Latest / Night Science Stories / Special Relativity_ What the Speed of Light Really Means

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Special Relativity_ What the Speed of Light Really Means · Night Science Stories

• 0:00
  Speaker 1: Good evening, and welcome to the Sleepy Scientist. I hope
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  Speaker 1: And if you've been here for a while already, thank
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  Speaker 1: you for continuing to spend part of your evenings with me. Tonight,
• 1:01
  Speaker 1: we're going to take something that sounds wonderfully simple and
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  Speaker 1: discover that it quietly rearranges almost everything we thought we
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  Speaker 1: knew about space and time. The speed of light is
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  Speaker 1: usually introduced as a very large number, roughly 300,000 kilometres
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  Speaker 1: every second, fast enough to travel around Earth several times
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  Speaker 1: before you could comfortably finish saying the sentence. But that
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  Speaker 1: number is not really the strange part. The strange part
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  Speaker 1: is that everyone measures it to be the same. You
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  Speaker 1: can chase a beam of light, move towards it, move
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  Speaker 1: away from it, or watch it from somewhere completely different
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  Speaker 1: and somehow nature refuses to let the answer change. To
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  Speaker 1: make that possible, something else has to give. Time. Distance.
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  Speaker 1: Even the idea that two things happened at the same moment.
• 1:52
  Speaker 1: which is mildly inconvenient for anyone hoping the universe would
• 1:55
  Speaker 1: keep things straightforward this evening. So get comfortable, let your
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  Speaker 1: thoughts slow down, and we'll begin with a deceptively simple question.
• 2:05
  Speaker 1: What does the speed of light really mean? The speed
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  Speaker 1: of light is one of those numbers that sounds enormous
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  Speaker 1: even before we understand why it matters. In empty space,
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  Speaker 1: light travels at approximately 300,000 kilometres every second. That is
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  Speaker 1: roughly one billion kilometres an hour. In the time it
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  Speaker 1: takes to blink, light can travel tens of thousands of kilometres.
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  Speaker 1: Given a single second, it could circle the Earth more
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  Speaker 1: than seven times. It is difficult to build any useful
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  Speaker 1: intuition for a speed like that. Human experience simply does
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  Speaker 1: not operate on those scales. Even the fastest aircraft, spacecraft
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  Speaker 1: and projectiles we have ever built move at a tiny
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  Speaker 1: fraction of the speed of light. But the remarkable thing
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  Speaker 1: about this number is not really how large it is.
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  Speaker 1: The remarkable thing is what it means. At first glance,
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  Speaker 1: we might imagine that the speed of light is simply
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  Speaker 1: a property of light, rather like the top speed of
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  Speaker 1: a particular vehicle. Perhaps photons simply happen to move extremely quickly,
• 3:09
  Speaker 1: and 300,000 kilometres per second is the speed nature assigned
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  Speaker 1: to them. Special relativity reveals something far deeper. the speed
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  Speaker 1: of light in vacuum is connected to the structure of
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  Speaker 1: space and time themselves. It is woven into the rules
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  Speaker 1: governing motion, distance, duration, energy, and even which events in
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  Speaker 1: the universe are capable of influencing one another. And the
• 3:33
  Speaker 1: first clue that something unusual was happening comes from a
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  Speaker 1: very ordinary idea. Speeds normally add, imagine standing beside a
• 3:41
  Speaker 1: road while a car passes you at 50km per hour,
• 3:45
  Speaker 1: Someone inside the car throws a ball forward at 10km
• 3:48
  Speaker 1: per hour relative to the car. From your position beside
• 3:52
  Speaker 1: the road, the ball will be moving at roughly 60km
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  Speaker 1: per hour. Nothing about this seems strange. The motion of
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  Speaker 1: the car and the motion of the ball simply combine.
• 4:02
  Speaker 1: If the passenger throws the ball backwards instead, the result
• 4:04
  Speaker 1: changes accordingly. Everyday motion behaves in a way that feels
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  Speaker 1: almost embarrassingly sensible. So we might expect light to behave
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  Speaker 1: in exactly the same way. If a lamp were carried
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  Speaker 1: aboard an extremely fast spacecraft and switched on, perhaps the
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  Speaker 1: light moving forward should travel at the ordinary speed of
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  Speaker 1: light plus the speed of the spacecraft. And if another
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  Speaker 1: observer raced after the beam, perhaps that observer should measure
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  Speaker 1: the light travelling somewhat more slowly. That would fit beautifully
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  Speaker 1: with ordinary intuition. Nature, unfortunately for ordinary intuition, has other arrangements.
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  Speaker 1: Observers moving at different constant velocities still measure the same
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  Speaker 1: speed for light travelling through vacuum. They may disagree about distances.
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  Speaker 1: They may disagree about how much time has passed. They
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  Speaker 1: may even disagree about whether two distant events happened at
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  Speaker 1: the same moment. But when each observer carefully measures the
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  Speaker 1: speed of the same beam of light, they obtain the
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  Speaker 1: same fundamental value. Understanding why physicists eventually took this seriously
• 5:08
  Speaker 1: requires going back to the 19th century and to the
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  Speaker 1: work of the Scottish physicist James Clerk Maxwell. Maxwell brought
• 5:16
  Speaker 1: together discoveries about electricity and magnetism that had previously seemed
• 5:20
  Speaker 1: related but distinct. His theory showed that electric fields and
• 5:25
  Speaker 1: magnetic fields could interact with one another in a remarkable way.
• 5:30
  Speaker 1: A changing electric field could produce a magnetic field. A
• 5:34
  Speaker 1: changing magnetic field could produce an electric field. Together, these
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  Speaker 1: changing fields could move through space as a self-sustaining electromagnetic wave.
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  Speaker 1: And Maxwell's theory predicted that these waves should propagate at
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  Speaker 1: a definite speed. When that predicted speed was calculated using
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  Speaker 1: quantities already known from experiments involving electricity and magnetism, the
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  Speaker 1: result was strikingly close to the measured speed of light.
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  Speaker 1: This was not treated as a curious coincidence. It suggested
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  Speaker 1: something profound. Light itself appeared to be an electromagnetic wave.
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  Speaker 1: Visible light was therefore not some entirely separate phenomenon. It
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  Speaker 1: belonged to the same physical framework as electricity and magnetism.
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  Speaker 1: That achievement was one of the great unifications in physics.
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  Speaker 1: But it also created an awkward question. Waves, as physicists
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  Speaker 1: understood them at the time, usually travelled through something. Sound
• 6:33
  Speaker 1: travels through air, water or some other material. Ocean waves
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  Speaker 1: involve the movement of water. Vibrations along a string require
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  Speaker 1: the string itself. So if light was a wave, what
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  Speaker 1: exactly was waving? And perhaps even more importantly, relative to
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  Speaker 1: what was its speed being measured? If someone tells you
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  Speaker 1: that a train is travelling at 100km per hour, the
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  Speaker 1: natural response is that it is travelling at 100km per
• 7:01
  Speaker 1: hour relative to the ground. Motion usually needs a reference.
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  Speaker 1: Physicists therefore suspected that light might also travel through some
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  Speaker 1: hidden medium filling space. If such a medium existed, then
• 7:13
  Speaker 1: perhaps the speed appearing in Maxwell's theory was really the
• 7:17
  Speaker 1: speed of electromagnetic waves relative to that medium. For a time,
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  Speaker 1: this seemed perfectly reasonable. The difficulty was that nature did
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  Speaker 1: not cooperate. The deeper scientists looked, the harder it became
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  Speaker 1: to preserve the comfortable classical picture of absolute space and
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  Speaker 1: universal time. The speed of a light sat directly at
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  Speaker 1: the centre of the problem. Eventually, Albert Einstein would take
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  Speaker 1: the strange behaviour of light seriously enough to reverse the
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  Speaker 1: usual question. Instead of asking how the speed of light
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  Speaker 1: could be made to fit into the familiar rules of
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  Speaker 1: space and time, he asked what the rules of space
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  Speaker 1: and time would have to become if the speed of
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  Speaker 1: light really was the same for every inertial observer. That
• 8:00
  Speaker 1: change in viewpoint would transform physics. Special relativity is sometimes
• 8:06
  Speaker 1: summarised rather casually as the theory saying that nothing can
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  Speaker 1: travel faster than light. That is true only in a
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  Speaker 1: limited sense, and it misses most of what makes the
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  Speaker 1: theory extraordinary. Special relativity changes how different observers compare distances.
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  Speaker 1: It changes how they compare durations. It changes what they
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  Speaker 1: mean by simultaneous events. It changes how velocities combine, how
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  Speaker 1: energy and momentum behave, and how cause and effect are
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  Speaker 1: organised across spacetime. The speed of light is not merely
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  Speaker 1: the fastest thing in a race. It is part of
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  Speaker 1: the rulebook describing what a race, a clock, a distance
• 8:44
  Speaker 1: and even a moment actually are. And that is why
• 8:47
  Speaker 1: this one very large number turned out to be far
• 8:50
  Speaker 1: stranger than anyone first expected. For a long time, physics
• 8:55
  Speaker 1: rested on a picture of space and time that felt
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  Speaker 1: completely natural. It was the picture inherited from Isaac Newton.
• 9:03
  Speaker 1: In Newtonian physics, space was treated as an enormous fixed
• 9:07
  Speaker 1: stage on which everything in the universe moved. Time flowed
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  Speaker 1: steadily in the background, the same for everyone, everywhere, whether
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  Speaker 1: they were standing still, travelling in a carriage, crossing an ocean,
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  Speaker 1: or orbiting a distant star. Two observers might disagree about
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  Speaker 1: where an object was or how quickly it was moving,
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  Speaker 1: but they were assumed to agree about the distance between
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  Speaker 1: events and about how much time had passed. There was,
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  Speaker 1: in this view, one underlying space and one universal time.
• 9:38
  Speaker 1: And for ordinary motion, it worked extraordinarily well. This idea
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  Speaker 1: fitted neatly with what became known as Galilean relativity, named
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  Speaker 1: after Galileo Galilei. The central principle was simple. If you
• 9:53
  Speaker 1: are moving smoothly at a constant velocity, the basic laws
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  Speaker 1: of mechanics behave exactly as they would if you were
• 10:00
  Speaker 1: standing still Imagine sitting inside a train travelling along a
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  Speaker 1: perfectly straight track at a constant speed If the windows
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  Speaker 1: were covered and the ride were perfectly smooth you could
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  Speaker 1: toss a ball into the air and catch it again
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  Speaker 1: You could pour water into a glass You could walk
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  Speaker 1: from one end of the carriage to the other Nothing
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  Speaker 1: inside the train would reveal, through an ordinary mechanical experiment,
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  Speaker 1: whether the train was stationary or moving steadily. This is
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  Speaker 1: a powerful idea. There is no obvious mechanical experiment that
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  Speaker 1: allows you to distinguish uniform motion from rest without comparing
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  Speaker 1: yourself with something outside. But classical physics also gave a
• 10:41
  Speaker 1: straightforward rule for comparing speeds between different observers. Suppose the
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  Speaker 1: train is moving at 100km per hour relative to the ground.
• 10:51
  Speaker 1: A passenger inside throws a ball forward at 20km per
• 10:54
  Speaker 1: hour relative to the train. Someone standing beside the track
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  Speaker 1: would measure the ball travelling at roughly 120km per hour.
• 11:03
  Speaker 1: If the ball were thrown backwards instead, the person beside
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  Speaker 1: the track would measure roughly 80km per hour. The velocities
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  Speaker 1: simply add or subtract. This is so intuitive that it
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  Speaker 1: hardly feels like a physical theory at all. It feels
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  Speaker 1: like arithmetic. And for balls, trains, ships, arrows, falling objects,
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  Speaker 1: and almost everything else in ordinary life, that intuition works beautifully.
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  Speaker 1: So when physicists in the 19th century began thinking seriously
• 11:34
  Speaker 1: about light as a wave, it seemed natural to assume
• 11:37
  Speaker 1: that light should obey a similar rule. If light travelled
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  Speaker 1: as a wave, then perhaps it should move at a
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  Speaker 1: particular speed relative to something. That expectation came largely from
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  Speaker 1: experience with every other type of wave scientists knew. Sound
• 11:51
  Speaker 1: waves require matter through which to travel. In air, the
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  Speaker 1: molecules jostle one another and pass the disturbance onward. Water
• 12:01
  Speaker 1: waves involve motion through water. A wave travelling along a
• 12:06
  Speaker 1: rope requires the rope. So when James Clerk Maxwell's electromagnetic
• 12:11
  Speaker 1: theory indicated that light was an electromagnetic wave, physicists faced
• 12:17
  Speaker 1: a seemingly obvious question. What was the medium? The proposed
• 12:22
  Speaker 1: answer became known as the luminiferous ether. The ether was
• 12:26
  Speaker 1: imagined as an invisible substance filling all of space, including
• 12:30
  Speaker 1: the apparent emptiness between planets and stars. electromagnetic waves could
• 12:35
  Speaker 1: travel through this medium in much the same way that
• 12:38
  Speaker 1: sound travelled through air. The idea was speculative, but at
• 12:43
  Speaker 1: the time it was far from foolish. If light had
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  Speaker 1: a definite speed relative to the aether, then Earth's motion
• 12:50
  Speaker 1: through this invisible medium should create something rather like a wind.
• 12:56
  Speaker 1: Earth moves around the Sun at roughly 30 kilometres per second.
• 13:01
  Speaker 1: If the aether remained fixed while Earth travelled through it,
• 13:05
  Speaker 1: then an experiment on Earth should sometimes be moving with
• 13:08
  Speaker 1: this aether wind and sometimes across it. That should affect
• 13:12
  Speaker 1: the measured travel time of light. The challenge was detecting
• 13:16
  Speaker 1: an effect that was expected to be extremely small. In 1887,
• 13:21
  Speaker 1: Albert Abraham Shulson and Edward Williams Morley performed the experiment
• 13:25
  Speaker 1: that would become one of the most famous measurements in
• 13:28
  Speaker 1: the history of physics. They used an instrument called an interferometer.
• 13:33
  Speaker 1: The device divided a beam of light into two paths
• 13:35
  Speaker 1: arranged at right angles to one another. The beams travelled
• 13:39
  Speaker 1: along their separate routes, reflected back, and were then recombined.
• 13:45
  Speaker 1: If Earth were moving through a stationary aether, the light
• 13:48
  Speaker 1: travelling along the direction of Earth's motion should take a
• 13:50
  Speaker 1: slightly different amount of time from the light travelling across
• 13:53
  Speaker 1: that motion. When the beams recombined, That difference should reveal
• 13:58
  Speaker 1: itself through a shift in the interference pattern. The expected
• 14:01
  Speaker 1: effect did not appear. The result became famous as a
• 14:05
  Speaker 1: null result. But it is important not to turn this
• 14:09
  Speaker 1: into a story in which one experiment immediately killed the
• 14:12
  Speaker 1: aether and everyone quietly went home. Science was much messier
• 14:17
  Speaker 1: than that. Physicists explored several possible explanations. Perhaps Earth dragged
• 14:24
  Speaker 1: the aether with it, Perhaps the apparatus itself changed in
• 14:28
  Speaker 1: some subtle way as it moved. Perhaps the underlying assumptions
• 14:31
  Speaker 1: about motion needed modification. Among the physicists who worked on
• 14:36
  Speaker 1: this problem were Hendrik Antoon Lawrence and George Francis Fitzgerald.
• 14:41
  Speaker 1: They independently considered the possibility that objects moving through the
• 14:44
  Speaker 1: aether might contract slightly in the direction of motion. If
• 14:48
  Speaker 1: the measuring apparatus itself became shorter by precisely the right amount,
• 14:52
  Speaker 1: the expected difference in light travel times might disappear. This
• 14:56
  Speaker 1: became associated with what is now called Lawrence-Fitzgerald contraction. Lawrence
• 15:02
  Speaker 1: developed these ideas much further, constructing mathematical transformations that altered
• 15:07
  Speaker 1: measurements of both space and time between moving systems. The
• 15:11
  Speaker 1: mathematics worked remarkably well. But its meaning was still tied
• 15:16
  Speaker 1: to attempts to preserve the older aether picture. By the
• 15:20
  Speaker 1: end of the 19th century, physics had therefore developed an
• 15:23
  Speaker 1: uncomfortable split Newtonian mechanics worked brilliantly for ordinary objects. Maxwellian
• 15:30
  Speaker 1: electromagnetism worked brilliantly for electric fields, magnetic fields, and light.
• 15:37
  Speaker 1: Yet the two frameworks seem to disagree about how motion
• 15:40
  Speaker 1: should work. Newtonian mechanics said velocity should add in the
• 15:44
  Speaker 1: familiar way. Electromagnetic theory appeared to contain a special speed
• 15:49
  Speaker 1: that did not fit comfortably into that rule. Something had
• 15:53
  Speaker 1: to give. Either Maxwell's theory was incomplete, or experiments had
• 15:58
  Speaker 1: somehow failed to reveal the aether, or the deeply familiar
• 16:01
  Speaker 1: assumptions about space, time and motion were not as universal
• 16:05
  Speaker 1: as everyone had imagined. The strange behaviour of light had
• 16:09
  Speaker 1: exposed a crack running through classical physics, and the eventual
• 16:14
  Speaker 1: solution would not come from discovering a better invisible medium.
• 16:18
  Speaker 1: It would come from changing what physicists meant by space
• 16:21
  Speaker 1: and time themselves. In 1905, Albert Einstein published a paper
• 16:26
  Speaker 1: with a rather restrained title. It was called On the
• 16:29
  Speaker 1: Electrodynamics of Moving Bodies. There was nothing especially dramatic about
• 16:33
  Speaker 1: the name. It did not announce that space and time
• 16:36
  Speaker 1: were about to be reconsidered. It did not promise to
• 16:39
  Speaker 1: overturn centuries of intuition. It simply addressed a problem involving motion, electricity,
• 16:45
  Speaker 1: magnetism and light. But the ideas inside it would become
• 16:50
  Speaker 1: the special theory of relativity. Einstein approached the problem in
• 16:55
  Speaker 1: a remarkably economical way. Rather than trying to preserve the
• 16:59
  Speaker 1: old picture by adding increasingly complicated machinery, he began with
• 17:03
  Speaker 1: two basic physical principles and asked what the universe would
• 17:06
  Speaker 1: have to be like if both were true. The first
• 17:10
  Speaker 1: principle was an extension of the relativity already familiar from
• 17:13
  Speaker 1: Galileo Galilei. The laws of physics must take the same
• 17:17
  Speaker 1: form in every inertial reference frame. An inertial reference frame
• 17:22
  Speaker 1: is simply a viewpoint moving at constant velocity, without acceleration.
• 17:27
  Speaker 1: A laboratory drifting smoothly through empty space at a constant
• 17:31
  Speaker 1: speed can be treated as an inertial frame, so can
• 17:35
  Speaker 1: another laboratory moving steadily past it. By contrast, a laboratory
• 17:40
  Speaker 1: that is speeding up, slowing down, turning or rotating is
• 17:44
  Speaker 1: not an inertial frame throughout that motion. Acceleration matters. So
• 17:50
  Speaker 1: does gravity, once it becomes important, although a full treatment
• 17:54
  Speaker 1: of gravity belongs to Einstein's later general theory of relativity.
