:55:16
  Speaker 2: means that time has somehow become unreliable. Quite the opposite.
• 1:55:21
  Speaker 2: General relativity provides precise mathematical relationships for predicting how different
• 1:55:27
  Speaker 2: clocks behave, and the predictions have been confirmed through increasingly
• 1:55:32
  Speaker 2: sensitive experiments. The extraordinary conclusion is that time does not
• 1:55:37
  Speaker 2: pass at one universal rate throughout a gravitational field. A
• 1:55:42
  Speaker 2: clock near Earth's surface and another high above it can
• 1:55:45
  Speaker 2: accumulate different amounts of time, and in much stronger gravitational
• 1:55:49
  Speaker 2: environments such as those surrounding neutron stars or black holes,
• 1:55:53
  Speaker 2: the differences can become far more dramatic. Gravity therefore does
• 1:55:57
  Speaker 2: considerably more than determine how objects move through space. It
• 1:56:01
  Speaker 2: influences the relationship between space and time themselves, and the
• 1:56:06
  Speaker 2: same invariant speed of light that helps explain why moving
• 1:56:10
  Speaker 2: clocks disagree remains fundamental to understanding how clocks behave in
• 1:56:14
  Speaker 2: a curved universe. Even here on Earth, where gravitational time
• 1:56:18
  Speaker 2: dilation is usually almost impossibly small, the effect is present.
• 1:56:24
  Speaker 2: Every mountain summit, every valley, and every carefully measured difference
• 1:56:28
  Speaker 2: in height provides another reminder that time is inseparably connected
• 1:56:33
  Speaker 2: to the geometry of the universe, and what feels like
• 1:56:36
  Speaker 2: one perfectly steady passage of seconds is, in reality, something
• 1:56:41
  Speaker 2: a little more extraordinary. Imagine opening a map on your
• 1:56:45
  Speaker 2: phone and asking it to show you where you are.
• 1:56:48
  Speaker 2: Within a few moments, a small blue dot appears on
• 1:56:51
  Speaker 2: the screen, marking your position with remarkable accuracy. You might
• 1:56:56
  Speaker 2: be standing outside a railway station, walking through an unfamiliar town,
• 1:57:00
  Speaker 2: or trying to remember exactly where you parked the car.
• 1:57:04
  Speaker 2: The technology seems almost effortlessly convenient. But behind that little
• 1:57:09
  Speaker 2: blue dot lies something rather extraordinary. For the system to
• 1:57:13
  Speaker 2: work properly, engineers must account for the fact that time
• 1:57:16
  Speaker 2: passes at different rates in different places. And without Einstein's
• 1:57:21
  Speaker 2: theories of relativity, modern satellite navigation would become increasingly inaccurate.
• 1:57:27
  Speaker 2: The technology responsible is called the Global Positioning System. It
• 1:57:31
  Speaker 2: uses a network of satellites orbiting Earth, each carrying extremely
• 1:57:36
  Speaker 2: accurate atomic clocks. These satellites continually broadcast radio signals containing
• 1:57:42
  Speaker 2: information about their positions and the times at which their
• 1:57:45
  Speaker 2: signals were transmitted. A receiver on the ground, such as
• 1:57:49
  Speaker 2: the one inside a smartphone, uses those signals to calculate
• 1:57:53
  Speaker 2: its location. The basic principle is surprisingly straightforward. Because radio
• 1:57:59
  Speaker 2: waves travel through a vacuum at the speed of light,
• 1:58:02
  Speaker 2: the time taken for a signal to reach the receiver
• 1:58:05
  Speaker 2: tells us something about the distance it has travelled. If
• 1:58:08
  Speaker 2: a signal takes one thousandth of a second to arrive,
• 1:58:12
  Speaker 2: light travels approximately 300 kilometres during that interval. With sufficiently
• 1:58:17
  Speaker 2: accurate timing, the receiver can determine how far away a
• 1:58:20
  Speaker 2: satellite appears to be, but knowing the distance to one
• 1:58:24
  Speaker 2: satellite isn't enough to establish an exact position. The receiver
• 1:58:28
  Speaker 2: needs information from several satellites, usually at least four, to
• 1:58:33
  Speaker 2: solve for its three-dimensional position and the difference between its
• 1:58:36
  Speaker 2: own clock and the satellite system's time. And this is
• 1:58:40
  Speaker 2: where accurate timekeeping becomes absolutely essential. Light travels approximately 30
• 1:58:46
  Speaker 2: centimetres in a single nanosecond. A nanosecond is one billionth
• 1:58:50
  Speaker 2: of a second. so a timing error of only a
• 1:58:53
  Speaker 2: few nanoseconds can introduce an error of roughly a metre
• 1:58:57
  Speaker 2: into an individual distance measurement. A larger timing error could
• 1:59:01
  Speaker 2: make the calculated position increasingly unreliable. Fortunately, the satellites carry
• 1:59:07
  Speaker 2: atomic clocks, which measure time using extremely regular transitions between
• 1:59:11
  Speaker 2: energy states within atoms. These clocks are far more stable
• 1:59:16
  Speaker 2: than ordinary mechanical or electronic timekeeping devices, But even an
• 1:59:20
  Speaker 2: exceptionally accurate clock cannot escape the effects of relativity. Global
• 1:59:25
  Speaker 2: positioning system satellites orbit approximately 20,200 kilometres above Earth's surface.
• 1:59:32
  Speaker 2: They travel around the planet at roughly 3.9 kilometres per second,
• 1:59:36
  Speaker 2: completing an orbit in approximately 12 hours. And their circumstances
• 1:59:41
  Speaker 2: are quite different from those experienced by clocks on the ground.
• 1:59:45
  Speaker 2: There are two important relativistic effects to consider. The first
• 1:59:49
  Speaker 2: comes from special relativity. Because the satellites are moving rapidly
• 1:59:54
  Speaker 2: relative to a suitable Earth-centred reference frame, their clocks accumulate
• 1:59:59
  Speaker 2: slightly less time than comparable clocks that are stationary in
• 2:00:02
  Speaker 2: that frame. The difference amounts to approximately seven microseconds each day.
• 2:00:07
  Speaker 2: A microsecond is one millionth of a second. Seven microseconds
• 2:00:12
  Speaker 2: might sound almost insignificant, but for a navigation system, depending
• 2:00:16
  Speaker 2: upon precise radio signals, it matters enormously. However, this is
• 2:00:21
  Speaker 2: only part of the calculation. The satellites are also much
• 2:00:24
  Speaker 2: farther from Earth's centre than the clocks on the ground,
• 2:00:28
  Speaker 2: and that means they experience a different gravitational environment. According
• 2:00:32
  Speaker 2: to general relativity, clocks farther from Earth, where the gravitational
• 2:00:36
  Speaker 2: potential is higher, tend to accumulate time faster than clocks
• 2:00:41
  Speaker 2: closer to the surface. For navigation satellites, this gravitational effect
• 2:00:46
  Speaker 2: amounts to approximately 45 microseconds per day. Notice that the
• 2:00:51
  Speaker 2: two effects act in opposite directions. The motion-related effect makes
• 2:00:56
  Speaker 2: the satellite clocks run more slowly in the chosen comparison.
• 2:01:00
  Speaker 2: The gravitational effect makes them run faster, and because the
• 2:01:03
  Speaker 2: gravitational effect is larger, it wins by a considerable margin.
• 2:01:09
  Speaker 2: When the two contributions are combined, satellite clocks would run
• 2:01:12
  Speaker 2: approximately 38 microseconds faster per day than the corresponding reference
• 2:01:17
  Speaker 2: clocks on Earth, without the appropriate corrections. That might not
• 2:01:21
  Speaker 2: sound particularly dramatic. 38 millionths of a second is an
• 2:01:26
  Speaker 2: interval far too brief for us to notice, but light
• 2:01:30
  Speaker 2: travels more than 11 kilometres during that time. If such
• 2:01:34
  Speaker 2: clock rate differences were ignored, The resulting navigation errors would
• 2:01:38
  Speaker 2: grow rapidly. A system designed to tell you which street
• 2:01:42
  Speaker 2: you're standing on could eventually struggle to identify the correct
• 2:01:45
  Speaker 2: part of a city, which would rather defeat the purpose
• 2:01:48
  Speaker 2: of asking it for directions. Engineers therefore incorporate relativistic corrections
• 2:01:54
  Speaker 2: into the system's design and operation. The satellite's clock frequencies
• 2:01:58
  Speaker 2: are adjusted, and additional timing corrections account for changes in
• 2:02:02
  Speaker 2: their orbits and other relevant effects. The calculations also require
• 2:02:07
  Speaker 2: careful treatment of Earth's rotation. Because our planet turns while
• 2:02:12
  Speaker 2: radio signals travel between satellites and receivers, the geometry of
• 2:02:16
  Speaker 2: their journeys changes during transmission. This produces a correction commonly
• 2:02:21
  Speaker 2: associated with the Sanak effect. The system must also account
• 2:02:25
  Speaker 2: for signal delays caused by Earth's ionosphere and atmosphere, alongside
• 2:02:29
  Speaker 2: the precise coordinate reference system used to describe satellite positions.
• 2:02:35
  Speaker 2: These considerations are distinct from the basic difference in clock
• 2:02:38
  Speaker 2: rates caused by motion and gravity. All of them matter
• 2:02:42
  Speaker 2: when measurements depend upon extraordinarily small intervals of time, and
• 2:02:47
  Speaker 2: the precision required has inspired remarkable developments in the science
• 2:02:52
  Speaker 2: of clocks themselves. The National Institute of Standards and Technology
• 2:02:57
  Speaker 2: in the United States has contributed extensively to the development
• 2:03:01
  Speaker 2: of atomic and optical clocks. Traditional caesium atomic clocks use
• 2:03:06
  Speaker 2: transitions associated with microwave frequencies. Optical atomic clocks use much
• 2:03:12
  Speaker 2: higher frequency transitions, allowing researchers to measure time with exceptional precision.