• 17:58
  Speaker 1: For special relativity, the simplest setting is therefore one in
• 18:01
  Speaker 1: which observers move steadily relative to one another. The first
• 18:05
  Speaker 1: postulate says that there is no experiment you can perform
• 18:09
  Speaker 1: entirely inside such a laboratory that will reveal some hidden
• 18:13
  Speaker 1: absolute state of rest. Imagine a perfectly smooth spacecraft travelling
• 18:18
  Speaker 1: through deep space. You close every window. The engines are
• 18:23
  Speaker 1: switched off so the spacecraft simply coasts at constant velocity. Inside,
• 18:28
  Speaker 1: you bounce a ball, boil water, perform electrical experiments, watch
• 18:33
  Speaker 1: a pendulum, or measure the behaviour of atoms. Nothing about
• 18:37
  Speaker 1: those experiments tells you whether the spacecraft is moving at
• 18:40
  Speaker 1: 10km per second, 10,000km per second, or not moving at
• 18:46
  Speaker 1: all relative to some supposedly universal background. Uniform motion has
• 18:52
  Speaker 1: no privileged status. There is no special inertial observer who
• 18:56
  Speaker 1: can honestly announce that everyone else is moving, while they
• 19:00
  Speaker 1: alone are truly standing still. Each inertial observer is equally
• 19:04
  Speaker 1: entitled to treat themselves as being at rest. That principle
• 19:08
  Speaker 1: on its own was not completely revolutionary. The second one
• 19:12
  Speaker 1: was where things became strange. Einstein proposed that the speed
• 19:16
  Speaker 1: of light in vacuum is the same for every inertial observer,
• 19:19
  Speaker 1: regardless of the motion of the source emitting the light
• 19:22
  Speaker 1: and regardless of the motion of the observer measuring it.
• 19:26
  Speaker 1: This was deeply at odds with ordinary experience. Return to
• 19:30
  Speaker 1: the moving train. Suppose the train travels at 100 km
• 19:34
  Speaker 1: per hour. A passenger throws a ball forward at 20
• 19:38
  Speaker 1: km per hour relative to the carriage. The passenger measures
• 19:41
  Speaker 1: the ball moving at 20 km per hour. Someone standing
• 19:45
  Speaker 1: beside the track measures it moving at roughly 120km per hour.
• 19:50
  Speaker 1: No mystery there. Now replace the ball with a beam
• 19:53
  Speaker 1: of light. The train switches on a lamp pointing forward.
• 19:58
  Speaker 1: The passenger measures the light travelling at approximately 300,000km per second.
• 20:04
  Speaker 1: Classical intuition says that someone beside the track should measure
• 20:08
  Speaker 1: the light travelling slightly faster, because the speed of the
• 20:11
  Speaker 1: train ought to be added to the speed of the beam.
• 20:14
  Speaker 1: But that is not what special relativity predicts. The observer
• 20:18
  Speaker 1: beside the track also measures the light at approximately 300,000
• 20:22
  Speaker 1: km per second. Now imagine an observer moving towards the beam.
• 20:27
  Speaker 1: Ordinary reasoning suggests that the light should rush towards that
• 20:30
  Speaker 1: observer even faster. It does not. That observer also measures
• 20:35
  Speaker 1: the same speed of light in vacuum. Move away from
• 20:38
  Speaker 1: the beam and the result remains the same. Move towards
• 20:42
  Speaker 1: it and the result remains the same. Change the speed
• 20:45
  Speaker 1: of the source and the result remains the same. This
• 20:49
  Speaker 1: sounds impossible only because we are quietly assuming that space
• 20:52
  Speaker 1: and time behave in the old Newtonian way. If distance
• 20:56
  Speaker 1: is universal and time is universal, then velocity should add
• 21:00
  Speaker 1: in the familiar way. Einstein's insight was not to treat
• 21:04
  Speaker 1: light as a peculiar exception, while leaving everything else untouched. Instead,
• 21:10
  Speaker 1: he changed the structure underneath the problem. If every inertial
• 21:14
  Speaker 1: observer must obtain the same value for the speed of light,
• 21:18
  Speaker 1: then observers moving relative to one another cannot always agree
• 21:22
  Speaker 1: about distance and time. Those quantities themselves must depend on
• 21:26
  Speaker 1: the observer's state of motion. That is the crucial shift.
• 21:31
  Speaker 1: The speed of light remains invariant. Measurements of space and
• 21:35
  Speaker 1: time do not. This does not mean that space and
• 21:39
  Speaker 1: time become arbitrary, or that everyone is free to measure
• 21:43
  Speaker 1: whatever they like. The relationships are precise. Different observers obtain
• 21:49
  Speaker 1: different measurements according to exact mathematical rules, and those rules
• 21:54
  Speaker 1: preserve the same physical laws for everyone. Once this is accepted,
• 21:58
  Speaker 1: several famous consequences of special relativity follow naturally. Moving clocks
• 22:04
  Speaker 1: run differently when compared between frames. Lengths measured along the
• 22:09
  Speaker 1: direction of motion change. Events that are simultaneous for one
• 22:13
  Speaker 1: observer need not be simultaneous for another. Velocities no longer
• 22:18
  Speaker 1: combine through simple addition, when the speeds involved become a
• 22:22
  Speaker 1: significant fraction of the speed of light. None of these
• 22:26
  Speaker 1: effects was inserted into the theory afterward to make it
• 22:29
  Speaker 1: more interesting. They are consequences of the two starting principles.
• 22:34
  Speaker 1: If the laws of physics are the same in every
• 22:37
  Speaker 1: inertial frame, and if the speed of a light is invariant,
• 22:41
  Speaker 1: then the old universal ideas of space and time cannot
• 22:44
  Speaker 1: survive unchanged. This is also why the phrase relativity can
• 22:48
  Speaker 1: sometimes be misleading. Special relativity does not say that everything
• 22:53
  Speaker 1: is relative. Quite the opposite. Certain quantities are preserved so
• 22:58
  Speaker 1: strictly that space and time must adjust around them. The
• 23:02
  Speaker 1: speed of light is one of those invariant quantities. The
• 23:06
  Speaker 1: laws of physics are another. What becomes relative are the
• 23:10
  Speaker 1: measurements used by different observers to describe events. One observer
• 23:15
  Speaker 1: may calculate a different elapsed time from another. One may
• 23:18
  Speaker 1: measure a different distance. They may disagree about which distant
• 23:22
  Speaker 1: event happened first. Yet both descriptions can be correct within
• 23:26
  Speaker 1: their own inertial frames. Neither observer occupies the centre of
• 23:31
  Speaker 1: the universe. Neither possesses a privileged clock. Neither has access
• 23:36
  Speaker 1: to some hidden master ruler against which all other measurements
• 23:39
  Speaker 1: can be judged. There is no preferred inertial frame waiting
• 23:43
  Speaker 1: quietly in the background. That is one of the most
• 23:46
  Speaker 1: profound departures from Newtonian thinking. The universe does not provide
• 23:51
  Speaker 1: a universal state of rest. Instead, it provides relationships. And
• 23:56
  Speaker 1: the remarkable role of light is that its speed remains
• 23:58
  Speaker 1: the same while those relationships change. What initially appears to
• 24:02
  Speaker 1: be a strange property of a beam of light therefore
• 24:05
  Speaker 1: turns out to be something much more fundamental. It is
• 24:08
  Speaker 1: a clue that motion does not take place against an
• 24:11
  Speaker 1: unchanging backdrop of universal space and universal time. Space and
• 24:17
  Speaker 1: time themselves participate in the physics, and once that is
• 24:21
  Speaker 1: accepted the world begins to look very different indeed. There
• 24:26
  Speaker 1: is one consequence of special relativity that reaches deeper than
• 24:29
  Speaker 1: moving clocks or shrinking distances. It is the unsettling idea
• 24:34
  Speaker 1: that two people can disagree about whether two events happened
• 24:37
  Speaker 1: at the same time and both can be correct. In
• 24:41
  Speaker 1: everyday life, simultaneity seems almost too obvious to question. If
• 24:45
  Speaker 1: two bells ring at exactly noon, then surely they rang
• 24:49
  Speaker 1: at exactly noon. If two lights flash at the same moment,
• 24:53
  Speaker 1: then surely there must be some universal answer to the
• 24:56
  Speaker 1: question of whether they were simultaneous. Newtonian physics assumed exactly that.
• 25:03
  Speaker 1: Time flowed uniformly through the universe, providing one shared present
• 25:08
  Speaker 1: against which every event could be placed. Special relativity removes
• 25:13
  Speaker 1: that universal present. To see why, imagine a long railway
• 25:18
  Speaker 1: platform with an equally long train moving steadily past it.
• 25:22
  Speaker 1: Suppose lightning strikes the track at two different places, one
• 25:26
  Speaker 1: near the front of the passing train and one near
• 25:28
  Speaker 1: the rear. An observer stands exactly halfway between the two
• 25:32
  Speaker 1: strike locations on the platform. Light from both flashes travels
• 25:36
  Speaker 1: towards this observer. If the observer receives both flashes at
• 25:40
  Speaker 1: the same moment and knows that the two strike locations
• 25:43
  Speaker 1: were equally distant, they conclude that the lightning strikes occurred simultaneously.
• 25:48
  Speaker 1: So far, everything seems perfectly straightforward. Now consider a passenger
• 25:54
  Speaker 1: sitting exactly halfway along the moving train. At the instant
• 25:58
  Speaker 1: the lightning strikes occur, according to the Platform Observer, the
• 26:01
  Speaker 1: train is moving forwards. This means the passenger is moving
• 26:05
  Speaker 1: towards the location where the front flash occurred and away
• 26:08
  Speaker 1: from the location where the rear flash occurred. Light from
• 26:11
  Speaker 1: both strikes still travels at exactly the same speed relative
• 26:15
  Speaker 1: to the passenger. That point is crucial. The passenger does
• 26:19
  Speaker 1: not see the forward travelling light slow down because the
• 26:22
  Speaker 1: train is moving away from it, nor the backward travelling
• 26:25
  Speaker 1: light sped up because the train is moving towards it.
• 26:29
  Speaker 1: Both beams travel through vacuum at the same invariant speed.
• 26:33
  Speaker 1: Because the passenger is moving towards one flash and away
• 26:36
  Speaker 1: from the other, the light from the front strike reaches
• 26:39
  Speaker 1: the passenger first. The passenger therefore concludes that the front
• 26:43
  Speaker 1: lightning strike happened before the rear lightning strike. The platform
• 26:47
  Speaker 1: observer says the strikes were simultaneous. The train passenger says
• 26:51
  Speaker 1: they were not. This can initially sound like nothing more
• 26:54
  Speaker 1: than a problem caused by light taking time to travel.
• 26:57
  Speaker 1: Perhaps the passenger simply sees one flash before the other
• 27:01
  Speaker 1: because of where the passenger happens to be moving. But
• 27:04
  Speaker 1: that is not the real issue. Physicists know perfectly well
• 27:07
  Speaker 1: that light takes time to travel. Observers can account for
• 27:11
  Speaker 1: that delay. They can record where they were, how fast
• 27:15
  Speaker 1: they were moving, how far away the events occurred, and
• 27:18
  Speaker 1: how long the signals took to reach them. After making
• 27:21
  Speaker 1: all of those corrections, the disagreement remains. The platform observer
• 27:26
  Speaker 1: still concludes that the strikes were simultaneous in the platform's
• 27:29
  Speaker 1: inertial reference frame. The passenger still concludes that the strikes
• 27:33
  Speaker 1: occurred at different times in the train's inertial reference frame.
• 27:37
  Speaker 1: This is the relativity of simultaneity. It is not an
• 27:41
  Speaker 1: optical illusion. It is not a failure of measurement. and
• 27:45
  Speaker 1: it is not caused by one observer being less informed
• 27:48
  Speaker 1: than the other. The disagreement is built into the structure
• 27:52
  Speaker 1: of special relativity. Each observer divides space-time into a different
• 27:57
  Speaker 1: collection of events regarded as happening now. For events occurring
• 28:01
  Speaker 1: at the same location, this rarely causes conceptual trouble. But
• 28:05
  Speaker 1: when events are widely separated in space, different observers moving
• 28:09
  Speaker 1: relative to one another need not agree about which distant
• 28:12
  Speaker 1: events are simultaneous. This destroys the old idea of a
• 28:16
  Speaker 1: single cosmic present shared throughout the universe. There is no
• 28:20
  Speaker 1: universal slice of reality labelled now that every possible inertial
• 28:25
  Speaker 1: observer must accept. One observer's present can include events that
• 28:29
  Speaker 1: another observer places slightly in their past or slightly in
• 28:33
  Speaker 1: their future. At ordinary human speeds, the differences are extraordinarily small,
• 28:39
  Speaker 1: which is why nobody notices relativity of simultaneity while walking
• 28:43
  Speaker 1: down the street. But the principle is still there. As
• 28:48
  Speaker 1: relative velocities become a significant fraction of the speed of light,
• 28:52
  Speaker 1: the differences become impossible to ignore. The reason again leads
• 28:57
  Speaker 1: directly back to the invariant speed of light. If all
• 29:00
  Speaker 1: observers shared the same universal time and the same universal
• 29:04
  Speaker 1: notion of simultaneity … then observers moving relative to one
• 29:08
  Speaker 1: another would naturally measure different speeds for the same light beam.
• 29:12
  Speaker 1: That is exactly what classical velocity addition would predict. But
• 29:17
  Speaker 1: nature does not behave that way. Every inertial observer must
• 29:21
  Speaker 1: measure the same vacuum speed of light. For that to
• 29:25
  Speaker 1: be possible, the observers must disagree about how measurements of
• 29:29
  Speaker 1: space and time are divided up. Simultaneity is one of
• 29:33
  Speaker 1: the things that has to change. The issue becomes especially
• 29:36
  Speaker 1: clear when we think about clocks. Suppose we want to
• 29:39
  Speaker 1: play two clocks at opposite ends of a very long
• 29:42
  Speaker 1: spacecraft and make sure they show the same time. With
• 29:45
  Speaker 1: the clocks sitting far apart, we cannot simply place them
• 29:48
  Speaker 1: side by side and compare them. One method is to
• 29:52
  Speaker 1: use light signals. A signal can be sent from one
• 29:55
  Speaker 1: clock to the other, reflected and returned. By assuming that
• 30:00
  Speaker 1: light travels at the same speed in both directions within
• 30:03
  Speaker 1: an inertial frame, the travel time can be divided appropriately
• 30:08
  Speaker 1: and the distant clocks can be synchronised. This procedure is
• 30:12
  Speaker 1: known as Einstein synchronisation. Within that reference frame, the clocks
• 30:17
  Speaker 1: can then provide a consistent definition of what it means
• 30:20
  Speaker 1: for distant events to occur simultaneously, but another observer moving
• 30:24
  Speaker 1: relative to those clocks will not generally judge them to
• 30:27
  Speaker 1: be synchronised. that observer has a different set of distant
• 30:31
  Speaker 1: events that count as simultaneous. Once again, neither set of
• 30:35
  Speaker 1: clocks is broken. Neither observer has performed the experiment incorrectly.
• 30:40
  Speaker 1: Each system is internally consistent. This can feel peculiar because
• 30:45
  Speaker 1: human beings naturally imagine time as something universal. We picture
• 30:49
  Speaker 1: the entire universe progressing together, moment after moment, like frames
• 30:55
  Speaker 1: in an enormous film. Special relativity tells us that this
• 30:59
  Speaker 1: picture is not generally available. There is no single universal
• 31:03
  Speaker 1: arrangement of distant events into past, present and future that
• 31:08
  Speaker 1: all inertial observers share, and this is one reason the
• 31:11
  Speaker 1: speed of a light means so much more than the
• 31:13
  Speaker 1: speed of a particular kind of radiation. Keeping that speed
• 31:17
  Speaker 1: invariant forces us to reconsider what we mean by the
• 31:20
  Speaker 1: phrase at the same time. Once simultaneity becomes relative, some
• 31:24
  Speaker 1: of the other famous effects of special relativity become less mysterious.
• 31:29
  Speaker 1: If observers do not agree about which distant events occur simultaneously,
• 31:34
  Speaker 1: then it should no longer be surprising that they also
• 31:37
  Speaker 1: disagree about how long a process lasts or how long
• 31:40
  Speaker 1: a moving object is. Time dilation and length contraction are
• 31:45
  Speaker 1: not isolated oddities floating around the theory. They grow from
• 31:48
  Speaker 1: the same deeper change. Space and time are no longer
• 31:52
  Speaker 1: fixed backgrounds upon which everyone agrees. Different observers divide them differently.
• 31:58
  Speaker 1: And yet, beneath those disagreements, the laws of physics remain consistent.
• 32:04
  Speaker 1: The speed of light remains unchanged. The apparent confusion is
• 32:08
  Speaker 1: not a flaw in relativity. It is the price of
• 32:12
  Speaker 1: discovering that the universe never promised us a single, universal now.
• 32:18
  Speaker 1: One of the simplest ways to understand time dilation is
• 32:21
  Speaker 1: to imagine a clock built from almost nothing. No gears,
• 32:26
  Speaker 1: no hands, no pendulum. Just two mirrors and a pulse
• 32:30
  Speaker 1: of light. Picture the mirrors facing one another, one above
• 32:35
  Speaker 1: the other, with a small distance between them. A pulse
• 32:38
  Speaker 1: of light travels from the lower mirror to the upper mirror, reflects,
• 32:42
  Speaker 1: travels back down and repeats the journey. Each complete round
• 32:46
  Speaker 1: trip can serve as one tick of the clock. In
• 32:49
  Speaker 1: the reference frame, where this light clock is sitting still,
• 32:51
  Speaker 1: the geometry could hardly be simpler. The light travels straight upwards, reflects,
• 32:57
  Speaker 1: and travels straight down again. Because the distance between the
• 33:01
  Speaker 1: mirrors is fixed and the speed of light in vacuum
• 33:03
  Speaker 1: is fixed, every journey takes the same amount of time. Tick, tick, tick.
• 33:10
  Speaker 1: Nothing unusual has happened. Now imagine placing that clock inside
• 33:14
  Speaker 1: a spacecraft moving steadily past an observer. For someone travelling
• 33:18
  Speaker 1: with the spacecraft, the clock is still at rest. The
• 33:21
  Speaker 1: mirrors remain directly above one another and the light continues
• 33:25
  Speaker 1: to bounce vertically between them. But the observer watching the
• 33:29
  Speaker 1: spacecraft pass sees something different. While the light is travelling upwards,
• 33:33
  Speaker 1: the spacecraft is also moving sideways. The upper mirror does
• 33:38
  Speaker 1: not remain above the point from which the light began
• 33:40
  Speaker 1: its journey. It moves forwards with the spacecraft, so from
• 33:44
  Speaker 1: the outside observer's perspective, the light must travel diagonally upwards
• 33:49
  Speaker 1: in order to meet it. On the return journey, the
• 33:52
  Speaker 1: lower mirror has also moved farther forwards. The light therefore
• 33:56
  Speaker 1: follows another diagonal path back down. Instead of seeing the
• 34:00
  Speaker 1: light trace a straight vertical line, the outside observer sees
• 34:03
  Speaker 1: a longer zigzag path through space. And now we reach
• 34:07
  Speaker 1: the important part. Both observers must measure the same speed
• 34:11
  Speaker 1: of light. The person travelling with the clock measures the
• 34:14
  Speaker 1: light moving at approximately 300,000 km per second. The observer
• 34:19
  Speaker 1: watching the spacecraft pass must measure exactly the same vacuum speed.
• 34:24
  Speaker 1: The outside observer cannot explain the longer diagonal route by
• 34:27
  Speaker 1: saying that the light simply travels faster. Special relativity does
• 34:31
  Speaker 1: not allow that option. The speed remains the same. The
• 34:35
  Speaker 1: path is longer, so more time must pass. That is
• 34:38
  Speaker 1: the basic geometry behind time dilation. A clock moving relative
• 34:43
  Speaker 1: to an observer is measured to run more slowly than
• 34:46
  Speaker 1: clocks at rest, in that observer's own inertial frame. This
• 34:50
  Speaker 1: does not mean that anything is wrong with a moving clock.
• 34:54
  Speaker 1: Inside the spacecraft, everything appears perfectly normal. A wristwatch ticks normally.