• 2:03:18
  Speaker 2: Some of these instruments are now sensitive enough to detect
• 2:03:21
  Speaker 2: the gravitational influence of differences in height that would once
• 2:03:25
  Speaker 2: have seemed impossibly small. Researchers associated with the University of
• 2:03:30
  Speaker 2: Colorado Boulder including scientists working with the National Institute of
• 2:03:34
  Speaker 2: Standards and Technology, have demonstrated that clocks positioned at different
• 2:03:38
  Speaker 2: heights can accumulate measurably different amounts of time. In one
• 2:03:43
  Speaker 2: experiment reported in 2010, researchers detected gravitational time dilation between
• 2:03:49
  Speaker 2: clocks separated vertically by only about 33 centimetres. Later experiments
• 2:03:55
  Speaker 2: using advanced optical clocks demonstrated sensitivity to gravitational redshift across
• 2:04:01
  Speaker 2: even smaller height differences, approaching the millimetre scale. These measurements
• 2:04:07
  Speaker 2: are astonishing. They show that the difference in timekeeping between
• 2:04:11
  Speaker 2: the top and bottom of a laboratory can be detected
• 2:04:14
  Speaker 2: with sufficiently precise instruments. No spacecraft is required. No journey
• 2:04:20
  Speaker 2: towards a distant star is necessary. Even the difference between
• 2:04:24
  Speaker 2: two nearby heights on Earth is enough. The effects are
• 2:04:27
  Speaker 2: incredibly small, but they're physically real. and the same principles
• 2:04:32
  Speaker 2: apply to aircraft, satellites, precision laboratories and other systems in
• 2:04:37
  Speaker 2: which accurate timing matters. Relativity has therefore become much more
• 2:04:42
  Speaker 2: than an explanation of what might happen to astronauts travelling
• 2:04:46
  Speaker 2: close to the speed of light. It's a practical part
• 2:04:49
  Speaker 2: of the technology we use every day. Every time a
• 2:04:53
  Speaker 2: navigation receiver calculates its position, It relies upon a system
• 2:04:57
  Speaker 2: designed around the fact that time is not measured at
• 2:05:00
  Speaker 2: one universal rate. Clocks moving along different paths and occupying
• 2:05:05
  Speaker 2: different gravitational environments can accumulate different amounts of elapsed time,
• 2:05:10
  Speaker 2: but those differences are predictable. They follow mathematical relationships that
• 2:05:15
  Speaker 2: engineers can calculate, correct for, and use with extraordinary precision.
• 2:05:20
  Speaker 2: And perhaps that's the most remarkable aspect of all. An
• 2:05:24
  Speaker 2: idea that once seemed to challenge our most familiar understanding
• 2:05:27
  Speaker 2: of time now helps us find our way through the
• 2:05:30
  Speaker 2: ordinary world. The blue dot on your phone is there,
• 2:05:33
  Speaker 2: in part, because the universe doesn't have one universal clock,
• 2:05:38
  Speaker 2: and because scientists learned how to work with that extraordinary fact.
• 2:05:42
  Speaker 2: Every event in the universe has a relationship with the
• 2:05:45
  Speaker 2: events surrounding it. A stone falls into a pond and
• 2:05:49
  Speaker 2: ripples spread across the water. A distant star releases a
• 2:05:53
  Speaker 2: burst of radiation and millions of years later some of
• 2:05:57
  Speaker 2: that light reaches a telescope on Earth. A person presses
• 2:06:01
  Speaker 2: a button and a signal travels through a wire causing
• 2:06:04
  Speaker 2: a machine to begin working. In each case something happens
• 2:06:09
  Speaker 2: and that event produces a consequence somewhere else. Physicists describe
• 2:06:13
  Speaker 2: this relationship through a principle called causality. At its simplest
• 2:06:18
  Speaker 2: causality means that causes can produce effects. and that the
• 2:06:22
  Speaker 2: physical relationships between events follow consistent rules. But there's a
• 2:06:27
  Speaker 2: remarkable connection between causality and the speed of light. The
• 2:06:31
  Speaker 2: universe places a limit on how quickly information can travel,
• 2:06:35
  Speaker 2: and that limit helps determine which events can influence one another.
• 2:06:39
  Speaker 2: To understand why, imagine a sudden flash of light occurring
• 2:06:44
  Speaker 2: somewhere in otherwise empty space. At the instant the flash occurs,
• 2:06:48
  Speaker 2: its effects are confined to the location where it originated.
• 2:06:52
  Speaker 2: After one second, the light has traveled approximately 300,000 kilometers
• 2:06:57
  Speaker 2: in every direction. After two seconds, it has reached approximately
• 2:07:03
  Speaker 2: twice that distance. And as time continues, the expanding sphere
• 2:07:07
  Speaker 2: of light reaches progressively farther into space. Anything beyond that
• 2:07:12
  Speaker 2: expanding boundary cannot yet have received information about the original event.
• 2:07:18
  Speaker 2: No ordinary signal could have arrived there any faster. This
• 2:07:22
  Speaker 2: relationship is represented in relativity through something called a light cone.
• 2:07:26
  Speaker 2: A light cone describes the boundary separating events that can
• 2:07:30
  Speaker 2: be causally connected from events that cannot exchange signals within
• 2:07:35
  Speaker 2: the available time. The future light cone contains the events
• 2:07:39
  Speaker 2: that a particular occurrence could potentially influence. The past-like cone
• 2:07:43
  Speaker 2: contains events that could have influenced it, and outside these
• 2:07:47
  Speaker 2: regions lie events separated by distances too great for light,
• 2:07:52
  Speaker 2: or anything travelling more slowly to connect them within the
• 2:07:55
  Speaker 2: relevant interval. These different relationships are described using three categories
• 2:08:01
  Speaker 2: of space-time separation. Events with a time-like separation can be
• 2:08:06
  Speaker 2: connected by an object or signal traveling below the speed
• 2:08:09
  Speaker 2: of light. Events with a light-like separation can be connected
• 2:08:14
  Speaker 2: by light traveling through a vacuum. And events with a
• 2:08:17
  Speaker 2: space-like separation cannot be connected by any ordinary signal obeying
• 2:08:23
  Speaker 2: the relativistic speed limit. This distinction has an important consequence
• 2:08:29
  Speaker 2: for the order of events. Observers moving relative to one
• 2:08:32
  Speaker 2: another can disagree about whether two distant, space-like separated events
• 2:08:37
  Speaker 2: occurred simultaneously. They may even disagree about which event happened first.
• 2:08:44
  Speaker 2: But if one event can causally influence another through a
• 2:08:46
  Speaker 2: light speed or slower signal, every inertial observer agrees about
• 2:08:51
  Speaker 2: their order. The effect cannot occur before its cause in
• 2:08:55
  Speaker 2: another ordinary inertial reference frame. The speed of light therefore
• 2:09:00
  Speaker 2: protects a consistent causal structure, even though different observers do
• 2:09:04
  Speaker 2: not share one universal definition of the present. Now consider
• 2:09:09
  Speaker 2: what might happen if information could travel faster than light.
• 2:09:14
  Speaker 2: Imagine two distant spacecraft, each equipped with a hypothetical transmitter
• 2:09:19
  Speaker 2: capable of sending messages instantaneously, or at least faster than light.
• 2:09:25
  Speaker 2: One spacecraft sends a message to the other. Because the
• 2:09:29
  Speaker 2: transmission would connect space-like separated events, different inertial observers could
• 2:09:34
  Speaker 2: disagree about which happened first. In one reference frame, the
• 2:09:38
  Speaker 2: message is sent and then received. In another, moving relative
• 2:09:43
  Speaker 2: to the first. reception could be assigned an earlier time
• 2:09:46
  Speaker 2: than the transmission. This alone would not necessarily allow someone
• 2:09:50
  Speaker 2: to change the past. But suppose the second spacecraft could
• 2:09:54
  Speaker 2: send a faster-than-light reply using the same hypothetical capability within
• 2:10:00
  Speaker 2: its own reference frame. With suitable relative motion and signal speeds,
• 2:10:05
  Speaker 2: the reply could arrive at the first spacecraft before the
• 2:10:08
  Speaker 2: original message was sent. The sender might receive a warning
• 2:10:12
  Speaker 2: not to transmit the very message that prompted the warning.
• 2:10:16
  Speaker 2: This creates a causal paradox. The difficulty isn't simply that
• 2:10:20
  Speaker 2: information travels unusually quickly. It's that unrestricted, faster-than-light communication, combined
• 2:10:27
  Speaker 2: with the ordinary transformation rules of special relativity, can produce
• 2:10:31
  Speaker 2: arrangements in which causes and effects form inconsistent loops. These
• 2:10:37
  Speaker 2: arguments don't demonstrate that practical travel into the past has
• 2:10:40
  Speaker 2: been achieved, nor do they establish that every imaginable theory
• 2:10:44
  Speaker 2: involving faster-than-light phenomena must behave identically. They show why controllable
• 2:10:51
  Speaker 2: faster-than-light signalling creates serious problems for the familiar causal structure
• 2:10:56
  Speaker 2: of relativity. And so far, no experimentally established method allows
• 2:11:02
  Speaker 2: us to send usable information faster than light. There is, however,
• 2:11:07
  Speaker 2: a phenomenon in quantum physics that sometimes appears to challenge
• 2:11:11
  Speaker 2: this restriction. It's called quantum entanglement. When two quantum systems
• 2:11:16
  Speaker 2: become entangled, measurements performed on them can exhibit correlations that
• 2:11:21
  Speaker 2: cannot be explained by ordinary classical descriptions involving predetermined local properties.
• 2:11:27
  Speaker 2: The physicist John Stuart Bell demonstrated how particular statistical tests
• 2:11:32
  Speaker 2: could distinguish predictions of quantum mechanics from from those of
• 2:11:36
  Speaker 2: local hidden variable theories. Experiments have repeatedly confirmed the distinctive
• 2:11:42
  Speaker 2: correlations predicted by quantum mechanics. And some of these experiments
• 2:11:47
  Speaker 2: involve particles separated by considerable distances. This can make entanglement
• 2:11:52
  Speaker 2: sound rather like instantaneous communication. But there's an essential distinction.
• 2:11:58
  Speaker 2: The individual outcome of a quantum measurement cannot be freely
• 2:12:01
  Speaker 2: chosen to transmit a message through entanglement alone. An observer
• 2:12:06
  Speaker 2: measuring one part of an entangled system sees results whose
• 2:12:10
  Speaker 2: local statistics do not reveal which measurement was chosen at
• 2:12:13
  Speaker 2: the distant location. To identify the correlations, the observers must
• 2:12:18
  Speaker 2: compare their records using ordinary communication, and that communication remains
• 2:12:24
  Speaker 2: subject to the speed of light limit. This principle is
• 2:12:27
  Speaker 2: known as the no-signalling theorem. Quantum entanglement therefore produces extraordinary
• 2:12:33
  Speaker 2: correlations without providing a controllable faster-than-light messaging system. Gravity also
• 2:12:40
  Speaker 2: respects the causal structure of spacetime. In Newtonian gravity, gravitational
• 2:12:45
  Speaker 2: interactions were traditionally described through a mathematical framework that effectively
• 2:12:50
  Speaker 2: treated their influence as instantaneous. General relativity provides a different understanding.
• 2:12:57
  Speaker 2: Changes in the gravitational field propagate at a finite speed.
• 2:13:02
  Speaker 2: Gravitational waves, which are disturbances in spacetime curvature, travel through
• 2:13:08
  Speaker 2: a vacuum at the speed of light in Einstein's theory.
• 2:13:12
  Speaker 2: These waves can be produced by enormous accelerating masses, including
• 2:13:16
  Speaker 2: pairs of neutron stars and black holes orbiting one another.