• 34:59
  Speaker 1: A pendulum swings normally. Atoms behave normally. A passenger's heartbeat
• 35:05
  Speaker 1: does not suddenly become suspiciously leisurely. From the traveller's own
• 35:09
  Speaker 1: point of view, their time is passing exactly as it
• 35:12
  Speaker 1: always has. The difference appears when elapsed times are compared
• 35:16
  Speaker 1: between observers following different paths through spacetime. The time measured
• 35:21
  Speaker 1: by a clock travelling directly along its own path between
• 35:24
  Speaker 1: two events is known as proper time. Proper time is,
• 35:28
  Speaker 1: in a sense, the time actually recorded by that particular
• 35:31
  Speaker 1: clock along its worldline. If you carry a watch with
• 35:34
  Speaker 1: you from one event to another, The amount shown on
• 35:37
  Speaker 1: your watch between those events is your proper time for
• 35:39
  Speaker 1: that journey. Other observers, moving differently relative to those events,
• 35:45
  Speaker 1: may assign a larger interval of coordinate time between them.
• 35:48
  Speaker 1: This distinction is important because relativity is not claiming that
• 35:52
  Speaker 1: clocks are somehow being mechanically slowed by motion. There is
• 35:56
  Speaker 1: no hidden force reaching into the machinery. The effect applies
• 36:00
  Speaker 1: equally well regardless of what kind of clock is being used.
• 36:04
  Speaker 1: A mechanical clock experiences the same relativistic timing as an
• 36:07
  Speaker 1: atomic clock. The vibrations of atoms follow it, chemical reactions
• 36:13
  Speaker 1: follow it, electrical signals follow it, the decay of unstable
• 36:17
  Speaker 1: particles follows it, and biological ageing follows it as well.
• 36:22
  Speaker 1: If a person travels along a path through space-time that
• 36:25
  Speaker 1: accumulates less proper time than another person's path, that traveller
• 36:30
  Speaker 1: does not merely return with a watch showing a smaller number.
• 36:33
  Speaker 1: They have actually aged less. Their heart has beaten fewer times.
• 36:38
  Speaker 1: Their cells have undergone fewer processes. Their brain has experienced
• 36:42
  Speaker 1: fewer moments. Relativity does not slow clocks while leaving everything
• 36:47
  Speaker 1: else untouched. The clock is simply one convenient way of
• 36:51
  Speaker 1: revealing how much time has elapsed along a particular path.
• 36:55
  Speaker 1: There is another feature of this that can initially seem puzzling.
• 36:58
  Speaker 1: Suppose two spacecraft pass one another at constant velocity. From
• 37:03
  Speaker 1: the first spacecraft, the second spacecraft's clock is moving, so
• 37:06
  Speaker 1: its clock appears time-dilated. But from the second spacecraft, the
• 37:11
  Speaker 1: first spacecraft is the one moving. So the second observer
• 37:15
  Speaker 1: says that the first clock is running slowly. At first,
• 37:18
  Speaker 1: this can sound contradictory. How can each observer say that
• 37:22
  Speaker 1: the other's clock is slower? The answer lies in the
• 37:25
  Speaker 1: same relativity of simultaneity that appears when distant events are compared.
• 37:31
  Speaker 1: Two observers do not share a universal definition of which
• 37:34
  Speaker 1: distant clock readings should count as occurring at the same moment.
• 37:38
  Speaker 1: Their measurements are made within different inertial frames, each with
• 37:42
  Speaker 1: its own definition of simultaneity. As long as both observers
• 37:46
  Speaker 1: remain in uniform relative motion, the situation is genuinely symmetrical.
• 37:51
  Speaker 1: Each can regard themselves as being at rest, each can
• 37:55
  Speaker 1: regard the other as moving, and each will consistently measure
• 37:58
  Speaker 1: the other's moving clock as running slowly. The symmetry changes
• 38:02
  Speaker 1: only when their histories through spacetime cease to be equivalent.
• 38:06
  Speaker 1: For example, if one observer turns around and later reunites
• 38:09
  Speaker 1: with the other. For the moment, however, the essential point
• 38:13
  Speaker 1: is much simpler. Time dilation is a direct consequence of
• 38:18
  Speaker 1: preserving the same speed of light for every inertial observer.
• 38:22
  Speaker 1: At everyday speeds, the effect is extraordinarily small. A passenger
• 38:27
  Speaker 1: travelling in a car or aeroplane experiences relativistic time dilation.
• 38:31
  Speaker 1: but by an amount far too tiny to notice without
• 38:34
  Speaker 1: extremely precise equipment. Even a commercial aircraft, moving at around
• 38:39
  Speaker 1: 900km per hour, is travelling at only a minute fraction
• 38:42
  Speaker 1: of the speed of light. The difference between its elapsed
• 38:45
  Speaker 1: time and that of someone on the ground is correspondingly tiny.
• 38:49
  Speaker 1: But increase the speed enough, and the situation changes dramatically.
• 38:54
  Speaker 1: At half the speed of the light, relativistic effects have
• 38:57
  Speaker 1: become measurable but are still fairly modest. At roughly 87%
• 39:02
  Speaker 1: of the speed of light, the Lorentz factor reaches about 2,
• 39:06
  Speaker 1: meaning that one second of proper time on the moving
• 39:08
  Speaker 1: clock corresponds to about two seconds in the frame in
• 39:11
  Speaker 1: which that clock is moving. At around 99.5% of the
• 39:15
  Speaker 1: speed of light, the factor is close to 10. A
• 39:19
  Speaker 1: traveller moving at that speed could experience roughly one year
• 39:22
  Speaker 1: while about 10 years passed in the frame relative to
• 39:25
  Speaker 1: which they were travelling. Closer still to light speed, the
• 39:28
  Speaker 1: difference grows enormously The effect does not appear suddenly at
• 39:33
  Speaker 1: some magical threshold. It is present at every relative speed.
• 39:38
  Speaker 1: It simply remains so small in ordinary life that Newtonian
• 39:41
  Speaker 1: ideas provide an excellent approximation. This is why the world
• 39:46
  Speaker 1: around us does not look obviously relativistic. People do not
• 39:50
  Speaker 1: return from a train journey visibly younger than the relatives
• 39:53
  Speaker 1: who wave them goodbye. The velocities are simply far too low,
• 39:58
  Speaker 1: but the light clock shows that the principle is always there.
• 40:02
  Speaker 1: A longer path for light cannot be compensated by a
• 40:04
  Speaker 1: greater speed, because the speed of light is invariant. Instead,
• 40:10
  Speaker 1: observers must disagree about the time taken. And from that
• 40:14
  Speaker 1: simple requirement comes one of the most remarkable conclusions in physics.
• 40:18
  Speaker 1: Time is not a universal rhythm beating identically for everyone.
• 40:24
  Speaker 1: How much time passes depends, in part, on how you
• 40:27
  Speaker 1: move through space-time. Time dilation is only half of the story.
• 40:33
  Speaker 1: If observers moving relative to one another disagree about how
• 40:37
  Speaker 1: much time has passed, then they must also disagree about
• 40:40
  Speaker 1: certain distances. This effect is known as length contraction. It
• 40:46
  Speaker 1: is sometimes described rather dramatically. as though a fast-moving object
• 40:50
  Speaker 1: were physically being squeezed by some invisible force. But that
• 40:55
  Speaker 1: is not what special relativity says. Nothing is crushing the object.
• 41:00
  Speaker 1: Nothing is pressing on its surface. Instead, length contraction arises
• 41:06
  Speaker 1: because different observers divide space and time differently. The natural
• 41:10
  Speaker 1: place to begin is with what physicists call proper length.
• 41:15
  Speaker 1: The proper length of an object is the length measured
• 41:17
  Speaker 1: in the reference frame. that object is at rest. Imagine
• 41:22
  Speaker 1: a spacecraft sitting quietly in a hangar. Someone measures the
• 41:25
  Speaker 1: distance from its nose to its tail using a ruler.
• 41:29
  Speaker 1: Suppose the spacecraft is 100 metres long, that is its
• 41:32
  Speaker 1: proper length. Now let the spacecraft travel past Earth at
• 41:36
  Speaker 1: an enormous speed. An observer on Earth measures the spacecraft again.
• 41:42
  Speaker 1: According to special relativity, The Earth Observer finds that the
• 41:45
  Speaker 1: spacecraft is shorter than 100 metres along the direction in
• 41:48
  Speaker 1: which it is moving. The faster it moves, the greater
• 41:52
  Speaker 1: the contraction. At ordinary speeds, the difference is hopelessly small.
• 41:58
  Speaker 1: At a significant fraction of the speed of light, however,
• 42:01
  Speaker 1: it becomes substantial. At roughly 87% of the speed of light,
• 42:06
  Speaker 1: for example, a length measured along the direction of motion
• 42:10
  Speaker 1: is reduced to about half its proper length. The people
• 42:13
  Speaker 1: aboard the spacecraft notice nothing unusual. They can walk from
• 42:17
  Speaker 1: one end of the cabin to the other. Their furniture
• 42:20
  Speaker 1: has not suddenly become compressed. Their rulers have not shrunk
• 42:24
  Speaker 1: relative to everything around them. From their own point of view,
• 42:27
  Speaker 1: the spacecraft is still 100 metres long. Instead, it is
• 42:32
  Speaker 1: Earth that is moving relative to them, and distances measured
• 42:35
  Speaker 1: along Earth's direction of motion are the ones that appear contracted.
• 42:41
  Speaker 1: This sounds strange until we consider what measuring a moving
• 42:44
  Speaker 1: object's length actually requires. Suppose someone standing on Earth wants
• 42:49
  Speaker 1: to determine the length of a spacecraft flying past. They
• 42:53
  Speaker 1: need to determine the position of the nose and the
• 42:55
  Speaker 1: position of the tail, but those positions must be recorded
• 42:58
  Speaker 1: at the same time in the Earth Observer's reference frame.
• 43:02
  Speaker 1: Otherwise the spacecraft could move between one measurement and the other,
• 43:05
  Speaker 1: making the result meaningless. So length measurement contains a hidden requirement.
• 43:11
  Speaker 1: It depends on simultaneity, and simultaneity is relative. An observer
• 43:16
  Speaker 1: aboard the spacecraft does not agree with the Earth observer
• 43:20
  Speaker 1: about which events at the nose and tail happened at
• 43:22
  Speaker 1: the same moment. That disagreement changes the measured separation between
• 43:27
  Speaker 1: those points. Length contraction is therefore closely connected to the
• 43:31
  Speaker 1: relativity of simultaneity. Once there is no universal answer to
• 43:36
  Speaker 1: which distant events occur at the same time, There can
• 43:39
  Speaker 1: no longer be a universal answer to the length of
• 43:42
  Speaker 1: an object moving relative to an observer. The spacecraft is
• 43:46
  Speaker 1: not secretly one length, while somebody incorrectly measures another. Its
• 43:51
  Speaker 1: proper length is 100 metres in its own rest frame.
• 43:55
  Speaker 1: Its length in another inertial frame is different. Both measurements
• 43:59
  Speaker 1: are legitimate. This becomes particularly useful when considering journeys at
• 44:04
  Speaker 1: extremely high speed. Imagine a star located 10 light-years from Earth.
• 44:11
  Speaker 1: From Earth's reference frame, a spacecraft might travel towards that
• 44:15
  Speaker 1: star at a speed close to the speed of light.
• 44:18
  Speaker 1: Earth observers see the full 10 light-year distance and measure
• 44:22
  Speaker 1: the journey taking a little more than 10 years. The
• 44:26
  Speaker 1: travellers aboard the spacecraft describe things differently. Their clocks accumulate
• 44:30
  Speaker 1: less proper time because of time dilation. But they also
• 44:33
  Speaker 1: measure the distance between Earth and the destination star as shorter,
• 44:37
  Speaker 1: because that distance is moving relative to them. At a
• 44:41
  Speaker 1: sufficiently high speed, the travellers might measure the journey as
• 44:44
  Speaker 1: only a few light years long, so there is no
• 44:47
  Speaker 1: contradiction between them experiencing only a few years while Earth
• 44:51
  Speaker 1: measures a much longer interval. Their shorter travel time is
• 44:55
  Speaker 1: accompanied by a shorter measured distance. Space and time change together,
• 45:01
  Speaker 1: that is the important point. Relativity does not adjust one
• 45:05
  Speaker 1: quantity in isolation and then leave everything else untouched. The
• 45:09
  Speaker 1: measurements of distance and duration are linked, and the geometry
• 45:12
  Speaker 1: changes in precisely the way needed to preserve the same
• 45:16
  Speaker 1: measured speed of light. It is also important to be
• 45:19
  Speaker 1: clear about the direction in which length contraction occurs, only
• 45:23
  Speaker 1: the dimension parallel to the relative motion contracts. If a
• 45:27
  Speaker 1: spacecraft moves forwards, its measured nose to tail length changes.
• 45:31
  Speaker 1: Its width from left to right does not undergo Lorentz
• 45:35
  Speaker 1: contraction simply because of that forward motion. Its height also
• 45:40
  Speaker 1: remains unchanged in that sense. This prevents a common image
• 45:44
  Speaker 1: of relativistic objects shrinking equally in every direction like balloons
• 45:48
  Speaker 1: losing air. That is not the prediction. The contraction is
• 45:52
  Speaker 1: specifically along the direction of relative motion. The idea of
• 45:56
  Speaker 1: contraction appeared before Einstein's special theory of relativity. Hendrik Antoon
• 46:01
  Speaker 1: Lawrence and George Francis Fitzgerald had both considered the possibility
• 46:05
  Speaker 1: that moving objects might become shorter in the direction of motion.
• 46:10
  Speaker 1: Their motivation, however, belonged to the older aether picture. They
• 46:13
  Speaker 1: were trying to explain why experiments such as the Michelson-Morley
• 46:17
  Speaker 1: experiment had failed to reveal Earth's motion through the proposed
• 46:21
  Speaker 1: luminiferous aether. If an apparatus contracted by just the right
• 46:26
  Speaker 1: amount while moving through the aether was Perhaps the expected
• 46:29
  Speaker 1: effect would disappear? Einstein's interpretation was fundamentally different. There was
• 46:36
  Speaker 1: no need for an aether mechanically squeezing matter. There was
• 46:39
  Speaker 1: no preferred frame through which objects were really moving. Instead,
• 46:43
  Speaker 1: length contraction emerged naturally from the relationship between different inertial
• 46:47
  Speaker 1: reference frames. The contraction was not a mysterious deformation caused
• 46:52
  Speaker 1: by motion through some hidden substance. It was a consequence
• 46:56
  Speaker 1: of spacetime geometry. And once again, light sits at the
• 47:00
  Speaker 1: centre of the explanation. Suppose one observer measures a beam
• 47:04
  Speaker 1: of light crossing a certain distance in a certain amount
• 47:07
  Speaker 1: of time. Another observer moving relative to the first measures
• 47:11
  Speaker 1: different distance in a different elapsed time. Yet when each
• 47:15
  Speaker 1: divides the distance light travelled by the time it took,
• 47:18
  Speaker 1: both obtain the same vacuum speed of light. That consistency
• 47:22
  Speaker 1: is not accidental. Time dilation and length contraction are two
• 47:27
  Speaker 1: parts of the same relativistic structure. If moving observers kept
• 47:32
  Speaker 1: the same universal measurements of both space and time, they
• 47:35
  Speaker 1: could not all measure light at the same speed. Something
• 47:39
  Speaker 1: had to change. In special relativity, both do. So a
• 47:45
  Speaker 1: moving distance can become shorter without anything being physically crushed.
• 47:49
  Speaker 1: A moving clock can accumulate less time without anything being
• 47:53
  Speaker 1: mechanically slowed. Each effect reflects the same, deeper fact. Space
• 47:58
  Speaker 1: and time are not rigid, independent backgrounds. They adjust together
• 48:02
  Speaker 1: according to motion, and the speed of a light remains
• 48:05
  Speaker 1: the invariant thread running through them both. Behind the strange
• 48:09
  Speaker 1: effects of special relativity lies a mathematical rule that ties
• 48:13
  Speaker 1: them all together. It is called the Lorentz transformation. The
• 48:17
  Speaker 1: name comes from Hendrik Antun Lorentz. whose work on electromagnetism
• 48:21
  Speaker 1: and moving systems helped develop the mathematical structure that Albert
• 48:25
  Speaker 1: Einstein would later interpret within special relativity. The Lorentz transformation
• 48:30
  Speaker 1: tells us how two observers moving steadily relative to one
• 48:34
  Speaker 1: another compare their measurements of space and time. More specifically,
• 48:39
  Speaker 1: it converts the coordinates of an event in one inertial
• 48:41
  Speaker 1: reference frame into the coordinates assigned to that same event
• 48:45
  Speaker 1: in another. An event might be something as simple as
• 48:48
  Speaker 1: a flash of light, One observer records where the flash
• 48:52
  Speaker 1: happened and when it happened. Another observer moving past at
• 48:56
  Speaker 1: constant velocity records the same event. They are describing the
• 49:00
  Speaker 1: same physical occurrence. But they will not generally assign it
• 49:04
  Speaker 1: the same position or the same time. The Lorentz transformation
• 49:08
  Speaker 1: tells us exactly how their measurements are related. Before relativity,
• 49:13
  Speaker 1: physicists used a simpler relationship known as the Galilean transformation.
• 49:18
  Speaker 1: In Newtonian mechanics, this works very naturally. Imagine a train
• 49:22
  Speaker 1: moving steadily along a track. Someone inside the train records
• 49:25
  Speaker 1: where a ball is. Someone standing beside the track records
• 49:29
  Speaker 1: the same ball. To convert between the two descriptions, the
• 49:33
  Speaker 1: observer simply accounts for how far the train has moved
• 49:36
  Speaker 1: during the relevant amount of time. Time itself remains the
• 49:39
  Speaker 1: same for everyone. One second for the person on the
• 49:42
  Speaker 1: train is simply one second for the person beside the track.
• 49:46
  Speaker 1: Space changes between the two descriptions. Time does not. This
• 49:51
  Speaker 1: is the classical picture. And at everyday speeds it works
• 49:54
  Speaker 1: extremely well. The Lorentz transformation becomes necessary when relative speeds
• 50:00
  Speaker 1: are large enough that the invariance of the speed of
• 50:02
  Speaker 1: light can no longer be ignored. Unlike the Galilean transformation,
• 50:07
  Speaker 1: it does not treat space and time as completely separate quantities. Instead,
• 50:12
  Speaker 1: measurements of position depend partly on time, and measurements of
• 50:16
  Speaker 1: time depend partly on position. Space and time become mixed together.
• 50:21
  Speaker 1: That sounds more mysterious than it really is. It simply
• 50:25
  Speaker 1: means that when two observers move relative to one another,
• 50:29
  Speaker 1: they use different combinations of spatial and temporal measurements to
• 50:33
  Speaker 1: describe the same events. The amount of this mixing depends
• 50:36
  Speaker 1: on the relative velocity between them. At low speeds the
• 50:40
  Speaker 1: effect is tiny. At speeds approaching the speed of light
• 50:44
  Speaker 1: it becomes dramatic. A particularly important quantity in this relationship
• 50:48
  Speaker 1: is called the Lorentz factor. The Lorentz factor determines how
• 50:52
  Speaker 1: strongly relativistic effects appear. In spoken form, it can be
• 50:56
  Speaker 1: described through the relationship 1 divided by the square root
• 50:59
  Speaker 1: of 1 minus the speed multiplied by itself divided by
• 51:03
  Speaker 1: the speed of light multiplied by itself. The expression is
• 51:07
  Speaker 1: less important here than what it tells us physically. The
• 51:11
  Speaker 1: speed in the formula is the relative velocity between two
• 51:14
  Speaker 1: inertial observers. If that speed is very small compared with
• 51:18
  Speaker 1: the speed of light, the Lorentz factor is almost exactly one.