• 2:13:21
  Speaker 2: In 2017, observatories including the Laser Interferometer, Gravitational Wave Observatory
• 2:13:27
  Speaker 2: and Virgo detected gravitational waves from a merger of two
• 2:13:30
  Speaker 2: neutron stars. A gamma-ray burst was detected approximately 1.7 seconds
• 2:13:36
  Speaker 2: after the gravitational wave signal reached Earth. The waves and
• 2:13:41
  Speaker 2: electromagnetic radiation had travelled for roughly 130 million years. Their
• 2:13:47
  Speaker 2: remarkably close arrival times provided strong evidence that gravitational waves
• 2:13:51
  Speaker 2: propagate at essentially the same speed as light, allowing for
• 2:13:56
  Speaker 2: differences in when the signals were emitted. Gravity doesn't need
• 2:14:00
  Speaker 2: to communicate every change instantaneously across the universe. Its changing
• 2:14:05
  Speaker 2: influence follows the causal relationships established by spacetime geometry. And
• 2:14:10
  Speaker 2: this brings us to a remarkable conclusion. The speed of
• 2:14:14
  Speaker 2: light isn't simply a restriction on how quickly objects can move.
• 2:14:19
  Speaker 2: It determines the boundaries of possible physical influence. It establishes
• 2:14:24
  Speaker 2: which events can exchange information, which events may be causally connected,
• 2:14:29
  Speaker 2: and why the order of cause and effect remains consistent
• 2:14:32
  Speaker 2: between observers. Different people may disagree about the timing of
• 2:14:36
  Speaker 2: distant events. They may measure different durations and identify different
• 2:14:40
  Speaker 2: sets of events as simultaneous. But the causal relationships permitted
• 2:14:45
  Speaker 2: by the light cones remain consistent. And that is perhaps
• 2:14:49
  Speaker 2: one of the most beautiful features of relativity. The universe
• 2:14:53
  Speaker 2: allows time to be measured differently by different observers. without
• 2:14:57
  Speaker 2: allowing its ordinary causal structure to become arbitrary. Past and
• 2:15:02
  Speaker 2: future are not merely labels attached to a universal clock.
• 2:15:06
  Speaker 2: Their physical relationships are shaped by the maximum speed at
• 2:15:09
  Speaker 2: which information can travel. And the speed of light, familiar
• 2:15:13
  Speaker 2: to us as the speed of sunshine and starlight, turns
• 2:15:16
  Speaker 2: out to be one of the fundamental reasons the universe
• 2:15:19
  Speaker 2: possesses an orderly relationship between causes and their effects. Why
• 2:15:23
  Speaker 2: should the speed of light have anything to do with
• 2:15:25
  Speaker 2: the passage of time? It's a wonderfully simple question, but
• 2:15:29
  Speaker 2: the answer reaches into some of the deepest principles of
• 2:15:32
  Speaker 2: modern physics. We tend to think of light as something
• 2:15:36
  Speaker 2: that travels through the universe, illuminating objects and carrying information
• 2:15:40
  Speaker 2: from one place to another. And we think of time
• 2:15:43
  Speaker 2: as something entirely different. Clocks tick, days pass, and the
• 2:15:48
  Speaker 2: years gradually accumulate. At first, there seems to be no
• 2:15:53
  Speaker 2: obvious reason why the speed of one particular phenomenon should
• 2:15:56
  Speaker 2: determine how the other behaves. But the connection is much
• 2:16:00
  Speaker 2: more fundamental than it appears. The crucial discovery is not
• 2:16:04
  Speaker 2: that light somehow changes time as it travels. Light doesn't
• 2:16:07
  Speaker 2: interfere with clocks, slow down chemical reactions, or alter the
• 2:16:12
  Speaker 2: ageing process through some special influence. Instead, the speed of
• 2:16:16
  Speaker 2: light reveals something extraordinary about the underlying structure of the universe.
• 2:16:21
  Speaker 2: Space and time are connected, and the relationship between them
• 2:16:24
  Speaker 2: is governed by an invariant speed. This means that every
• 2:16:28
  Speaker 2: inertial observer, regardless of their relative motion, measures the same
• 2:16:33
  Speaker 2: speed for light travelling through a vacuum. And for this
• 2:16:36
  Speaker 2: to remain true, measurements of distance and duration cannot be
• 2:16:40
  Speaker 2: identical for everyone. That is the essential insight behind Albert
• 2:16:44
  Speaker 2: Einstein's special theory of relativity. It also explains why the
• 2:16:49
  Speaker 2: speed of light is not really a principle concerned exclusively
• 2:16:52
  Speaker 2: with light. Imagine a universe containing no visible light whatsoever.
• 2:16:58
  Speaker 2: Perhaps there are no glowing stars, no illuminated planets, and
• 2:17:02
  Speaker 2: no lamps or candles producing familiar beams of radiation. The
• 2:17:06
  Speaker 2: fundamental speed limit would still possess physical meaning. Gravitational waves
• 2:17:11
  Speaker 2: would still propagate at that speed in general relativity. and
• 2:17:15
  Speaker 2: massless particles would still follow the light-like paths permitted by
• 2:17:19
  Speaker 2: spacetime geometry. The invariant speed belongs to the structure of
• 2:17:24
  Speaker 2: relativistic physics itself. Light simply happens to provide one of
• 2:17:29
  Speaker 2: the clearest ways of discovering it. And once we recognise this,
• 2:17:34
  Speaker 2: several strange features of time begin to make sense. Consider
• 2:17:38
  Speaker 2: time dilation. Two observers moving relative to one another can
• 2:17:43
  Speaker 2: assign different durations to the same pair of events. A
• 2:17:47
  Speaker 2: clock travelling aboard a spacecraft can accumulate less time than
• 2:17:50
  Speaker 2: clocks at rest in another chosen reference frame. Yet the
• 2:17:55
  Speaker 2: moving clock is not malfunctioning. It measures the proper time
• 2:17:59
  Speaker 2: along its own journey through spacetime. The difference appears when
• 2:18:03
  Speaker 2: its measurements are compared with those made using another reference frame.
• 2:18:07
  Speaker 2: Length contraction follows from the same principles. A spacecraft moving
• 2:18:11
  Speaker 2: rapidly relative to Earth can have a shorter measured length
• 2:18:15
  Speaker 2: along its direction of motion than it possesses in its
• 2:18:18
  Speaker 2: own rest frame. And the relativity of simultaneity reveals that
• 2:18:22
  Speaker 2: two distant events occurring together in one reference frame need
• 2:18:25
  Speaker 2: not be simultaneous in another. These are not independent peculiarities.
• 2:18:30
  Speaker 2: They belong to one consistent mathematical description of spacetime. The
• 2:18:35
  Speaker 2: Lorentz transformations connect the measurements made by different inertial observers.
• 2:18:40
  Speaker 2: They explain how spatial and temporal coordinates change while preserving
• 2:18:44
  Speaker 2: the invariant speed of light. And although observers may disagree
• 2:18:49
  Speaker 2: about distances and durations, they agree upon an important geometric
• 2:18:53
  Speaker 2: quantity called the space-time interval. This is part of what
• 2:18:57
  Speaker 2: makes relativity so remarkable. Different measurements do not mean that
• 2:19:01
  Speaker 2: reality itself has become inconsistent. The relationships between those measurements
• 2:19:07
  Speaker 2: follow precise rules. and the rules have been tested with
• 2:19:10
  Speaker 2: extraordinary accuracy. Unstable particles travelling through Earth's atmosphere survive longer,
• 2:19:17
  Speaker 2: on average, in the Earth's reference frame because of relativistic
• 2:19:21
  Speaker 2: time dilation. Atomic clocks carried aboard aircraft accumulate slightly different
• 2:19:26
  Speaker 2: amounts of time from clocks remaining on the ground, and
• 2:19:29
  Speaker 2: satellite navigation systems must account for the combined effects of
• 2:19:34
  Speaker 2: motion and gravity to maintain accurate timing. These are measurable
• 2:19:39
  Speaker 2: consequences of space-time geometry. They demonstrate that time dilation applies
• 2:19:44
  Speaker 2: to genuine physical processes, not merely to our perception of
• 2:19:48
  Speaker 2: moving clocks. But this raises another interesting question. Why does
• 2:19:53
  Speaker 2: light travel at approximately 300,000 kilometres per second? Why not
• 2:19:59
  Speaker 2: twice that speed, or half of it? Part of the
• 2:20:02
  Speaker 2: answer concerns the way human beings measure distance and time.
• 2:20:06
  Speaker 2: The modern metre is defined using the speed of light,
• 2:20:10
  Speaker 2: giving that speed an exact value in metres per second.
• 2:20:14
  Speaker 2: Changing our units would change the numerical value without changing
• 2:20:17
  Speaker 2: the underlying physics. The deeper scientific question is why the
• 2:20:22
  Speaker 2: universe possesses a finite invariant speed at all. Special relativity
• 2:20:27
  Speaker 2: describes the consequences of that speed with remarkable precision, but
• 2:20:31
  Speaker 2: the theory does not independently explain why the fundamental structure
• 2:20:35
  Speaker 2: of our universe must have precisely these properties. We can
• 2:20:40
  Speaker 2: imagine mathematical descriptions of universes possessing different limiting speeds. Such
• 2:20:46
  Speaker 2: changes would alter the relationships between spatial distances and temporal intervals. However,
• 2:20:52
  Speaker 2: predicting the complete behaviour of a hypothetical universe requires more
• 2:20:56
  Speaker 2: than changing one number. Other physical laws and dimensionless relationships
• 2:21:01
  Speaker 2: would also need to be specified. So these possibilities remain
• 2:21:06
  Speaker 2: useful thought experiments rather than descriptions of realities we have observed.
• 2:21:11
  Speaker 2: What we do know is that the finite speed of
• 2:21:14
  Speaker 2: light shapes almost everything we can learn about the distant universe.
• 2:21:18
  Speaker 2: When astronomers observe a galaxy millions of light years away,
• 2:21:23
  Speaker 2: they receive light that began its journey millions of years earlier.
• 2:21:27
  Speaker 2: The image reveals the galaxy as it existed in the past.
• 2:21:31
  Speaker 2: The farther we look into space, the farther we generally
• 2:21:34
  Speaker 2: look back in cosmic history. This light travel delay is
• 2:21:38
  Speaker 2: different from relativistic time dilation, but both reflect the importance
• 2:21:42
  Speaker 2: of light's finite speed. The same speed that determines how
• 2:21:47
  Speaker 2: long a signal takes to reach us also defines the
• 2:21:50
  Speaker 2: causal boundaries of spacetime. It determines which events can influence
• 2:21:54
  Speaker 2: one another. It ensures that ordinary physical information cannot travel
• 2:21:58
  Speaker 2: outside the local light cones established by relativity. and it
• 2:22:02
  Speaker 2: helps preserve the distinction between causes and their effects. Even
• 2:22:07
  Speaker 2: gravity participates in this relationship. According to Einstein's general theory
• 2:22:12
  Speaker 2: of relativity, gravitational environments influence the geometry of spacetime and
• 2:22:17
  Speaker 2: the proper time accumulated by clocks. Clocks at different heights
• 2:22:21
  Speaker 2: above Earth can therefore run at measurably different rates. Yet
• 2:22:25
  Speaker 2: an observer measuring light locally in a vacuum still obtains
• 2:22:29
  Speaker 2: the same fundamental speed. the consistency of that local measurement
• 2:22:34
  Speaker 2: remains central to relativistic physics, and perhaps the most reassuring
• 2:22:38
  Speaker 2: part is that none of these extraordinary relationships makes our
• 2:22:42
  Speaker 2: own experience of time any less real. Your clock measures
• 2:22:46
  Speaker 2: the time accumulated along your particular journey through spacetime. Your heartbeat,
• 2:22:51
  Speaker 2: your thoughts, and the ordinary processes taking place around you
• 2:22:56
  Speaker 2: continue according to that same local passage of time. There
• 2:23:00
  Speaker 2: is no sensation of time slowing simply because another observer
• 2:23:03
  Speaker 2: moves differently, and there's no need for one universal clock
• 2:23:07
  Speaker 2: against which every experience must be judged. Instead, the universe
• 2:23:12
  Speaker 2: provides a consistent geometric structure within which different observers can
• 2:23:17
  Speaker 2: measure different amounts of elapsed time. All those measurements can
• 2:23:20
  Speaker 2: be related through the laws of relativity. The speed of light, therefore,
• 2:23:25
  Speaker 2: doesn't change how time works through some active influence upon
• 2:23:28
  Speaker 2: the world. Its invariance reveals how time has always worked.