• 51:23
  Speaker 1: And if the Lorentz factor is close to one, then
• 51:26
  Speaker 1: time dilation and length contraction are both extremely small. This
• 51:30
  Speaker 1: is why relativity does not make everyday life look strange.
• 51:34
  Speaker 1: A car moving along a motorway has a Lorentz factor
• 51:37
  Speaker 1: so close to one that the difference is utterly negligible
• 51:40
  Speaker 1: for ordinary purposes. The same is true for aircraft, trains,
• 51:45
  Speaker 1: ships and even most spacecraft. Newtonian physics remains an excellent approximation.
• 51:51
  Speaker 1: But as the relative velocity rises, the Lorentz factor begins
• 51:54
  Speaker 1: to grow. At half the speed of light, it is
• 51:57
  Speaker 1: a little above one. At roughly 87% of the speed
• 52:01
  Speaker 1: of light it reaches about 2. At around 99.5% of
• 52:06
  Speaker 1: light speed it is close to 10. Push even closer
• 52:09
  Speaker 1: to light speed and it rises very rapidly. This same
• 52:14
  Speaker 1: factor appears again and again throughout special relativity. It tells
• 52:18
  Speaker 1: us how much a moving clock is time dilated. It
• 52:21
  Speaker 1: tells us how much a moving length is contracted along
• 52:24
  Speaker 1: the direction of motion. It appears in relativistic energy and momentum.
• 52:29
  Speaker 1: and it is built directly into the Lorentz transformation itself.
• 52:33
  Speaker 1: This is one reason the famous effects of relativity should
• 52:37
  Speaker 1: not be thought of as unrelated curiosities. Time dilation is
• 52:41
  Speaker 1: not one trick. Length contraction is not another. Relativity of
• 52:47
  Speaker 1: simultaneity is not a third strange rule, added for good measure.
• 52:51
  Speaker 1: They are all consequences of the same transformation between inertial
• 52:55
  Speaker 1: reference frames. The Lorentz transformation also explains why the speed
• 53:00
  Speaker 1: of light remains unchanged. Suppose a pulse of light moves
• 53:05
  Speaker 1: through empty space. One observer measures the distance travelled by
• 53:09
  Speaker 1: the pulse and the time taken. Dividing one by the
• 53:12
  Speaker 1: other gives the speed of light. Now consider a second
• 53:16
  Speaker 1: observer moving relative to the first. This observer assigns different
• 53:20
  Speaker 1: spatial coordinates to the beginning and end of the light's journey.
• 53:25
  Speaker 1: The observer also assigns different times to those events. But
• 53:29
  Speaker 1: the Lorentz transformation changes the spatial separation and the time
• 53:34
  Speaker 1: separation together. It does so in exactly the right way
• 53:38
  Speaker 1: that when the second observer calculates the speed of the
• 53:40
  Speaker 1: light pulse, the result is still the same. This is
• 53:44
  Speaker 1: not a coincidence built into the mathematics after the fact.
• 53:48
  Speaker 1: Preserving the invariant speed of light is part of what
• 53:50
  Speaker 1: defines the transformation. the geometry of space and time changes
• 53:55
  Speaker 1: between observers so that light continues to occupy the same
• 53:59
  Speaker 1: special role. It is also worth making clear what the
• 54:02
  Speaker 1: Lorentz transformation is not. It is not an optical illusion.
• 54:07
  Speaker 1: It is not describing how objects merely look because light
• 54:10
  Speaker 1: takes time to reach someone's eyes. Those visual effects are
• 54:13
  Speaker 1: real too, but they are a separate issue. If a
• 54:17
  Speaker 1: fast spacecraft flies past, The image reaching your eyes can
• 54:21
  Speaker 1: be affected by changing light travel times, angles and relativistic
• 54:25
  Speaker 1: Doppler effects. But the Lorentz transformation is more fundamental than appearance.
• 54:31
  Speaker 1: It relates the actual coordinates assigned to events after observers
• 54:35
  Speaker 1: have corrected for the travel time of signals. If two
• 54:39
  Speaker 1: physicists know exactly how far away an event occurred, how
• 54:43
  Speaker 1: fast they are moving and how long the signal took
• 54:46
  Speaker 1: to arrive, they can account for all of that. After
• 54:49
  Speaker 1: doing so, the relativistic differences remain. The observers still disagree
• 54:54
  Speaker 1: about certain distances. They still disagree about certain time intervals.
• 54:58
  Speaker 1: They still disagree about simultaneity. Those disagreements are not caused
• 55:03
  Speaker 1: by poor eyesight. They come from the structure of space-time.
• 55:07
  Speaker 1: At the same time, special relativity does not overthrow Newtonian
• 55:11
  Speaker 1: physics in situations where Newtonian physics already works. Instead, it
• 55:16
  Speaker 1: contains it as an approximation. When velocities are tiny compared
• 55:20
  Speaker 1: with the speed of light, the Lorentz transformation becomes extremely
• 55:24
  Speaker 1: close to the old Galilean transformation. Time differences between observers
• 55:29
  Speaker 1: become negligible. Length contraction becomes negligible. Relativity of simultaneity becomes negligible.
• 55:37
  Speaker 1: Velocity addition looks almost ordinary. That is why Isaac Newton's
• 55:41
  Speaker 1: mechanics remained so successful for centuries. It was not useless
• 55:46
  Speaker 1: or fundamentally misguided in its proper domain. It was an
• 55:50
  Speaker 1: extraordinarily accurate description of a world where relative velocities are
• 55:54
  Speaker 1: small compared with the speed of light. Special relativity extends
• 55:58
  Speaker 1: that description into a wider regime. And once the Lorentz
• 56:02
  Speaker 1: transformation is taken seriously, the pieces begin to fit together.
• 56:07
  Speaker 1: Why do moving clocks accumulate less time? Because time coordinates
• 56:12
  Speaker 1: transform between inertial frames. Why do moving lengths become shorter?
• 56:17
  Speaker 1: Because spatial coordinates transform too. Why do observers disagree about simultaneity?
• 56:24
  Speaker 1: Because space and time are mixed in the transformation rather
• 56:27
  Speaker 1: than remaining universally separate. Why does everyone still measure light
• 56:32
  Speaker 1: at the same speed? Because the transformation preserves that invariant structure.
• 56:38
  Speaker 1: What once looked like several separate mysteries becomes one coherent idea.
• 56:43
  Speaker 1: Different observers do not merely look at the same fixed
• 56:46
  Speaker 1: space and universal time from different angles. They assign different
• 56:52
  Speaker 1: space and time coordinates to events. Yet the relationships between
• 56:56
  Speaker 1: those coordinates follow precise rules. The Lorentz transformation is those
• 57:01
  Speaker 1: rules written mathematically, and hidden inside them is the deeper
• 57:05
  Speaker 1: lesson special relativity has been quietly building towards. Space and
• 57:09
  Speaker 1: time are not independent stages. They are parts of one
• 57:13
  Speaker 1: connected structure, and motion determines how different observers divide that
• 57:17
  Speaker 1: structure into measurements of where and when. Once special relativity
• 57:22
  Speaker 1: has forced us to give up universal time and universal distance,
• 57:26
  Speaker 1: a natural question appears. If space and time are not independent,
• 57:31
  Speaker 1: what are they instead? The clearest answer emerged a few
• 57:35
  Speaker 1: years after Albert Einstein published Special Relativity. In 1908, The
• 57:40
  Speaker 1: mathematician Hermann Minkowski presented a new way of describing the theory.
• 57:46
  Speaker 1: Rather than treating space and time as separate backgrounds, Minkowski
• 57:50
  Speaker 1: united them into a single four-dimensional structure– spacetime. Three dimensions
• 57:56
  Speaker 1: describe where something happens. One dimension describes when it happens. Together,
• 58:03
  Speaker 1: they provide a complete description of an event. An event
• 58:07
  Speaker 1: in relativity is something that occurs at a particular place
• 58:10
  Speaker 1: and a particular time. A flash of light in a
• 58:13
  Speaker 1: laboratory is an event. Two particles colliding inside an accelerator
• 58:18
  Speaker 1: is an event. You switching off a lamp at a
• 58:21
  Speaker 1: particular moment is an event. Your position in space alone
• 58:24
  Speaker 1: is not enough to identify the occurrence. Neither is the
• 58:28
  Speaker 1: time alone. You need both where and when. That combination
• 58:33
  Speaker 1: becomes especially useful because different observers can assign different spatial
• 58:37
  Speaker 1: coordinates and different time coordinates to the same event, while
• 58:41
  Speaker 1: still agreeing that the event itself happened. Imagine two spacecraft
• 58:45
  Speaker 1: passing one another. Each crew records a flash of light.
• 58:49
  Speaker 1: They may disagree about how far away the flash occurred.
• 58:52
  Speaker 1: They may disagree about when it occurred. But they are
• 58:56
  Speaker 1: still describing the same point in space-time. This way of
• 59:00
  Speaker 1: thinking allows an entire physical history to be represented as
• 59:03
  Speaker 1: a sequence of events. Suppose you remain seated in a
• 59:06
  Speaker 1: chair for 10 minutes. In ordinary language, you might say
• 59:09
  Speaker 1: that you stayed in the same place. But in space-time,
• 59:13
  Speaker 1: your history is not a single point. At each moment,
• 59:16
  Speaker 1: there is a new event. You in the chair now.
• 59:19
  Speaker 1: You in the chair one second later. You in the
• 59:22
  Speaker 1: chair another second later. Connect all of those events together,
• 59:26
  Speaker 1: and they form what physicists call a world-line. A worldline
• 59:30
  Speaker 1: is the path an object traces through spacetime. Every particle
• 59:34
  Speaker 1: has one. Every person has one. Every clock, planet, spacecraft,
• 59:39
  Speaker 1: atom and drifting grain of dust can be represented by
• 59:43
  Speaker 1: a worldline. Even if an object is not moving through
• 59:46
  Speaker 1: space in some chosen reference frame, it is still progressing
• 59:49
  Speaker 1: through time, so its worldline continues through spacetime. This gives
• 59:55
  Speaker 1: relativity a very different feel from ordinary mechanics. Instead of
• 59:59
  Speaker 1: imagining objects simply moving through three-dimensional space as time passes
• 1:00:03
  Speaker 1: somewhere in the background, we can imagine complete paths through
• 1:00:07
  Speaker 1: a four-dimensional geometry. Different observers describe those paths using different coordinates,
• 1:00:14
  Speaker 1: but beneath those different descriptions, some quantities remain unchanged. One
• 1:00:19
  Speaker 1: of the most important is called the space-time interval. Suppose
• 1:00:23
  Speaker 1: two events occur. One observer measures a certain distance between
• 1:00:28
  Speaker 1: them and a certain amount of elapsed time. A second observer,
• 1:00:33
  Speaker 1: moving relative to the first, measures a different distance and
• 1:00:36
  Speaker 1: a different elapsed time. The individual measurements disagree. But special
• 1:00:42
  Speaker 1: relativity provides a particular combination of the spatial separation and
• 1:00:47
  Speaker 1: the temporal separation that both observers calculate to be the same.
• 1:00:51
  Speaker 1: That invariant quantity is the space-time interval. In ordinary geometry,
• 1:00:57
  Speaker 1: Something similar happens when we rotate our coordinate system. Imagine
• 1:01:01
  Speaker 1: an arrow drawn on a sheet of paper. One person
• 1:01:05
  Speaker 1: describes how far it extends horizontally and vertically. Another person
• 1:01:10
  Speaker 1: turns the sheet and uses a different set of horizontal
• 1:01:13
  Speaker 1: and vertical axes. The two people assign different components to
• 1:01:16
  Speaker 1: the arrow. Yet the actual length of the arrow remains unchanged.
• 1:01:21
  Speaker 1: The analogy is not perfect, but it is useful. In
• 1:01:25
  Speaker 1: special relativity, Observers moving relative to one another use different
• 1:01:30
  Speaker 1: mixtures of space and time coordinates. Their measurements of distance
• 1:01:34
  Speaker 1: and duration change, but the space-time interval remains invariant. This
• 1:01:39
  Speaker 1: is part of what the Lorentz transformation preserves. There is
• 1:01:43
  Speaker 1: another interesting role played here by the speed of light.
• 1:01:46
  Speaker 1: Space and time are usually measured in different units. Distance
• 1:01:50
  Speaker 1: might be given in metres or kilometres. Time might be
• 1:01:53
  Speaker 1: given in seconds. To combine the two into one geometric framework,
• 1:01:58
  Speaker 1: it is useful to place them on comparable footing. Multiplying
• 1:02:02
  Speaker 1: a time interval by the speed of light converts that
• 1:02:05
  Speaker 1: time into a corresponding distance. One second multiplied by the
• 1:02:09
  Speaker 1: speed of light corresponds to roughly 300,000 kilometers. This does
• 1:02:14
  Speaker 1: not mean that a second secretly is 300,000 kilometers. It
• 1:02:18
  Speaker 1: means that the speed of light provides a natural conversion
• 1:02:21
  Speaker 1: factor between temporal and spatial measurements. That is another reason
• 1:02:25
  Speaker 1: the speed of light appears so deeply embedded in relativity.
• 1:02:29
  Speaker 1: It does more than describe how quickly a photon crosses
• 1:02:32
  Speaker 1: empty space. It links the units we use to describe
• 1:02:36
  Speaker 1: where and when. But there is an important caution. Time
• 1:02:40
  Speaker 1: is not simply another spatial direction. Space-time has four dimensions.
• 1:02:46
  Speaker 1: But the time dimension does not behave exactly like the
• 1:02:49
  Speaker 1: three dimensions of space. In the mathematics of the space-time interval,
• 1:02:54
  Speaker 1: the temporal and spatial contributions enter differently. That difference is essential.
• 1:02:59
  Speaker 1: You can turn around in space. You can move north, south, left, right,
• 1:03:04
  Speaker 1: up or down. Your relationship with time is not symmetric
• 1:03:08
  Speaker 1: in the same ordinary sense. The geometry of space-time treats
• 1:03:12
  Speaker 1: temporal separation and spatial separation as fundamentally different kinds of contribution.
• 1:03:18
  Speaker 1: So when physicists say that time is the fourth dimension,
• 1:03:21
  Speaker 1: They do not mean that it is merely another direction
• 1:03:24
  Speaker 1: like height. It is part of the same geometric structure,
• 1:03:28
  Speaker 1: but it has a distinct role within that structure. Once
• 1:03:32
  Speaker 1: space-time is taken seriously, several strange effects become easier to interpret.
• 1:03:38
  Speaker 1: Time dilation is no longer simply a mysterious slowing of clocks.
• 1:03:43
  Speaker 1: Different world lines between events can contain different amounts of
• 1:03:46
  Speaker 1: proper time. Length contraction is no longer a bizarre squeezing
• 1:03:51
  Speaker 1: of objects. Different observers use different definitions of simultaneity when
• 1:03:56
  Speaker 1: measuring the endpoints of a moving object. Relativity of simultaneity
• 1:04:01
  Speaker 1: is no longer an awkward exception. It emerges naturally because
• 1:04:05
  Speaker 1: observers moving relative to one another slice spacetime into space
• 1:04:09
  Speaker 1: and time differently. The effects remain strange by everyday standards,
• 1:04:15
  Speaker 1: but they stop looking disconnected, They are all geometric consequences
• 1:04:19
  Speaker 1: of the same underlying structure. This is perhaps the greatest
• 1:04:23
  Speaker 1: conceptual gift of Minkowski's formulation. It turns special relativity from
• 1:04:29
  Speaker 1: a collection of surprising rules into a coherent picture. Observers
• 1:04:34
  Speaker 1: disagree about space. They disagree about time. But they agree
• 1:04:39
  Speaker 1: on the deeper space-time relationships between events. And light occupies
• 1:04:44
  Speaker 1: a very special place within that geometry. A pulse of
• 1:04:47
  Speaker 1: light follows a different kind of worldline from a massive object.
• 1:04:52
  Speaker 1: Its path marks the boundary between events that can be
• 1:04:55
  Speaker 1: connected by slower-than-light motion and events that cannot. The speed
• 1:05:02
  Speaker 1: of light therefore does more than set the rate at
• 1:05:04
  Speaker 1: which electromagnetic radiation moves. It helps define the geometry of
• 1:05:09
  Speaker 1: spacetime itself. It separates different kinds of relationships between events.
• 1:05:15
  Speaker 1: It tells us something about what can influence what. And
• 1:05:20
  Speaker 1: once space and time are viewed as a single connected structure,
• 1:05:24
  Speaker 1: that role begins to look less like a strange property
• 1:05:27
  Speaker 1: of light and more like one of the fundamental organising
• 1:05:30
  Speaker 1: principles of the universe. There is a wonderfully reliable rule
• 1:05:34
  Speaker 1: for motion that we use almost without thinking. If something
• 1:05:37
  Speaker 1: is moving inside something else that is also moving, we
• 1:05:40
  Speaker 1: add the two speeds together. A person walks forwards through
• 1:05:44
  Speaker 1: a train carriage. while the train moves along the track.
• 1:05:48
  Speaker 1: Someone standing beside the railway sees the person's walking speed
• 1:05:52
  Speaker 1: added to the speed of the train. Throw a ball
• 1:05:55
  Speaker 1: forwards from that same train and the same reasoning works again.
• 1:05:59
  Speaker 1: For the slow speeds of ordinary life, this rule is
• 1:06:02
  Speaker 1: so accurate that there is rarely any reason to question it.
• 1:06:06
  Speaker 1: Special relativity does not say that this familiar arithmetic was useless.
• 1:06:11
  Speaker 1: It says that it was an approximation. and the closer
• 1:06:14
  Speaker 1: we move towards the speed of light, the more obvious
• 1:06:16
  Speaker 1: that approximation becomes. Imagine a spacecraft passing Earth at 80%
• 1:06:23
  Speaker 1: of the speed of light. Now suppose that this spacecraft
• 1:06:26
  Speaker 1: somehow launches a smaller craft forwards, and the smaller craft
• 1:06:30
  Speaker 1: travels at 80% of the speed of light relative to
• 1:06:33
  Speaker 1: the larger spacecraft. Using ordinary velocity addition, we would simply
• 1:06:38
  Speaker 1: add the two numbers. 80% plus 80% would give 160%
• 1:06:44
  Speaker 1: of the speed of light. So according to classical reasoning,
• 1:06:47
  Speaker 1: someone on Earth should see the smaller spacecraft travelling considerably
• 1:06:52
  Speaker 1: faster than light, but they would not. Using relativistic velocity addition,
• 1:06:58
  Speaker 1: the Earth Observer would measure the smaller craft travelling at
• 1:07:01
  Speaker 1: a little under 98% of the speed of light, still
• 1:07:04
  Speaker 1: extraordinarily fast, but still below the fundamental limit. The difference
• 1:07:10
  Speaker 1: appears because the Earth observer and the people aboard the
• 1:07:13
  Speaker 1: spacecraft do not agree about distances and time intervals. If
• 1:07:17
  Speaker 1: everyone shared the same universal space and the same universal time,
• 1:07:22
  Speaker 1: ordinary velocity addition would work perfectly. But special relativity has
• 1:07:27
  Speaker 1: already taken those assumptions away. Since measurements of distance and
• 1:07:31
  Speaker 1: duration depend upon the observer's inertial frame, velocities must transform
• 1:07:37
  Speaker 1: differently as well. The relativistic rule for combining velocities accounts
• 1:07:41
  Speaker 1: for this. Conceptually, it begins with something resembling ordinary addition,
• 1:07:46
  Speaker 1: but includes a correction that grows as the velocities become
• 1:07:49
  Speaker 1: significant compared with the speed of light. At small speeds,
• 1:07:54
  Speaker 1: the correction is almost non-existent. At very high speeds, it
• 1:07:58
  Speaker 1: becomes essential. This produces an interesting pattern. Suppose the first
• 1:08:03
  Speaker 1: spacecraft travels at 50% of the speed of light relative
• 1:08:07
  Speaker 1: to Earth. while the second craft moves forwards at 50%
• 1:08:11
  Speaker 1: of the speed of light relative to the first. Classical
• 1:08:14
  Speaker 1: addition would predict the second craft reaching exactly the speed
• 1:08:18
  Speaker 1: of light relative to Earth. Relativity gives a lower value.