• 2:23:33
  Speaker 2: Time is not an independent rhythm flowing identically throughout the universe.
• 2:23:39
  Speaker 2: It is part of space-time, inseparably connected to distance, motion,
• 2:23:44
  Speaker 2: gravity and causality. And what began as a question about
• 2:23:49
  Speaker 2: the speed of a beam of light becomes something considerably
• 2:23:52
  Speaker 2: more profound. The discovery that time itself is not absolute,
• 2:23:57
  Speaker 2: A clock can measure its own passing seconds perfectly accurately,
• 2:24:01
  Speaker 2: while another clock following a different path accumulates a different
• 2:24:04
  Speaker 2: amount of time. Both belong to the same universe, both
• 2:24:08
  Speaker 2: obey the same laws, and neither needs to be wrong.
• 2:24:13
  Speaker 2: The remarkable thing is not that time occasionally behaves strangely.
• 2:24:16
  Speaker 2: It's that the ordinary passage of time has always been
• 2:24:20
  Speaker 2: part of a much richer and more beautiful structure than
• 2:24:23
  Speaker 2: we could ever have guessed simply by watching the hands
• 2:24:26
  Speaker 2: of a clock. There is something rather wonderful about discovering
• 2:24:30
  Speaker 2: that one of the most familiar things in life is
• 2:24:32
  Speaker 2: not quite what we imagined. Time seems so dependable. Seconds
• 2:24:38
  Speaker 2: become minutes, minutes become hours, and the years pass without
• 2:24:42
  Speaker 2: us ever needing to think about the extraordinary physics taking
• 2:24:46
  Speaker 2: place beneath it all. And yet, the simple fact that
• 2:24:50
  Speaker 2: light travels at one particular speed has revealed something remarkable
• 2:24:54
  Speaker 2: about the nature of time itself. The speed of light
• 2:24:59
  Speaker 2: doesn't physically interfere with clocks or somehow change the way
• 2:25:03
  Speaker 2: our bodies experience the passing seconds. Instead, its invariance reveals
• 2:25:08
  Speaker 2: that space and time are connected in ways that everyday
• 2:25:12
  Speaker 2: experience rarely allows us to notice. Different observers can measure
• 2:25:16
  Speaker 2: different distances and durations while agreeing upon the same fundamental
• 2:25:21
  Speaker 2: speed of light. And this means there is no single
• 2:25:24
  Speaker 2: universal clock governing the entire universe. It took centuries for
• 2:25:29
  Speaker 2: scientists to arrive at this understanding. Galileo Galilei attempted to
• 2:25:33
  Speaker 2: investigate whether light travelled instantaneously using an experiment involving distant lanterns.
• 2:25:40
  Speaker 2: Olaruma later discovered evidence that light required time to travel
• 2:25:44
  Speaker 2: between Jupiter and Earth, and through increasingly sophisticated experiments, researchers
• 2:25:49
  Speaker 2: such as Ippolit Fizeau and Albert Abraham Michelson improved measurements
• 2:25:54
  Speaker 2: of its extraordinary speed. James Clerk Maxwell's equations then revealed
• 2:25:59
  Speaker 2: that light was an electromagnetic wave connecting its speed to
• 2:26:03
  Speaker 2: the fundamental properties of electricity and magnetism. But it was
• 2:26:07
  Speaker 2: Albert Einstein's special theory of relativity that transformed what this
• 2:26:11
  Speaker 2: discovery meant. Light's speed through a vacuum wasn't simply enormous,
• 2:26:16
  Speaker 2: it was invariant. And if every inertial observer must measure
• 2:26:20
  Speaker 2: the same speed, then measurements of distance and time cannot
• 2:26:24
  Speaker 2: remain identical for everyone. The light-clock thought experiment illustrates this beautifully.
• 2:26:30
  Speaker 2: A pulse of light bouncing between two mirrors travels directly
• 2:26:34
  Speaker 2: upwards and downwards for someone accompanying the clock, but an
• 2:26:38
  Speaker 2: observer who sees the clock moving measures a longer diagonal path.
• 2:26:42
  Speaker 2: Because both must agree on light speed, they assign different
• 2:26:45
  Speaker 2: durations to its journey. This is the essential geometry behind
• 2:26:50
  Speaker 2: time dilation. A moving clock can accumulate less time than
• 2:26:54
  Speaker 2: clock stationary in another chosen reference frame, even though the
• 2:26:57
  Speaker 2: person accompanying it experiences nothing unusual. Their thoughts continue normally,
• 2:27:03
  Speaker 2: their heartbeat remains familiar, and every second feels exactly as
• 2:27:08
  Speaker 2: it always has. The relativity of simultaneity reveals something equally surprising.