• 1:08:23
  Speaker 1: Earth would measure it moving at 80% of the speed
• 1:08:25
  Speaker 1: of light, increase both velocities to 90% of the speed
• 1:08:30
  Speaker 1: of light and the classical answer becomes 180%. The relativistic result, however,
• 1:08:37
  Speaker 1: is only a little under 99.5% of the speed of light.
• 1:08:41
  Speaker 1: The closer the individual speeds become to light speed, the
• 1:08:45
  Speaker 1: more strongly the relativistic correction prevents the combined speed from
• 1:08:49
  Speaker 1: crossing that boundary. There is no sudden intervention by nature
• 1:08:53
  Speaker 1: at the final moment. No invisible speed camera appears beside
• 1:08:57
  Speaker 1: the spacecraft. The addition rule it has changed, and light
• 1:09:02
  Speaker 1: provides the most striking example. Imagine again that a fast-moving
• 1:09:06
  Speaker 1: spacecraft shines a beam of light forwards. The spacecraft crew
• 1:09:10
  Speaker 1: measures that light travelling at approximately 300,000 km per second.
• 1:09:15
  Speaker 1: An observer on Earth sees the spacecraft moving quickly in
• 1:09:18
  Speaker 1: the same direction. Ordinary arithmetic might suggest that the spacecraft's
• 1:09:23
  Speaker 1: velocity should be added to the velocity of the beam.
• 1:09:26
  Speaker 1: Relativistic velocity addition does not produce that result. When one
• 1:09:30
  Speaker 1: of the velocities being combined is exactly the invariant speed
• 1:09:34
  Speaker 1: of light in vacuum, the transformed result is still exactly
• 1:09:38
  Speaker 1: the invariant speed of light. The Earth Observer measures the
• 1:09:41
  Speaker 1: same light speed as the spacecraft crew. Now turn the
• 1:09:45
  Speaker 1: beam around and shine it backwards. Again, Every inertial observer
• 1:09:50
  Speaker 1: measures its vacuum speed to have the same magnitude. This
• 1:09:53
  Speaker 1: is not an extra rule added to special relativity to
• 1:09:56
  Speaker 1: rescue it from an inconvenient answer. Relativistic velocity addition comes
• 1:10:02
  Speaker 1: directly from the Lorentz transformation. The Lorentz transformation tells observers
• 1:10:07
  Speaker 1: how their measurements of space and time are related. Velocity
• 1:10:10
  Speaker 1: is simply distance divided by elapsed time. So once distance
• 1:10:16
  Speaker 1: and time transform according to Lorentz's relationships, the rule for
• 1:10:20
  Speaker 1: transforming velocity follows naturally. All of these effects are therefore
• 1:10:24
  Speaker 1: different faces of the same underlying structure. Relativity of simultaneity
• 1:10:29
  Speaker 1: changes which separated events observers consider simultaneous. Time dilation changes
• 1:10:36
  Speaker 1: measured durations. Length contraction changes measured distances along the direction
• 1:10:41
  Speaker 1: of motion. and relativistic velocity addition determines how those altered
• 1:10:45
  Speaker 1: measurements of distance and time combine into measurements of speed.
• 1:10:49
  Speaker 1: At the velocities familiar to human life, none of this
• 1:10:53
  Speaker 1: causes as much trouble. Suppose a train moves at 100
• 1:10:56
  Speaker 1: km per hour and someone throws a ball forwards at
• 1:10:59
  Speaker 1: 20 km per hour. The relativistic answer differs from 120
• 1:11:04
  Speaker 1: km per hour by an amount so absurdly tiny that
• 1:11:07
  Speaker 1: ordinary arithmetic is more than adequate. The correction exists. It
• 1:11:11
  Speaker 1: simply does not matter. This is why Newtonian mechanics feel
• 1:11:15
  Speaker 1: so natural. Human beings evolved in a world where objects
• 1:11:19
  Speaker 1: usually move at metres per second, or perhaps tens or
• 1:11:22
  Speaker 1: hundreds of metres per second. The speed of light is
• 1:11:26
  Speaker 1: almost 300 million metres per second. Our normal movements occupy
• 1:11:31
  Speaker 1: an extraordinarily slow corner of the relativistic world. There is
• 1:11:36
  Speaker 1: one distinction that is worth making carefully. When physicists describe
• 1:11:41
  Speaker 1: the speed of light as the invariant speed, they mean
• 1:11:44
  Speaker 1: the speed of light in vacuum. Light can propagate more
• 1:11:47
  Speaker 1: slowly through transparent materials such as water or glass. Inside matter,
• 1:11:53
  Speaker 1: electromagnetic radiation interacts with the atoms and electrons of the material,
• 1:11:58
  Speaker 1: and the resulting propagation of the light signal through that
• 1:12:01
  Speaker 1: medium can be slower than the fundamental vacuum speed. This
• 1:12:05
  Speaker 1: does not mean that the basic speed limit of relativity
• 1:12:08
  Speaker 1: has changed. In fact, a charged particle can sometimes move
• 1:12:13
  Speaker 1: through a material faster than light, propagates through that particular
• 1:12:17
  Speaker 1: material while still remaining slower than light in vacuum. When
• 1:12:21
  Speaker 1: that happens, it can produce Cherenkov radiation, often seen as
• 1:12:25
  Speaker 1: a distinctive blue glow around nuclear reactors. Nothing has outrun
• 1:12:30
  Speaker 1: the invariant speed. It has merely outrun the reduced propagation
• 1:12:34
  Speaker 1: speed of a light in that medium. That distinction helps
• 1:12:38
  Speaker 1: reveal what the speed of light really represents. The fundamental
• 1:12:42
  Speaker 1: constant is not simply a rule stating how quickly visible
• 1:12:46
  Speaker 1: light is allowed to travel under every circumstance. It is
• 1:12:49
  Speaker 1: the invariant speed built into the transformation laws of spacetime.
• 1:12:53
  Speaker 1: That is why ordinary velocities approach it differently. That is
• 1:12:57
  Speaker 1: why light in vacuum retains it between inertial frames. And
• 1:13:01
  Speaker 1: that is why simply adding speeds eventually stops working. The
• 1:13:06
  Speaker 1: universe has not imposed an arbitrary speed limit on top
• 1:13:09
  Speaker 1: of otherwise Newtonian motion. The limit emerges from the way
• 1:13:13
  Speaker 1: space and time themselves fit together. Once the speed of
• 1:13:17
  Speaker 1: light is understood as part of the structure of space-time,
• 1:13:20
  Speaker 1: a natural question appears. What actually happens if we keep
• 1:13:25
  Speaker 1: pushing a massive object faster and faster? Imagine a spacecraft
• 1:13:30
  Speaker 1: in deep space. Its engines fire and it begins to accelerate.
• 1:13:36
  Speaker 1: At first, everything seems familiar. Add energy and the spacecraft
• 1:13:40
  Speaker 1: speeds up. Add more energy and it speeds up again.
• 1:13:44
  Speaker 1: That is exactly what everyday experience suggests should happen. So perhaps,
• 1:13:49
  Speaker 1: given enough fuel and enough patience, we might expect the
• 1:13:53
  Speaker 1: spacecraft eventually to reach the speed of light. Special relativity
• 1:13:58
  Speaker 1: says it cannot. An object with non-zero rest mass can
• 1:14:02
  Speaker 1: move extraordinarily close to the speed of light. In principle,
• 1:14:06
  Speaker 1: it can approach that speed as closely as we like,
• 1:14:10
  Speaker 1: but it can never quite arrive. The reason is not
• 1:14:13
  Speaker 1: that empty space begins pushing back. There is no relativistic wind.
• 1:14:18
  Speaker 1: There is no hidden friction with the vacuum. And there
• 1:14:21
  Speaker 1: is certainly no invisible wall waiting at 300,000 km per second.
• 1:14:27
  Speaker 1: The limit emerges from the way energy and momentum behave
• 1:14:30
  Speaker 1: in special relativity. At low speeds, the relationship between force,
• 1:14:35
  Speaker 1: energy and motion looks very close to the familiar Newtonian picture.
• 1:14:41
  Speaker 1: If you add kinetic energy to an object, its speed
• 1:14:44
  Speaker 1: increases in a straightforward way. Double the kinetic energy of
• 1:14:48
  Speaker 1: a slow-moving object and you produce a predictable increase in
• 1:14:52
  Speaker 1: its velocity. But as the object's speed becomes a substantial
• 1:14:57
  Speaker 1: fraction of the speed of light, the relationship begins to change.
• 1:15:01
  Speaker 1: The Lorentz factor becomes larger. Relativistic momentum rises more rapidly
• 1:15:07
  Speaker 1: than classical mechanics would predict. And increasingly, large amounts of
• 1:15:11
  Speaker 1: energy are required to produce increasingly small increases in speed.
• 1:15:15
  Speaker 1: Suppose a massive particle has already reached 90% of the
• 1:15:19
  Speaker 1: speed of light. Giving it more energy certainly makes a difference.
• 1:15:23
  Speaker 1: Its momentum increases. Its total energy increases. Its speed also increases.
• 1:15:30
  Speaker 1: But the increase in speed is smaller than our classical
• 1:15:33
  Speaker 1: instincts might suggest. Push it to 99% of the speed
• 1:15:37
  Speaker 1: of light and the same pattern becomes even more pronounced.
• 1:15:41
  Speaker 1: Then 99.9%, then 99.99%. Each additional 9 can demand dramatically
• 1:15:48
  Speaker 1: more energy. The particle continues getting closer to the speed
• 1:15:52
  Speaker 1: of light, but the final gap never disappears. Mathematically, this
• 1:15:58
  Speaker 1: is tied to the Lorentz factor. As the velocity of
• 1:16:01
  Speaker 1: a massive object approaches the speed of light, the Lorentz
• 1:16:05
  Speaker 1: factor grows without bound. Relativistic energy and momentum contain this factor,
• 1:16:11
  Speaker 1: so they too grow without bound as the limiting speed
• 1:16:14
  Speaker 1: is approached. This leads to the crucial result. For an
• 1:16:18
  Speaker 1: object with non-zero rest mass to be accelerated all the
• 1:16:22
  Speaker 1: way to exactly the speed of light would require an
• 1:16:25
  Speaker 1: unlimited amount of energy, not merely a very large amount.
• 1:16:30
  Speaker 1: not more energy than humanity happens to possess, an unbounded amount.
• 1:16:35
  Speaker 1: That makes the final step physically unattainable. Older explanations of
• 1:16:40
  Speaker 1: relativity sometimes describe this by saying that an object's mass
• 1:16:44
  Speaker 1: increases with speed and eventually becomes infinite. That language can
• 1:16:49
  Speaker 1: still be encountered, but modern physics usually avoids it because
• 1:16:52
  Speaker 1: it can obscure what is actually happening. The object's rest
• 1:16:56
  Speaker 1: mass does not change simply because it is moving quickly.
• 1:17:00
  Speaker 1: An electron remains an electron with the same invariant rest mass.
• 1:17:05
  Speaker 1: A proton retains its rest mass. A spacecraft does not
• 1:17:09
  Speaker 1: gradually become intrinsically more massive merely because it is travelling
• 1:17:13
  Speaker 1: faster relative to someone else. What increases dramatically is the
• 1:17:18
  Speaker 1: object's relativistic energy and momentum. That description is both cleaner
• 1:17:23
  Speaker 1: and more consistent with modern usage. The distinction matters because
• 1:17:28
  Speaker 1: rest mass is an intrinsic property of the object, while
• 1:17:32
  Speaker 1: energy and momentum depend partly on the reference frame used
• 1:17:35
  Speaker 1: to describe its motion. A fast-moving proton can carry an
• 1:17:39
  Speaker 1: enormous amount of energy without its rest mass changing. Particle
• 1:17:45
  Speaker 1: accelerators demonstrate this beautifully in machines designed to accelerate charged
• 1:17:50
  Speaker 1: particles electric fields repeatedly add energy to protons, electrons or
• 1:17:56
  Speaker 1: other particles. At relatively low speeds, adding energy produces substantial
• 1:18:02
  Speaker 1: increases in velocity. But once the particles are travelling close
• 1:18:06
  Speaker 1: to the speed of light, their velocities change very little,
• 1:18:11
  Speaker 1: even when enormous amounts of additional energy are supplied. Instead,
• 1:18:16
  Speaker 1: Most of that added energy appears as increased relativistic energy
• 1:18:21
  Speaker 1: and momentum. The European Organisation for Nuclear Research provides one
• 1:18:26
  Speaker 1: of the most impressive examples. Inside the Large Hadron Collider,
• 1:18:30
  Speaker 1: protons are accelerated around a circular tunnel roughly 27 kilometres
• 1:18:36
  Speaker 1: in circumference. By the time they reach their highest operating energies,
• 1:18:40
  Speaker 1: they are travelling extraordinarily close to the speed of light.
• 1:18:44
  Speaker 1: The difference between their velocity and the vacuum speed of
• 1:18:47
  Speaker 1: light is tiny, yet it is not zero. No matter
• 1:18:52
  Speaker 1: how much more energy was supplied, as long as those
• 1:18:54
  Speaker 1: protons remained massive particles, they could be pushed closer and
• 1:18:59
  Speaker 1: closer to the limit without actually reaching it. This can
• 1:19:02
  Speaker 1: initially seem peculiar. If a particle is already moving at
• 1:19:06
  Speaker 1: something like 99.999% of the speed of light, where does
• 1:19:11
  Speaker 1: additional energy go if its velocity can barely increase? Into
• 1:19:15
  Speaker 1: its energy and momentum. Its momentum can continue increasing enormously,
• 1:19:21
  Speaker 1: even while its speed changes by an almost imperceptible amount.
• 1:19:26
  Speaker 1: This is why collisions inside particle accelerators can become vastly
• 1:19:30
  Speaker 1: more energetic without requiring the particles to move noticeably faster.
• 1:19:35
  Speaker 1: The extra energy becomes available when particles collide, allowing new
• 1:19:39
  Speaker 1: particles to be created or revealing structures that would otherwise
• 1:19:43
  Speaker 1: remain inaccessible. The speed has nearly saturated, the energy has not,
• 1:19:49
  Speaker 1: and this distinction reveals something important about the light speed limit.
• 1:19:53
  Speaker 1: The limit is not enforced by a physical obstacle. Imagine
• 1:19:57
  Speaker 1: accelerating through empty space. Nothing suddenly appears in front of
• 1:20:02
  Speaker 1: you as you approach light speed. There is no region
• 1:20:04
  Speaker 1: where the vacuum becomes thicker. There is no surface to strike. Instead,
• 1:20:10
  Speaker 1: each additional increase in velocity requires more energy than the
• 1:20:13
  Speaker 1: one before. The barrier is built into the mathematical relationship
• 1:20:18
  Speaker 1: between velocity, energy, momentum and spacetime. The closer a massive
• 1:20:24
  Speaker 1: object gets to the invariant speed, the more stubbornly its
• 1:20:28
  Speaker 1: velocity resists further increase. This is also why photons should
• 1:20:32
  Speaker 1: not be imagined as ordinary particles that somehow manage to
• 1:20:36
  Speaker 1: accelerate harder than everything else. Lie is not faster because
• 1:20:40
  Speaker 1: photons possess exceptionally powerful engines. Photons belong to a different category.
• 1:20:46
  Speaker 1: A photon has zero rest mass. In vacuum, it does
• 1:20:50
  Speaker 1: not begin at rest and then accelerate until it reaches
• 1:20:53
  Speaker 1: the speed of light. There is no valid inertial rest
• 1:20:57
  Speaker 1: frame in which a photon is sitting still waiting to
• 1:20:59
  Speaker 1: get moving. Massless particles travel at the invariant speed in
• 1:21:04
  Speaker 1: vacuum as part of their basic relativistic nature. Massive particles
• 1:21:09
  Speaker 1: behave differently. They possess rest mass and follow time-like paths
• 1:21:14
  Speaker 1: through space-time. They may move slowly. They may move quickly.
• 1:21:19
  Speaker 1: They may be brought to rest in an appropriate inertial frame.
• 1:21:22
  Speaker 1: But they cannot be accelerated onto a light-like path. That
• 1:21:26
  Speaker 1: distinction is more fundamental than a simple race between objects.
• 1:21:31
  Speaker 1: A proton and a photon are not contestants following the
• 1:21:34
  Speaker 1: same rules, while one happens to be faster. They occupy
• 1:21:37
  Speaker 1: different classes of motion within relativistic spacetime. For massive objects,
• 1:21:43
  Speaker 1: the speed of light is approached but never reached. For
• 1:21:46
  Speaker 1: massless particles in vacuum, that invariant speed is the only
• 1:21:51
  Speaker 1: physically allowed local speed. This is why the light speed
• 1:21:55
  Speaker 1: limit is so deeply connected to the rest of special relativity.
• 1:22:00
  Speaker 1: It comes from the same space-time structure that produces time dilation,
• 1:22:05
  Speaker 1: length contraction and the Lorentz transformation. The limit is not
• 1:22:11
  Speaker 1: placed on top of the theory as an additional restriction.
• 1:22:14
  Speaker 1: It grows naturally out of the theory itself. Keep adding
• 1:22:18
  Speaker 1: energy to a massive object and its momentum can rise
• 1:22:22
  Speaker 1: without limit. Its total energy can rise without limit. Its
• 1:22:27
  Speaker 1: speed can creep ever closer to the speed of light.
• 1:22:31
  Speaker 1: But the final step remains unreachable. Not because light is
• 1:22:36
  Speaker 1: simply very fast, but because the geometry of spacetime draws
• 1:22:41
  Speaker 1: a fundamental distinction between objects that possess rest mass and
• 1:22:45
  Speaker 1: those that do not. Light occupies a very unusual place
• 1:22:49
  Speaker 1: in special relativity. Massive objects can move slowly. They can
• 1:22:54
  Speaker 1: speed up. They can slow down again. And in the
• 1:22:58
  Speaker 1: right inertial reference frame they can be brought completely to rest.
• 1:23:03
  Speaker 1: A car can be at rest relative to a road.
• 1:23:06
  Speaker 1: A spacecraft can be at rest relative to its crew.
• 1:23:10
  Speaker 1: A proton can be at rest in one frame even
• 1:23:13
  Speaker 1: while another observer sees it moving extremely quickly. Photons are different.
• 1:23:18
  Speaker 1: A photon travelling through vacuum has zero rest mass and
• 1:23:21
  Speaker 1: moves at the invariant speed of light. It does not
• 1:23:24
  Speaker 1: begin below that speed and then accelerate up to it.
• 1:23:28
  Speaker 1: It does not have a slower mode available, and there
• 1:23:31
  Speaker 1: is no valid inertial reference frame in which the photon
• 1:23:34
  Speaker 1: is sitting still. That last point is one of the
• 1:23:36
  Speaker 1: most important and most frequently misunderstood ideas in relativity. It
• 1:23:41
  Speaker 1: is tempting to imagine chasing a beam of light faster
• 1:23:44
  Speaker 1: and faster until eventually we catch up with it. Perhaps,
• 1:23:48
  Speaker 1: from that point of view, the photon would appear frozen
• 1:23:51
  Speaker 1: beside us. Special relativity does not allow that frame to exist.