• 2:27:14
  Speaker 2: Two distant events that occur together in one reference frame
• 2:27:18
  Speaker 2: need not be simultaneous in another. There is no universal
• 2:27:22
  Speaker 2: present moment shared by every observer, independently of their motion,
• 2:27:27
  Speaker 2: and because measurements of space and time are connected, objects
• 2:27:31
  Speaker 2: moving at relativistic speeds can also exhibit length, along their
• 2:27:37
  Speaker 2: direction of motion. The Lorentz transformations describe these relationships mathematically.
• 2:27:43
  Speaker 2: Hermann Minkowski's geometric understanding of spacetime brought them together into
• 2:27:48
  Speaker 2: one consistent picture. Within that geometry, every physical clock follows
• 2:27:53
  Speaker 2: a worldline and measures the proper time accumulated along its journey.
• 2:27:57
  Speaker 2: and different journeys between the same events can produce different
• 2:28:01
  Speaker 2: amounts of elapsed time. This is why the famous twin
• 2:28:04
  Speaker 2: paradox has such an extraordinary answer. Two people can begin together,
• 2:28:10
  Speaker 2: follow different paths through spacetime, and eventually reunite having genuinely
• 2:28:15
  Speaker 2: aged by different amounts. Neither person has experienced a malfunction
• 2:28:20
  Speaker 2: in time. Their clocks have simply measured different journeys, and
• 2:28:24
  Speaker 2: these ideas have been confirmed through real experiments. Muons created
• 2:28:29
  Speaker 2: high in Earth's atmosphere survive long enough to reach the
• 2:28:32
  Speaker 2: ground in numbers explained by relativistic time dilation. Particle accelerators
• 2:28:38
  Speaker 2: reveal the same effect under carefully controlled conditions, and atomic
• 2:28:43
  Speaker 2: clocks carried aboard aircraft have demonstrated measurable differences in elapsed time.
• 2:28:49
  Speaker 2: Even gravity participates in this remarkable relationship. Einstein's general theory
• 2:28:54
  Speaker 2: of relativity describes how gravitational environments influence spacetime geometry and
• 2:29:00
  Speaker 2: the passage of time. Clocks at different heights above Earth
• 2:29:04
  Speaker 2: can accumulate slightly different durations. Satellite navigation systems must account
• 2:29:09
  Speaker 2: for both gravitational time dilation and the effects of orbital
• 2:29:13
  Speaker 2: motion to calculate positions accurately. What sounds like an extraordinary
• 2:29:19
  Speaker 2: feature of distant spacecraft is therefore part of the technology
• 2:29:23
  Speaker 2: we use in ordinary life. Light itself occupies a particularly
• 2:29:27
  Speaker 2: interesting place within this picture. Photons travel along light-like paths
• 2:29:32
  Speaker 2: through space-time, for which the proper time interval is zero.
• 2:29:37
  Speaker 2: But this doesn't mean that photons possess a viewpoint from
• 2:29:40
  Speaker 2: which the universe appears frozen. A photon has no valid
• 2:29:44
  Speaker 2: inertial rest frame. Its mathematical relationship with proper time is
• 2:29:48
  Speaker 2: not the same as an observer experiencing the passing seconds.
• 2:29:52
  Speaker 2: And the speed of light also determines something even more
• 2:29:55
  Speaker 2: fundamental– causality. The finite speed at which information can travel
• 2:30:02
  Speaker 2: establishes which events can influence one another. Light cones define
• 2:30:07
  Speaker 2: the boundaries of possible causal relationships, preserving the ordering of
• 2:30:12
  Speaker 2: causes and effects even when observers disagree about the timing
• 2:30:16
  Speaker 2: of distant events. All of this comes from a speed
• 2:30:20
  Speaker 2: whose numerical value depends upon the units we've chosen to
• 2:30:23
  Speaker 2: measure distance and time. The modern value of approximately 300,000
• 2:30:28
  Speaker 2: kilometres per second is familiar, but the deeper physical principle
• 2:30:33
  Speaker 2: is the existence of a finite invariant speed built into spacetime,
• 2:30:37
  Speaker 2: and that brings us to the heart of the matter.
• 2:30:40
  Speaker 2: Time is not an illusion, nor is it a universal
• 2:30:44
  Speaker 2: rhythm flowing independently of everything else. It is a measurable
• 2:30:48
  Speaker 2: part of the physical universe, connected to distance, motion, gravity
• 2:30:53
  Speaker 2: and the geometry of spacetime. Different observers can experience different
• 2:30:58
  Speaker 2: amounts of elapsed time while remaining entirely consistent with the
• 2:31:03
  Speaker 2: same laws of physics. And perhaps that's what makes the
• 2:31:07
  Speaker 2: discovery so beautiful. Here, in the ordinary world, the seconds
• 2:31:11
  Speaker 2: continue passing just as they always have. Clocks tick, days
• 2:31:16
  Speaker 2: turn into nights, and life carries on at its familiar pace.
• 2:31:20
  Speaker 2: But beneath that reassuring simplicity lies a universe in which
• 2:31:24
  Speaker 2: time is far richer than we once imagined. A universe
• 2:31:28
  Speaker 2: where two perfectly accurate clocks can disagree, where the present
• 2:31:32
  Speaker 2: is not quite universal, and where the speed of light
• 2:31:35
  Speaker 2: connects the measurement of space with the passage of time.
• 2:31:39
  Speaker 2: And through it all, every one of us continues along
• 2:31:42
  Speaker 2: our own path through space-time. experiencing each passing moment as
• 2:31:46
  Speaker 2: perfectly ordinary, even though the reality behind those moments is
• 2:31:51
  Speaker 2: anything but.