• 1:23:57
  Speaker 1: The Lorentz transformations relate inertial observers moving at speeds below
• 1:24:02
  Speaker 1: the speed of light relative to one another. As the
• 1:24:05
  Speaker 1: relative speed approaches the invariant speed, the Lorentz factor grows
• 1:24:10
  Speaker 1: without bound. At exactly the speed of light, the ordinary
• 1:24:14
  Speaker 1: transformation into a rest frame ceases to be defined, so
• 1:24:18
  Speaker 1: there is no legitimate inertial coordinate system moving alongside a photon.
• 1:24:23
  Speaker 1: That means familiar questions, such as what does the photon see,
• 1:24:27
  Speaker 1: or what does the universe look like from the photon's
• 1:24:30
  Speaker 1: point of view, do not have ordinary answers within special relativity.
• 1:24:35
  Speaker 1: A photon does not possess a valid rest frame in
• 1:24:37
  Speaker 1: which we can place a clock beside it, arrange rulers
• 1:24:40
  Speaker 1: around it, and describe the rest of the universe as
• 1:24:43
  Speaker 1: moving past. This matters because popular explanations sometimes speak very
• 1:24:48
  Speaker 1: casually about the experience of light. You may hear that
• 1:24:52
  Speaker 1: a photon experiences no time, or that, from the photon's perspective,
• 1:24:57
  Speaker 1: emission and absorption happen instantaneously. These phrases are trying to
• 1:25:02
  Speaker 1: express something mathematically real, but they can easily suggest more
• 1:25:06
  Speaker 1: than the theory actually says. The precise statement involves proper time.
• 1:25:11
  Speaker 1: For a massive object, proper time is the time measured
• 1:25:14
  Speaker 1: by a clock moving along that object's own worldline. A
• 1:25:18
  Speaker 1: person carries a clock. A spacecraft carries a clock. A Mern,
• 1:25:22
  Speaker 1: in principle, has an internal physical history along a time-like trajectory.
• 1:25:27
  Speaker 1: Different world lines can accumulate different amounts of proper time.
• 1:25:32
  Speaker 1: Light follows a different kind of path through spacetime. The
• 1:25:35
  Speaker 1: world line of a photon in vacuum is called light-like,
• 1:25:38
  Speaker 1: or null. Along such an ideal light-like trajectory, the spacetime
• 1:25:43
  Speaker 1: interval is zero, and correspondingly, The proper time between two
• 1:25:47
  Speaker 1: events connected by that light-like path is also zero. Suppose
• 1:25:52
  Speaker 1: a photon is emitted by an atom in a distant
• 1:25:54
  Speaker 1: star and later absorbed by a detector. For observers with
• 1:25:58
  Speaker 1: ordinary inertial frames, the photon may have travelled for seconds, years,
• 1:26:04
  Speaker 1: or billions of years depending on the distance involved. Those
• 1:26:08
  Speaker 1: observers can assign perfectly meaningful coordinates to the emission and
• 1:26:11
  Speaker 1: absorption events. But the proper time along the photon's null
• 1:26:15
  Speaker 1: trajectory is zero. That is a mathematical statement about spacetime geometry.
• 1:26:22
  Speaker 1: It does not automatically create a photon's perspective. There is
• 1:26:25
  Speaker 1: no clock travelling in the photon's rest frame because there
• 1:26:28
  Speaker 1: is no photon rest frame. So it is safer to
• 1:26:31
  Speaker 1: say that the proper time along a light-like worldline is
• 1:26:34
  Speaker 1: zero than to say that the photon personally experiences everything instantaneously.
• 1:26:41
  Speaker 1: The difference may sound subtle. but it protects us from
• 1:26:44
  Speaker 1: smuggling ordinary observer language into a situation where the theory
• 1:26:48
  Speaker 1: does not support it. The same caution applies to the
• 1:26:51
  Speaker 1: phrase time stops at the speed of light. For a
• 1:26:55
  Speaker 1: massive object moving faster and faster relative to a chosen observer,
• 1:26:59
  Speaker 1: time dilation becomes increasingly large. From that observer's frame, a
• 1:27:05
  Speaker 1: clock moving at 90% of light speed runs slower than
• 1:27:08
  Speaker 1: one moving at ordinary speeds. At 99.9% the effect is
• 1:27:13
  Speaker 1: much stronger. It can be tempting to imagine continuing this
• 1:27:17
  Speaker 1: pattern until the clock reaches light speed and simply stops.
• 1:27:22
  Speaker 1: But a massive clock cannot be accelerated to light speed.
• 1:27:26
  Speaker 1: The exact light speed case does not belong to the
• 1:27:28
  Speaker 1: family of valid inertial frames available to massive observers. There
• 1:27:33
  Speaker 1: is no final frame at the end of the sequence
• 1:27:35
  Speaker 1: where we can place ourselves beside a photon and calmly
• 1:27:38
  Speaker 1: report that time has reached zero. The limit exists mathematically.
• 1:27:43
  Speaker 1: The corresponding photon rest frame does not. This distinction becomes
• 1:27:48
  Speaker 1: clearer when spacetime intervals are considered. Events connected by the
• 1:27:52
  Speaker 1: possible motion of a massive object are separated by what
• 1:27:56
  Speaker 1: is called a timelike interval. A person can travel from
• 1:28:00
  Speaker 1: one event to the other while moving below the speed
• 1:28:03
  Speaker 1: of light. A physical clock can accompany that journey and
• 1:28:07
  Speaker 1: record a non-zero amount of proper time. Events connected exactly
• 1:28:11
  Speaker 1: by light are different. Their separation is light-like. The space-time
• 1:28:16
  Speaker 1: interval between them is zero. And events separated too widely
• 1:28:20
  Speaker 1: in space, for light to travel between them in the
• 1:28:23
  Speaker 1: available time, are described as space-like separated. These categories are
• 1:28:28
  Speaker 1: not merely mathematical labels. They reflect fundamentally different possibilities for
• 1:28:33
  Speaker 1: motion and causal connection. Massive objects inhabit time-like trajectories. Light
• 1:28:39
  Speaker 1: in vacuum form null trajectories, and the invariant speed marks
• 1:28:43
  Speaker 1: the boundary between them. There is another misconception that can
• 1:28:47
  Speaker 1: arise from the fact that photons have zero rest mass.
• 1:28:51
  Speaker 1: It is easy to hear the word massless and imagine
• 1:28:54
  Speaker 1: something physically insubstantial, but photons can carry both energy and momentum.
• 1:28:59
  Speaker 1: They can transfer momentum when they interact with matter. Light
• 1:29:03
  Speaker 1: can exert radiation pressure. Photons can knock electrons from materials
• 1:29:08
  Speaker 1: in the photoelectric effect. They can be scattered by particles.
• 1:29:12
  Speaker 1: They can heat matter. They can contribute to the dynamics
• 1:29:15
  Speaker 1: of stars and gas clouds. Solar sails can even make
• 1:29:19
  Speaker 1: use of the momentum carried by light to produce a
• 1:29:21
  Speaker 1: small but continuous push. So zero rest mass does not
• 1:29:25
  Speaker 1: mean zero physical influence. For a photon, energy is related
• 1:29:30
  Speaker 1: to its frequency. Higher frequency photons carry more energy than
• 1:29:34
  Speaker 1: lower frequency photons. A gamma ray photon can carry vastly
• 1:29:38
  Speaker 1: more energy than a photon of visible red light, even
• 1:29:41
  Speaker 1: though both travel through vacuum at the same invariant speed.
• 1:29:45
  Speaker 1: Their speed does not increase with energy. That is another
• 1:29:49
  Speaker 1: contrast with massive particles. A massive particle can gain energy
• 1:29:53
  Speaker 1: and move faster, at least until its velocity becomes extremely
• 1:29:58
  Speaker 1: close to the speed of light. A photon gains or
• 1:30:01
  Speaker 1: loses energy through changes in frequency while continuing to travel
• 1:30:06
  Speaker 1: at the invariant speed and vacuum. This reinforces the idea
• 1:30:10
  Speaker 1: that light is not simply an ordinary object travelling unusually quickly.
• 1:30:14
  Speaker 1: Its motion belongs to a different category within relativistic spacetime.
• 1:30:20
  Speaker 1: Massive objects can have rest frames. Photons cannot. Massive objects
• 1:30:25
  Speaker 1: accumulate proper time along time-like world lines. Ideal light-like world
• 1:30:30
  Speaker 1: lines have zero proper time. Massive objects can move at
• 1:30:34
  Speaker 1: many different speeds below the invariant limit. Photons in vacuum
• 1:30:38
  Speaker 1: travel at that invariant speed. The speed of light therefore
• 1:30:42
  Speaker 1: acts as much more than the upper edge of a speedometer.
• 1:30:45
  Speaker 1: It separates different kinds of space-time motion. On one side
• 1:30:49
  Speaker 1: are time-like paths available to massive matter. At the boundary
• 1:30:53
  Speaker 1: are the null paths followed by light and other massless disturbances.
• 1:30:58
  Speaker 1: And that boundary is so fundamental that even the ordinary
• 1:31:02
  Speaker 1: idea of an observer travelling alongside light stops making sense.
• 1:31:07
  Speaker 1: The strangeness does not come from photons somehow behaving badly.
• 1:31:12
  Speaker 1: It comes from trying to apply the rules of massive
• 1:31:15
  Speaker 1: observers to something that occupies a fundamentally different place in spacetime.
• 1:31:21
  Speaker 1: The speed of light does more than tell us how
• 1:31:23
  Speaker 1: quickly a beam can cross empty space. It also helps
• 1:31:26
  Speaker 1: determine which events in the universe can influence one another.
• 1:31:30
  Speaker 1: This is where special relativity begins to connect motion with causality.
• 1:31:35
  Speaker 1: Causality is the simple idea that causes must be able
• 1:31:38
  Speaker 1: to produce their effects. If you press a switch and
• 1:31:41
  Speaker 1: a lamp turns on, information about the switch being pressed
• 1:31:45
  Speaker 1: must somehow reach the lamp. If one particle strikes another
• 1:31:49
  Speaker 1: and changes its motion, there must be a physical interaction
• 1:31:53
  Speaker 1: linking those events. In relativity, the speed of light helps
• 1:31:57
  Speaker 1: define how quickly such influence can propagate. A useful way
• 1:32:01
  Speaker 1: to picture this is with something called a light cone.
• 1:32:04
  Speaker 1: Imagine a single event in spacetime. Perhaps a lamp flashes
• 1:32:09
  Speaker 1: once in an otherwise empty room. From that event, light
• 1:32:12
  Speaker 1: travels outward in every direction. After one second, the light
• 1:32:16
  Speaker 1: has reached a spherical shell almost 300,000 kilometres away. After
• 1:32:21
  Speaker 1: two seconds, it has travelled almost twice as far. After
• 1:32:25
  Speaker 1: three seconds, farther still. If we represent space and time
• 1:32:29
  Speaker 1: together on a spacetime diagram, with time extending in one
• 1:32:33
  Speaker 1: direction and space extending in another, the expanding sphere of
• 1:32:38
  Speaker 1: light forms the surface of a cone. This is the
• 1:32:41
  Speaker 1: future light cone. Everything inside it represents events that could,
• 1:32:46
  Speaker 1: in principle, be influenced by the original flash without requiring
• 1:32:50
  Speaker 1: anything to travel faster than light. A slower signal could
• 1:32:54
  Speaker 1: reach points inside the cone. A massive spacecraft could travel
• 1:32:59
  Speaker 1: to some of them. A light signal would trace the
• 1:33:01
  Speaker 1: boundary itself. Anything outside the cone is too far away,
• 1:33:05
  Speaker 1: given the available time to be reached by any ordinary
• 1:33:08
  Speaker 1: causal influence travelling at or below the invariant speed. So
• 1:33:13
  Speaker 1: the light cone is not really about light alone. It
• 1:33:16
  Speaker 1: is a map of what can possibly affect what. There
• 1:33:20
  Speaker 1: is also a cone extending in the opposite temporal direction.
• 1:33:23
  Speaker 1: This is the past light cone. It contains all earlier
• 1:33:27
  Speaker 1: events from which a signal travelling at or below the
• 1:33:30
  Speaker 1: speed of light could have reached the chosen event. If
• 1:33:33
  Speaker 1: you are sitting in a room at this moment, everything
• 1:33:35
  Speaker 1: that can have influenced you physically must lie somewhere within
• 1:33:39
  Speaker 1: your past light cone. The light from the lamp above
• 1:33:42
  Speaker 1: you A sound produced a moment ago. Sunlight that left
• 1:33:46
  Speaker 1: the sun roughly eight minutes earlier. Light from a nearby
• 1:33:50
  Speaker 1: star that began its journey years ago. Radiation from a
• 1:33:54
  Speaker 1: distant galaxy that may have been travelling towards Earth for
• 1:33:57
  Speaker 1: millions or billions of years. Your past light cone contains
• 1:34:01
  Speaker 1: the events capable of contributing to your present state through
• 1:34:04
  Speaker 1: causal connections. Your future light cone contains the events you
• 1:34:09
  Speaker 1: may someday influence. Between these two regions lies something stranger.
• 1:34:14
  Speaker 1: Consider two events separated by such a great distance, and
• 1:34:17
  Speaker 1: by such a short amount of time, that even light
• 1:34:21
  Speaker 1: could not travel from one to the other. These events
• 1:34:24
  Speaker 1: are said to be space-like separated. Imagine one event taking
• 1:34:29
  Speaker 1: place on Earth, and another taking place on a distant
• 1:34:32
  Speaker 1: planet at almost the same moment. If the planet is
• 1:34:36
  Speaker 1: ten light years away, then no signal from Earth can
• 1:34:39
  Speaker 1: reach it in less than about 10 years. If the
• 1:34:42
  Speaker 1: two events occur only one second apart, according to some observer,
• 1:34:47
  Speaker 1: neither could possibly have caused the other through any influence
• 1:34:50
  Speaker 1: limited by the speed of light. They lie outside one
• 1:34:53
  Speaker 1: another's light cones. This produces one of the more surprising
• 1:34:57
  Speaker 1: consequences of relativity. Different inertial observers can disagree about the
• 1:35:02
  Speaker 1: order of space-like separated events. One observer may say that
• 1:35:07
  Speaker 1: event 1 happened first. Another observer moving relative to the
• 1:35:11
  Speaker 1: first may say that event 2 happened first. A third
• 1:35:14
  Speaker 1: may even judge them to be simultaneous. That sounds alarming
• 1:35:18
  Speaker 1: until we remember that the events cannot be causally connected.
• 1:35:21
  Speaker 1: Neither can send a light speed or slower signal to
• 1:35:24
  Speaker 1: the other in time to influence it. So changing their
• 1:35:28
  Speaker 1: temporal order between reference frames creates no contradiction. There is
• 1:35:32
  Speaker 1: no observer who sees an effect occur before its cause,
• 1:35:35
  Speaker 1: because no causal relationship exists between the two events in
• 1:35:39
  Speaker 1: the first place. The situation is different for events separated
• 1:35:43
  Speaker 1: by a time-like or light-like interval. If event 1 causes
• 1:35:47
  Speaker 1: event 2 through a massive object, a signal or a
• 1:35:49
  Speaker 1: beam of light, then all inertial observers agree about their
• 1:35:53
  Speaker 1: causal order. They may disagree about how much time separates
• 1:35:57
  Speaker 1: the events, they may disagree about the distance between them,
• 1:36:01
  Speaker 1: but they cannot reverse which event came first. If a
• 1:36:04
  Speaker 1: radioactive atom emits a photon, and that photon is later
• 1:36:08
  Speaker 1: absorbed by a detector, every inertial observer agrees that the
• 1:36:12
  Speaker 1: emission happened before the absorption. The measured times may differ.
• 1:36:17
  Speaker 1: The order does not. That is one of the most
• 1:36:19
  Speaker 1: important roles of the light cone. It protects causal structure
• 1:36:23
  Speaker 1: even while simultaneity remains relative. The speed of light divides
• 1:36:28
  Speaker 1: space-time into different regions. Inside the future light cone are
• 1:36:32
  Speaker 1: events that can be influenced. Inside the past light cone
• 1:36:35
  Speaker 1: are events that could have exerted influence. Outside, both are
• 1:36:39
  Speaker 1: events that are space-like, separated and therefore causally disconnected from
• 1:36:44
  Speaker 1: the chosen event, at least at that moment. This is
• 1:36:47
  Speaker 1: also why faster-than-light communication creates such serious difficulties in special relativity.
• 1:36:54
  Speaker 1: Suppose there were some method of sending a controllable message
• 1:36:57
  Speaker 1: faster than light. The message could travel outside the sender's
• 1:37:00
  Speaker 1: future light cone. Once that happens, the relativity of simultaneity
• 1:37:05
  Speaker 1: becomes dangerous. Because different inertial observers disagree about the ordering
• 1:37:10
  Speaker 1: of space-like separated events, some observers could describe the message
• 1:37:14
  Speaker 1: as arriving before it was sent. With suitably arranged motion
• 1:37:19
  Speaker 1: and return signals, it becomes possible in the mathematics of
• 1:37:22
  Speaker 1: ordinary special relativity to construct situations in which a reply
• 1:37:27
  Speaker 1: arrives before the original message was transmitted. The result is
• 1:37:31
  Speaker 1: a causal paradox. Imagine sending yourself a message saying not
• 1:37:35
  Speaker 1: to send the message. The problem quickly becomes less relaxing.
• 1:37:40
  Speaker 1: This is why the speed of light is often described
• 1:37:42
  Speaker 1: more carefully as the maximum speed at which usable information
• 1:37:47
  Speaker 1: or ordinary causal influence can propagate locally. Visible light happens
• 1:37:51
  Speaker 1: to travel at this speed in vacuum. So do other
• 1:37:54
  Speaker 1: massless disturbances under established physics. But the deeper significance is
• 1:37:59
  Speaker 1: not that light has won some cosmic speed competition. The
• 1:38:03
  Speaker 1: invariant speed defines the causal architecture of spacetime. It separates
• 1:38:08
  Speaker 1: events that can be connected from events that cannot. It
• 1:38:11
  Speaker 1: determines which parts of the future are physically reachable from
• 1:38:14
  Speaker 1: a given event. It determines which parts of the past
• 1:38:17
  Speaker 1: could have contributed to the present. And it ensures that
• 1:38:21
  Speaker 1: although observers may disagree about time and simultaneity, they still
• 1:38:25
  Speaker 1: agree on the causal order of events that can actually
• 1:38:28
  Speaker 1: influence one another. This gives the speed of light an
• 1:38:31
  Speaker 1: even more profound role than before. It is a conversion
• 1:38:35
  Speaker 1: factor between space and time. It is the limiting speed
• 1:38:39
  Speaker 1: for massive objects. It defines null paths followed by light,
• 1:38:44
  Speaker 1: and through the light cone it draws the boundaries of
• 1:38:47
  Speaker 1: cause and effect. The universe may allow different observers to
• 1:38:51
  Speaker 1: disagree about when distant events happened, but it does not
• 1:38:54
  Speaker 1: allow them to casually rearrange which causes produced which effects.
• 1:38:59
  Speaker 1: The speed of light is part of what keeps that
• 1:39:01
  Speaker 1: order intact. One of the most famous equations in science
• 1:39:05
  Speaker 1: emerged from the same relativistic framework that changed our understanding
• 1:39:09
  Speaker 1: of space and time. It is usually written in just
• 1:39:12
  Speaker 1: a few symbols, but spoken aloud the relationship is simply this.
• 1:39:17
  Speaker 1: Energy equals mass multiplied by the speed of light multiplied
• 1:39:21
  Speaker 1: by the speed of light. The equation is often treated
• 1:39:24
  Speaker 1: as a kind of scientific slogan. It appears on posters,
• 1:39:28
  Speaker 1: television programmes, book covers, and the occasional coffee mug attempting
• 1:39:32
  Speaker 1: to look more intelligent than the coffee inside it. But
• 1:39:36
  Speaker 1: the idea it expresses is genuinely profound. Mass and energy
• 1:39:40
  Speaker 1: are not entirely separate ingredients of nature. They are deeply connected.
• 1:39:45
  Speaker 1: An object with rest mass possesses energy simply because that
• 1:39:48
  Speaker 1: mass exists. Even if the object is perfectly stationary in
• 1:39:52
  Speaker 1: a chosen inertial frame, with no kinetic energy from motion,
• 1:39:57
  Speaker 1: it still has what physicists call rest energy. That is
• 1:40:00
  Speaker 1: what the famous equation describes. The amount of rest energy
• 1:40:04
  Speaker 1: associated with a mass is found by multiplying that mass
• 1:40:08
  Speaker 1: by the speed of light twice. And because the speed
• 1:40:11
  Speaker 1: of light is enormous, Squaring it produces an even more
• 1:40:14
  Speaker 1: enormous conversion factor. The speed of light is almost 300
• 1:40:18
  Speaker 1: million metres per second. Multiply that number by itself and
• 1:40:22
  Speaker 1: the result is roughly 90 quadrillion in the appropriate units.
• 1:40:27
  Speaker 1: That means even a small amount of mass corresponds to
• 1:40:30
  Speaker 1: an astonishing amount of energy. One gram of matter has
• 1:40:33
  Speaker 1: a rest energy equivalent of roughly 90 trillion joules. That
• 1:40:38
  Speaker 1: does not mean a one gram object is constantly exploding
• 1:40:41
  Speaker 1: with that amount of usable energy. Most of its rest
• 1:40:44
  Speaker 1: energy is locked into the physical system and cannot simply
• 1:40:47
  Speaker 1: be extracted at will. But it demonstrates just how deep
• 1:40:51
  Speaker 1: the connection between mass and energy really is. A tiny
• 1:40:55
  Speaker 1: change in mass can correspond to a very large release
• 1:40:57
  Speaker 1: of energy. This is exactly what happens in many nuclear processes.
• 1:41:03
  Speaker 1: Inside the sun, hydrogen nuclei eventually combine through a chain
• 1:41:07
  Speaker 1: of reactions that produces helium. The final helium nucleus has
• 1:41:12
  Speaker 1: slightly less mass than the total mass of the original
• 1:41:15
  Speaker 1: particles that contributed to its formation. That missing mass has
• 1:41:20
  Speaker 1: not vanished. It has appeared as energy. Some of that
• 1:41:24
  Speaker 1: energy eventually works its way out of the Sun and
• 1:41:27
  Speaker 1: travels through space as electromagnetic radiation. A tiny portion reaches
• 1:41:33
  Speaker 1: Earth as sunlight. So the warmth on your face during
• 1:41:37
  Speaker 1: a sunny afternoon ultimately owes something to small differences in
• 1:41:41
  Speaker 1: rest mass inside the sun. Nuclear fission works through the
• 1:41:45
  Speaker 1: same broad principle. When a heavy atomic nuclear splits into
• 1:41:50
  Speaker 1: smaller products, the total rest mass of those products can
• 1:41:53
  Speaker 1: be slightly lower than the rest mass of the original system.
• 1:41:57
  Speaker 1: The difference appears as kinetic energy, radiation and other forms
• 1:42:01
  Speaker 1: of energy. Mass and energy are being accounted for together.
• 1:42:05
  Speaker 1: There is an important detail, however. The famous equation is
• 1:42:09
  Speaker 1: not the complete relativistic description of energy. It gives the
• 1:42:13
  Speaker 1: rest energy associated with mass. For a particle that is moving,
• 1:42:18
  Speaker 1: momentum must also be included. The full relationship connects total energy, momentum,
• 1:42:25
  Speaker 1: rest mass, and the speed of light. Written entirely in
• 1:42:30
  Speaker 1: spoken language,
• 1:42:51
  Speaker 1: It sounds rather
• 1:42:55
  Speaker 1: less elegant once the symbols are removed, but the physical
• 1:42:59
  Speaker 1: meaning is worth understanding. A particle's total relativistic energy contains
• 1:43:05
  Speaker 1: both its rest energy and the contribution associated with its momentum.
• 1:43:10
  Speaker 1: For a massive particle at rest, the momentum is zero.
• 1:43:14
  Speaker 1: The complete relationship then reduces to the familiar rest energy equation.
• 1:43:21
  Speaker 1: For a moving massive particle, the momentum is not zero
• 1:43:24
  Speaker 1: and the total energy is greater than the rest energy alone.
• 1:43:28
  Speaker 1: This is why extremely fast particles inside accelerators can carry
• 1:43:32
  Speaker 1: enormous energies without their rest mass changing. Modern physics usually
• 1:43:38
  Speaker 1: treats rest mass as an invariant property. A proton does
• 1:43:42
  Speaker 1: not acquire a different intrinsic mass simply because an observer
• 1:43:45
  Speaker 1: sees it moving rapidly. Its total energy and momentum depend
• 1:43:50
  Speaker 1: on the observer's reference frame. Its rest mass does not.
• 1:43:55
  Speaker 1: This avoids the older language in which people sometimes said
• 1:43:57
  Speaker 1: that a particle's mass increases with speed. That language can
• 1:44:01
  Speaker 1: reproduce certain calculations, but it tends to hide the cleaner
• 1:44:05
  Speaker 1: relativistic picture. Mass remains the invariant rest mass. Energy and
• 1:44:11
  Speaker 1: momentum change with motion. The distinction becomes especially important for photons.
• 1:44:17
  Speaker 1: A photon has zero rest mass. If we used only
• 1:44:21
  Speaker 1: the famous rest energy equation, We might be tempted to
• 1:44:24
  Speaker 1: conclude that a photon should therefore have zero energy. But
• 1:44:28
  Speaker 1: that would be wrong. The complete relativistic relationship includes momentum.
• 1:44:34
  Speaker 1: For a massless photon, the mass term disappears while the
• 1:44:37
  Speaker 1: momentum term remains. The relationship becomes energy equals momentum multiplied
• 1:44:43
  Speaker 1: by the speed of light. So a photon can possess
• 1:44:46
  Speaker 1: both energy and momentum while having no rest mass. This
• 1:44:51
  Speaker 1: is not merely a mathematical curiosity. The momentum of light
• 1:44:55
  Speaker 1: has real physical effects. Photons can transfer momentum when they
• 1:45:00
  Speaker 1: strike matter. Light can exert radiation pressure. A sufficiently large
• 1:45:05
  Speaker 1: lightweight reflective sail can be pushed by sunlight. Laser beams
• 1:45:10
  Speaker 1: can manipulate tiny particles. Radiation pressure can even become important
• 1:45:15
  Speaker 1: in astrophysical environments. helping influence the motion of gas and
• 1:45:19
  Speaker 1: dust around luminous stars. The energy carried by a photon
• 1:45:23
  Speaker 1: depends on its frequency. A photon of high frequency radiation
• 1:45:27
  Speaker 1: carries more energy than a photon of low frequency radiation.
• 1:45:32
  Speaker 1: Yet both travel at the same invariant speed in vacuum.
• 1:45:36
  Speaker 1: This is another reminder that greater energy does not make
• 1:45:38
  Speaker 1: light travel faster. For massive objects, adding energy can increase speed.
• 1:45:44
  Speaker 1: although by smaller and smaller amounts as the light speed
• 1:45:47
  Speaker 1: limit is approached. For photons, changes in energy alter frequency
• 1:45:52
  Speaker 1: and momentum instead. The vacuum speed remains unchanged. The appearance
• 1:45:57
  Speaker 1: of the speed of light throughout these energy relationships is
• 1:46:00
  Speaker 1: not accidental. The same constant already appeared when space and
• 1:46:05
  Speaker 1: time were connected through the Lorentz transformation. It appeared in
• 1:46:09
  Speaker 1: time dilation. It appeared in length contraction. It defined the
• 1:46:13
  Speaker 1: limiting speed for massive motion. It defined the null paths
• 1:46:17
  Speaker 1: followed by light. And now it appears again as the
• 1:46:20
  Speaker 1: conversion factor connecting mass, energy and momentum. That repetition is
• 1:46:26
  Speaker 1: telling us something. The speed of a light is not
• 1:46:30
  Speaker 1: merely a number associated with electromagnetic radiation. It is woven
• 1:46:35
  Speaker 1: into the structure linking some of the most fundamental quantities
• 1:46:38
  Speaker 1: in physics, space, time, energy … They are not isolated
• 1:46:47
  Speaker 1: concepts placed side by side. Relativity reveals mathematical relationships between them.
• 1:46:53
  Speaker 1: Particle physics provides countless examples. When particles collide at very
• 1:46:58
  Speaker 1: high energies, some of their kinetic energy can be converted
• 1:47:02
  Speaker 1: into the rest mass of entirely new particles. Energy becomes
• 1:47:06
  Speaker 1: available to create matter, provided all the relevant conservation laws
• 1:47:10
  Speaker 1: are satisfied. The reverse can happen as well. A particle
• 1:47:14
  Speaker 1: and its antiparticle can annihilate, with their rest energy appearing
• 1:47:18
  Speaker 1: in other forms, often including energetic photons. So the relationship
• 1:47:23
  Speaker 1: works in both directions. Mass can contribute to released energy.
• 1:47:28
  Speaker 1: Energy concentrated in the right physical circumstances can contribute to
• 1:47:32
  Speaker 1: the creation of massive particles. This does not mean that
• 1:47:37
  Speaker 1: matter is simply made of energy in some vague sense.
• 1:47:41
  Speaker 1: Mass and energy remain distinct physical quantities with different roles,
• 1:47:45
  Speaker 1: but they belong to a unified relativistic accounting system, and
• 1:47:49
  Speaker 1: once again the speed of light sits directly inside that system.
• 1:47:54
  Speaker 1: The famous equation is therefore more than a memorable piece
• 1:47:57
  Speaker 1: of algebra. It is another clue to what special relativity
• 1:48:00
  Speaker 1: is really saying. The constant that determines how different observers
• 1:48:05
  Speaker 1: relate space and time also governs how mass and energy
• 1:48:09
  Speaker 1: fit together. The speed of light is not standing at
• 1:48:12
  Speaker 1: the edge of physics as the speed of one particular phenomenon.
• 1:48:16
  Speaker 1: It is embedded deep inside the framework. And the more
• 1:48:20
  Speaker 1: places it appears, the clearer it becomes that this single
• 1:48:23
  Speaker 1: constant is part of the basic architecture through which the
• 1:48:26
  Speaker 1: universe organises motion, matter, energy and space-time itself. Special relativity
• 1:48:34
  Speaker 1: can sound almost too strange to belong to the ordinary
• 1:48:36
  Speaker 1: physical world. Clocks disagree about elapsed time. Moving distances contract.
• 1:48:43
  Speaker 1: Simultaneity depends on motion. Energy and momentum behave differently as
• 1:48:48
  Speaker 1: objects approach the speed of light. These are remarkable claims. Fortunately,
• 1:48:53
  Speaker 1: they are not claims that physics asks us to accept
• 1:48:56
  Speaker 1: simply because the mathematics is elegant. Special relativity has been
• 1:49:01
  Speaker 1: tested again and again for more than a century. Its
• 1:49:04
  Speaker 1: predictions appear in laboratories, atomic clocks, particle accelerators. cosmic rays
• 1:49:11
  Speaker 1: and the behaviour of unstable particles moving at enormous speeds.
• 1:49:17
  Speaker 1: One particularly elegant test arrives naturally from space. Earth is
• 1:49:21
  Speaker 1: constantly being struck by cosmic rays. These are highly energetic particles,
• 1:49:27
  Speaker 1: many of them protons and atomic nuclei, travelling through space
• 1:49:31
  Speaker 1: at speeds close to the speed of light. When they
• 1:49:35
  Speaker 1: collide with atoms high in Earth's atmosphere, They produce showers
• 1:49:39
  Speaker 1: of secondary particles. Among those particles are muons. A muon
• 1:49:43
  Speaker 1: is similar in some ways to an electron, but considerably
• 1:49:46
  Speaker 1: more massive and unstable. A muon at rest has an
• 1:49:49
  Speaker 1: average lifetime of only about 2.2 millionths of a second
• 1:49:52
  Speaker 1: before it decays into other particles. That is not very long.
• 1:49:57
  Speaker 1: If classical physics alone described the situation, even a muon
• 1:50:00
  Speaker 1: travelling extremely quickly would cover only a modest distance during
• 1:50:05
  Speaker 1: such a short lifetime. Many muons created high in the
• 1:50:09
  Speaker 1: atmosphere should decay long before reaching detectors at Earth's surface,
• 1:50:14
  Speaker 1: and yet large numbers of them do reach the ground.
• 1:50:17
  Speaker 1: Special relativity explains why. From Earth's reference frame, the muons
• 1:50:22
  Speaker 1: are moving extremely close to the speed of light. Their
• 1:50:26
  Speaker 1: internal decay process is therefore affected by relativistic time dilation.
• 1:50:31
  Speaker 1: The moving muon's clock, in the broad physical sense, accumulates
• 1:50:36
  Speaker 1: less time than clocks at rest on Earth. So although
• 1:50:39
  Speaker 1: the muon's own proper lifetime remains about 2.2 microseconds on average,
• 1:50:45
  Speaker 1: Earth observers measure its lifetime as longer. A sufficiently energetic
• 1:50:50
  Speaker 1: muon can therefore travel many kilometres through the atmosphere before decaying.
• 1:50:55
  Speaker 1: The particle survives long enough to reach the surface. The
• 1:50:58
  Speaker 1: same situation has an equally valid description from the muon's
• 1:51:02
  Speaker 1: reference frame. The Moon does not regard its own lifetime
• 1:51:05
  Speaker 1: as extended. Its own proper time proceeds normally. Instead, the
• 1:51:11
  Speaker 1: atmosphere is moving rapidly towards it. Because of a length contraction,
• 1:51:16
  Speaker 1: the distance from the upper atmosphere to Earth's surface is
• 1:51:18
  Speaker 1: shorter in the Moon's frame. The Moon therefore has less
• 1:51:22
  Speaker 1: distance to cross during its short lifetime. Earth observers describe
• 1:51:27
  Speaker 1: time dilation. The Moon frame describes length contraction Both descriptions
• 1:51:32
  Speaker 1: predict the same detection at the ground. It is a
• 1:51:35
  Speaker 1: wonderfully compact demonstration of how the different pieces of special
• 1:51:38
  Speaker 1: relativity remain consistent with one another. Particle accelerators provide even
• 1:51:44
  Speaker 1: more precise tests. Inside modern accelerators, charged particles are deliberately
• 1:51:50
  Speaker 1: pushed to velocities extremely close to the speed of light.
• 1:51:54
  Speaker 1: At those speeds, Newtonian mechanics is no longer remotely sufficient.
• 1:51:59
  Speaker 1: Relativistic energy and momentum must be used to predict how
• 1:52:02
  Speaker 1: the particles respond to electromagnetic fields, how they move through
• 1:52:06
  Speaker 1: the machine, and what happens when they collide. At the
• 1:52:10
  Speaker 1: European Organization for Nuclear Research, the Large Hadron Collider accelerates
• 1:52:15
  Speaker 1: protons to energies of several trillion electron volts. Their speed
• 1:52:20
  Speaker 1: becomes extraordinarily close to the vacuum speed of light, but
• 1:52:24
  Speaker 1: increasing their energy further produces only a tiny additional increase
• 1:52:28
  Speaker 1: in velocity. Their momentum and total energy continue to grow enormously,
• 1:52:33
  Speaker 1: exactly as special relativity predicts. Without relativistic equations, the machine
• 1:52:39
  Speaker 1: would not merely be slightly inaccurate. Its particle dynamics would
• 1:52:44
  Speaker 1: be described incorrectly. The same is true in accelerator laboratories
• 1:52:48
  Speaker 1: around the world. Relativistic corrections are not decorative additions applied
• 1:52:53
  Speaker 1: after the important work has been done. They are part
• 1:52:56
  Speaker 1: of the important work. unstable particles provide another test. Some
• 1:53:01
  Speaker 1: particles produced in accelerators survive much longer in the laboratory
• 1:53:05
  Speaker 1: frame when travelling at relativistic speeds than they would if
• 1:53:08
  Speaker 1: they were at rest. The increase in observed lifetime follows
• 1:53:12
  Speaker 1: the same Lorentz factor that governs time dilation. Different particles,
• 1:53:17
  Speaker 1: different energies, different experimental arrangements, and yet the same relativistic
• 1:53:23
  Speaker 1: structure continues to appear. Clocks provide a more familiar demonstration.
• 1:53:28
  Speaker 1: Modern atomic clocks measure time with extraordinary precision. This allows
• 1:53:33
  Speaker 1: physicists to compare clocks that have followed different motions and
• 1:53:36
  Speaker 1: detect differences far too small for ordinary mechanical clocks to reveal.
• 1:53:41
  Speaker 1: Experiments using atomic clocks transported aboard aircraft have measured differences
• 1:53:46
  Speaker 1: in accumulated time consistent with relativistic predictions. One famous example
• 1:53:52
  Speaker 1: was carried out in 1971 by Joseph Haefel and Richard Keating.
• 1:53:57
  Speaker 1: who flew atomic clocks around the world on commercial airliners
• 1:54:00
  Speaker 1: and compared them with reference clocks that remained on the ground.
• 1:54:05
  Speaker 1: The full interpretation required both special relativistic effects from motion
• 1:54:10
  Speaker 1: and general relativistic effects from differences in gravitational potential. That
• 1:54:15
  Speaker 1: distinction is important. Motion produces special relativistic time dilations. gravity
• 1:54:22
  Speaker 1: produces additional effects described by Albert Einstein's general theory of relativity.
• 1:54:28
  Speaker 1: In real experiments near Earth, both can sometimes matter at
• 1:54:32
  Speaker 1: the same time. More controlled clock experiments have isolated velocity-dependent
• 1:54:37
  Speaker 1: effects with increasing precision, confirming that accumulated proper time depends
• 1:54:42
  Speaker 1: on the path a clock follows through spacetime. The principle
• 1:54:46
  Speaker 1: is important enough to appear in technology as well as experiments.
• 1:54:50
  Speaker 1: Satellite navigation systems require relativistic corrections because clocks aboard satellites
• 1:54:56
  Speaker 1: do not accumulate time at exactly the same rate as
• 1:55:00
  Speaker 1: clocks on Earth's surface. Part of that difference comes from
• 1:55:03
  Speaker 1: their motion, which produces special relativistic time dilation. Another part
• 1:55:09
  Speaker 1: comes from gravity, which requires general relativity. The corrections must
• 1:55:14
  Speaker 1: be handled correctly, or positioning errors would accumulate rapidly. Special
• 1:55:20
  Speaker 1: relativity has also been tested through increasingly sensitive searches for
• 1:55:24
  Speaker 1: violations of Lorentz invariance. Lorentz invariance is the underlying symmetry,
• 1:55:30
  Speaker 1: expressing the idea that the laws of physics take the
• 1:55:33
  Speaker 1: appropriate same form for inertial observers related by Lorentz transformations.
• 1:55:39
  Speaker 1: Researchers have looked for tiny indications that the behaviour of light, particles,
• 1:55:44
  Speaker 1: Atomic transitions or other physical systems might depend upon an
• 1:55:48
  Speaker 1: absolute direction or preferred state of uniform motion. So far,
• 1:55:53
  Speaker 1: no established violation has required special relativity to be replaced
• 1:55:57
  Speaker 1: within the enormous range over which it has been tested.
• 1:56:01
  Speaker 1: That does not mean physicists simply declare the theory untouchable.
• 1:56:05
  Speaker 1: Quite the opposite. Precision experiments continue looking for deviations because
• 1:56:09
  Speaker 1: even an extremely small one could reveal new physics. A
• 1:56:13
  Speaker 1: successful theory earns confidence not by avoiding difficult tests, but
• 1:56:18
  Speaker 1: by surviving them. And special relativity has survived an extraordinary variety.
• 1:56:24
  Speaker 1: Atmospheric muons behave as time dilation predicts. Moving unstable particles
• 1:56:30
  Speaker 1: exhibit relativistic lifetimes. Particle accelerators obey relativistic relationships between velocity,
• 1:56:38
  Speaker 1: momentum and energy. Precision clocks accumulate different amounts of time
• 1:56:43
  Speaker 1: depending upon their motion. Tests of Lorentz invariants continue to
• 1:56:48
  Speaker 1: agree with the symmetry structure on which the theory is built.
• 1:56:51
  Speaker 1: The evidence therefore goes far beyond measuring the speed of
• 1:56:54
  Speaker 1: light and noticing that it is very fast. Special relativity
• 1:56:59
  Speaker 1: makes a network of connected predictions. Change the rule governing
• 1:57:03
  Speaker 1: space and time, and consequences appear in particle lifetimes. They
• 1:57:08
  Speaker 1: appear in accelerator dynamics. They appear in clocks. They appear
• 1:57:12
  Speaker 1: in energy and momentum. They appear in the relationship between
• 1:57:16
  Speaker 1: different inertial observers. And across those very different situations, the
• 1:57:21
  Speaker 1: same framework works. That consistency is what makes special relativity
• 1:57:27
  Speaker 1: so powerful. The universe does not merely tolerate Einstein's unusual
• 1:57:31
  Speaker 1: description of space and time. Whenever we measure carefully enough,
• 1:57:36
  Speaker 1: it behaves as though those strange rules really are there.
• 1:57:39
  Speaker 1: By this point, the phrase speed of light has begun
• 1:57:42
  Speaker 1: to mean something much larger than it did at the beginning.
• 1:57:45
  Speaker 1: It is still true that light travels through vacuum at
• 1:57:48
  Speaker 1: a speed of exactly 299,792,458 metres per second. But that
• 1:57:50
  Speaker 1: number is not important merely because it tells us how
• 1:57:52
  Speaker 1: quickly light moves. The deeper idea is that this value
• 1:57:53
  Speaker 1: represents the invariant speed built into the structure of spacetime.
• 1:58:00
  Speaker 1: because it tells us how quickly light moves. The deeper
• 1:58:04
  Speaker 1: idea is that this value represents the invariant speed built
• 1:58:07
  Speaker 1: into the structure of spacetime. Light travels at that speed
• 1:58:11
  Speaker 1: in vacuum because photons are massless excitations of the electromagnetic field.
• 1:58:17
  Speaker 1: They do not happen to be the fastest things simply
• 1:58:20
  Speaker 1: because nature gave visible light an impressive top speed. Their
• 1:58:23
  Speaker 1: motion reflects a more fundamental property of the relativistic framework.
• 1:58:28
  Speaker 1: Massless disturbances propagate along null, or light-like, paths, and in
• 1:58:33
  Speaker 1: vacuum those paths are defined by the invariant speed. This
• 1:58:37
  Speaker 1: is why calling the constant the speed of light is useful,
• 1:58:40
  Speaker 1: but slightly misleading. Light reveals the constant very clearly, but
• 1:58:46
  Speaker 1: the constant belongs to spacetime. One way to see this
• 1:58:50
  Speaker 1: is to notice that light is not the only phenomenon
• 1:58:52
  Speaker 1: associated with it. gravitational waves also propagate through vacuum at
• 1:58:57
  Speaker 1: the same invariant speed, according to Albert Einstein's general theory
• 1:59:01
  Speaker 1: of relativity. These waves are disturbances in spacetime itself. They
• 1:59:07
  Speaker 1: are not electromagnetic radiation. They are not made of photons.
• 1:59:11
  Speaker 1: And yet observations of gravitational waves are consistent with them
• 1:59:14
  Speaker 1: travelling at the same fundamental speed as light in vacuum.
• 1:59:18
  Speaker 1: That tells us something important. The constant cannot be understood
• 1:59:22
  Speaker 1: merely as a private property of electromagnetism. It is part
• 1:59:26
  Speaker 1: of the causal and geometric structure shared by relativistic physics
• 1:59:30
  Speaker 1: more broadly. In fact, special relativity can be formulated without
• 1:59:35
  Speaker 1: beginning by talking about light at all. One can start
• 1:59:38
  Speaker 1: instead with the relativity principle and the existence of some
• 1:59:42
  Speaker 1: finite invariant speed that all inertial observers agree upon. The
• 1:59:47
  Speaker 1: mathematics then leads to Lorentz transformations rather than Galilean transformations.
• 1:59:53
  Speaker 1: Only afterward do we identify that invariant speed experimentally with
• 1:59:57
  Speaker 1: the vacuum propagation speed of light. Historically, light led physicists
• 2:00:02
  Speaker 1: toward the theory. Conceptually, however, the theory is deeper than
• 2:00:07
  Speaker 1: light itself. This helps explain why the same constant appears
• 2:00:12
  Speaker 1: in so many apparently different places. It connects space and
• 2:00:17
  Speaker 1: time in the Lorentz transformation. It determines the size of
• 2:00:21
  Speaker 1: time dilation at a given relative velocity. It sets the
• 2:00:25
  Speaker 1: scale of length contraction. It appears in the relationship between energy,
• 2:00:29
  Speaker 1: momentum and rest mass. It defines the null paths followed
• 2:00:34
  Speaker 1: by photons and it shapes the light cones that divide
• 2:00:38
  Speaker 1: space-time into regions that can and cannot be causally connected.
• 2:00:43
  Speaker 1: The same constant keeps reappearing because the phenomena are not
• 2:00:46
  Speaker 1: truly separate. They are different consequences of the same underlying
• 2:00:50
  Speaker 1: spacetime structure. There is another way to appreciate this. Space
• 2:00:55
  Speaker 1: and time are normally measured using different units. We might
• 2:00:58
  Speaker 1: measure distance in metres and time in seconds. That makes
• 2:01:01
  Speaker 1: them feel like entirely different kinds of quantity. But the
• 2:01:05
  Speaker 1: speed of light allows one to be converted into the
• 2:01:08
  Speaker 1: units of the other. Multiply a duration by the speed
• 2:01:12
  Speaker 1: of light and you obtain a distance. One second corresponds
• 2:01:16
  Speaker 1: to roughly 300,000 kilometres of light travel. One year corresponds
• 2:01:21
  Speaker 1: to one light year. This does not mean that time
• 2:01:25
  Speaker 1: and distance are literally interchangeable in every sense. They are not.
• 2:01:29
  Speaker 1: But it shows that the invariant speed provides a natural
• 2:01:32
  Speaker 1: conversion between temporal separation and spatial separation. That role becomes
• 2:01:39
  Speaker 1: especially clear in modern metrology. Today, the speed of light
• 2:01:43
  Speaker 1: in vacuum is not merely a measured quantity, with some
• 2:01:46
  Speaker 1: uncertainty attached to it. Its value is fixed exactly. The
• 2:01:52
  Speaker 1: metre is defined so that the speed of light in
• 2:01:55
  Speaker 1: vacuum is exactly 299,792,458 metres per second. In practical terms,
• 2:02:05
  Speaker 1: the meter is tied to how far light travels in
• 2:02:08
  Speaker 1: vacuum during a particular fraction of a second. That reverses
• 2:02:13
  Speaker 1: the historical relationship. Once scientists measured the meter and then
• 2:02:17
  Speaker 1: tried to measure the speed of light using it, now
• 2:02:20
  Speaker 1: the speed of light has an exact defined value and
• 2:02:23
  Speaker 1: the meter is realized through measurements ultimately linked to that definition.
• 2:02:28
  Speaker 1: This is possible because measurements of time have become extraordinarily precise.
• 2:02:33
  Speaker 1: The second is defined using a specific atomic transition in cesium.
• 2:02:38
  Speaker 1: With a precisely defined second and an exactly fixed speed
• 2:02:42
  Speaker 1: of light, distance can be anchored to the same physical framework.
• 2:02:46
  Speaker 1: There is something pleasing about that. A human unit of
• 2:02:50
  Speaker 1: length is now connected to one of the fundamental constants
• 2:02:54
  Speaker 1: governing spacetime. But even here, the particular number should not
• 2:02:58
  Speaker 1: be mistaken for the profound part. 299 million. 792,458 metres
• 2:03:07
  Speaker 1: per second is not a sacred number written into the
• 2:03:11
  Speaker 1: universe in those exact digits. The digits depend on our
• 2:03:15
  Speaker 1: chosen units. If human beings had chosen different definitions for
• 2:03:20
  Speaker 1: the metre and second, the numerical value would be different.
• 2:03:24
  Speaker 1: We could make it larger. We could make it smaller.
• 2:03:28
  Speaker 1: The physics would remain unchanged. What matters is not the
• 2:03:32
  Speaker 1: number itself. What matters is that an invariant finite speed exists.
• 2:03:38
  Speaker 1: That is why theoretical physicists often work with systems of
• 2:03:42
  Speaker 1: units in which the numerical value of the speed of
• 2:03:45
  Speaker 1: light is simply one. This does not mean they believe
• 2:03:48
  Speaker 1: light has somehow slowed down to one metre per second.
• 2:03:51
  Speaker 1: It means the units have been chosen so that the
• 2:03:54
  Speaker 1: conversion factor between space and time no longer needs to
• 2:03:57
  Speaker 1: be written explicitly. A second... and the corresponding light travel
• 2:04:02
  Speaker 1: distance can be treated in matching units. This can make
• 2:04:05
  Speaker 1: relativistic equations much cleaner. The constant has not disappeared from
• 2:04:10
  Speaker 1: the physics. Its role has been absorbed into the unit system.
• 2:04:15
  Speaker 1: That is a useful clue. If changing units can make
• 2:04:18
  Speaker 1: the numerical value of the speed of light equal to one,
• 2:04:21
  Speaker 1: then the important thing was never the numerical value. The
• 2:04:25
  Speaker 1: important thing was the invariant relationship. This is similar to
• 2:04:29
  Speaker 1: changing between kilometres and miles. The number describing a journey changes.
• 2:04:34
  Speaker 1: The journey does not. Likewise, changing units changes the numerical
• 2:04:40
  Speaker 1: value assigned to the speed of light. It does not
• 2:04:43
  Speaker 1: change the underlying geometry of spacetime, and that geometry is
• 2:04:46
  Speaker 1: what gives the constant its real significance. The invariant speed
• 2:04:51
  Speaker 1: determines how space and time mix between moving observers. It
• 2:04:55
  Speaker 1: separates time-like paths from light-like paths. It defines the edge
• 2:05:00
  Speaker 1: of every light cone. It limits the local propagation of
• 2:05:03
  Speaker 1: causal influence. It shapes the relationship between mass, momentum and energy.
• 2:05:10
  Speaker 1: And it ensures that different inertial observers can disagree about
• 2:05:13
  Speaker 1: distances and durations, while still preserving the same deeper physical structure.
• 2:05:19
  Speaker 1: Seen this way, light almost becomes the messenger rather than
• 2:05:22
  Speaker 1: the main subject. Photons reveal the invariant speed because they
• 2:05:27
  Speaker 1: are massless and therefore travel along null paths in vacuum.
• 2:05:31
  Speaker 1: But the speed itself belongs to the architecture underneath. This
• 2:05:35
  Speaker 1: is why the phrase speed of light is both perfectly
• 2:05:38
  Speaker 1: correct and slightly incomplete. It describes what light does. But
• 2:05:43
  Speaker 1: it also describes much more than light. It tells us
• 2:05:47
  Speaker 1: how space-time is organised. It tells us how cause and
• 2:05:51
  Speaker 1: effect are bounded. It tells us how space and time
• 2:05:54
  Speaker 1: are connected. And in that sense, one of the most
• 2:05:58
  Speaker 1: familiar numbers in physics is not really just a speed
• 2:06:01
  Speaker 1: at all. It is one of the constants that helps
• 2:06:04
  Speaker 1: define the shape of reality. Special relativity gives us a
• 2:06:09
  Speaker 1: remarkably powerful description of motion. But it does not describe
• 2:06:14
  Speaker 1: every possible situation in the universe. Its cleanest form applies
• 2:06:18
  Speaker 1: to inertial observers moving through flat spacetime. where gravity can
• 2:06:23
  Speaker 1: be neglected and where observers are not undergoing sustained acceleration.
• 2:06:28
  Speaker 1: Within that setting, the rules are beautifully precise. Different observers
• 2:06:33
  Speaker 1: can disagree about time, they can disagree about distance, they
• 2:06:37
  Speaker 1: can disagree about simultaneity, but they agree on the underlying
• 2:06:42
  Speaker 1: Lorentzian structure of spacetime and on the invariant speed that
• 2:06:46
  Speaker 1: light follows through vacuum. The difficulty begins when gravity enters
• 2:06:52
  Speaker 1: the picture. Albert Einstein eventually realised that gravity could not
• 2:06:56
  Speaker 1: simply be added to special relativity, as though it were
• 2:06:59
  Speaker 1: one more ordinary force. His general theory of relativity replaced
• 2:07:03
  Speaker 1: the idea of gravity as a conventional pull acting across
• 2:07:07
  Speaker 1: fixed space with a deeper picture in which matter and
• 2:07:10
  Speaker 1: energy influence the geometry of spacetime itself. Spacetime can curve.
• 2:07:16
  Speaker 1: Objects then follow path through that curved geometry. This means
• 2:07:21
  Speaker 1: special relativity is not wrong when gravity appears. It remains
• 2:07:25
  Speaker 1: locally valid. Imagine an observer freely falling through a gravitational field.
• 2:07:32
  Speaker 1: Within a sufficiently small region around that observer, the laws
• 2:07:35
  Speaker 1: of physics look very much like those of special relativity.
• 2:07:40
  Speaker 1: If the observer measures a beam of light passing nearby
• 2:07:42
  Speaker 1: in vacuum, the measured local speed is still the invariant
• 2:07:46
  Speaker 1: speed of light. That remains true even in strongly curved spacetime.
• 2:07:51
  Speaker 1: What can become complicated is the coordinate speed assigned to
• 2:07:54
  Speaker 1: light over large distances. Coordinates are tools for labelling events.
• 2:07:59
  Speaker 1: In curved spacetime there are many possible ways of choosing
• 2:08:03
  Speaker 1: those labels. Depending on the coordinates used, the calculated rate
• 2:08:07
  Speaker 1: at which light changes position can appear different from the
• 2:08:10
  Speaker 1: familiar vacuum speed. Near a black hole, for example, certain
• 2:08:15
  Speaker 1: coordinate systems can make outgoing light appear to slow dramatically
• 2:08:19
  Speaker 1: as it approaches the event horizon. That does not mean
• 2:08:22
  Speaker 1: a nearby freely falling observer watches the light itself crawl
• 2:08:26
  Speaker 1: past at a reduced local speed. Locally, light still passes
• 2:08:31
  Speaker 1: at the invariant speed. The apparent difference belongs to the
• 2:08:34
  Speaker 1: coordinate description across curved spacetime. This distinction between local measurements
• 2:08:40
  Speaker 1: and large-scale coordinates is extremely important. It also helps explain
• 2:08:45
  Speaker 1: one of the most common apparent violations of the light
• 2:08:47
  Speaker 1: speed limit. The universe is expanding. On sufficiently large scales,
• 2:08:52
  Speaker 1: distant galaxies can recede from us at a rate greater
• 2:08:55
  Speaker 1: than the speed of light. At first, that seems to
• 2:08:58
  Speaker 1: contradict everything special relativity has told us. If nothing locally
• 2:09:03
  Speaker 1: outruns light, how can a distant galaxy appear to retreat
• 2:09:06
  Speaker 1: faster than light? The answer is that cosmological recession is
• 2:09:11
  Speaker 1: not simply an object racing through nearby space in the
• 2:09:13
  Speaker 1: ordinary special relativistic sense. The distance between widely separated regions
• 2:09:19
  Speaker 1: can increase because the geometry of the expanding universe itself evolves.
• 2:09:24
  Speaker 1: General relativity describes that situation. A sufficiently distant galaxy can
• 2:09:29
  Speaker 1: therefore have a recession rate greater than the speed of light,
• 2:09:32
  Speaker 1: without locally passing an observer at a faster-than-light velocity. If
• 2:09:37
  Speaker 1: you placed an observer near that galaxy, the galaxy would
• 2:09:40
  Speaker 1: not shoot past them in violation of special relativity. Locally,
• 2:09:45
  Speaker 1: the same relativistic limits remain intact. This is why statements
• 2:09:49
  Speaker 1: such as nothing can ever move faster than light need
• 2:09:52
  Speaker 1: a little care. They're useful shorthand, but they can become
• 2:09:56
  Speaker 1: misleading when applied too broadly. The more precise statement is
• 2:10:00
  Speaker 1: that ordinary matter, signals and causal influences cannot locally propagate
• 2:10:04
  Speaker 1: through spacetime faster than the invariant speed. That is narrower claim,
• 2:10:10
  Speaker 1: and it is the one supported by relativity. There have
• 2:10:14
  Speaker 1: been hypothetical ideas involving faster-than-light particles. One of the most
• 2:10:18
  Speaker 1: famous is the tachyon. A tachyon would be a hypothetical
• 2:10:22
  Speaker 1: particle that always moved faster than light. In mathematical discussions,
• 2:10:27
  Speaker 1: such objects have occasionally appeared as possible solutions or speculative concepts.
• 2:10:32
  Speaker 1: But no verified tachyonic particle carrying ordinary usable information faster
• 2:10:36
  Speaker 1: than light has ever been observed. There is also a
• 2:10:40
  Speaker 1: deeper difficulty. Within ordinary special relativity, Controllable faster-than-light signalling tends
• 2:10:46
  Speaker 1: to create problems with causality. Because different observers disagree about
• 2:10:51
  Speaker 1: the ordering of space-like separated events, a faster-than-light signal can
• 2:10:56
  Speaker 1: appear in some frames to travel backwards in time. With
• 2:10:59
  Speaker 1: the right arrangement of observers and return messages, it becomes
• 2:11:03
  Speaker 1: possible to construct causal loops in which a reply arrives
• 2:11:06
  Speaker 1: before the original message is sent. That is not merely unusual.
• 2:11:11
  Speaker 1: It undermines the ordinary relationship between cause and effect. Quantum
• 2:11:15
  Speaker 1: physics introduces another source of confusion. Entanglement can produce correlations
• 2:11:21
  Speaker 1: between distant particles that are stronger than classical intuition would expect.
• 2:11:26
  Speaker 1: Measurements made on entangled particles can remain correlated even when
• 2:11:30
  Speaker 1: the particles are separated by enormous distances. Albert Einstein famously
• 2:11:35
  Speaker 1: found this kind of behaviour deeply troubling. It can sound
• 2:11:39
  Speaker 1: as though one particle must somehow send a message instantly
• 2:11:43
  Speaker 1: to the other. But quantum entanglement does not provide a
• 2:11:46
  Speaker 1: controllable method for transmitting usable information faster than light. The
• 2:11:51
  Speaker 1: outcome of an individual measurement cannot be chosen in the
• 2:11:54
  Speaker 1: way required to encode and send an ordinary message. When
• 2:11:58
  Speaker 1: two distant observers later compare their results, the correlations become visible.
• 2:12:04
  Speaker 1: But that comparison itself requires conventional communication, limited by the
• 2:12:10
  Speaker 1: causal structure of spacetime. So quantum mechanics can be profoundly
• 2:12:14
  Speaker 1: non-classical without giving us a faster-than-light telephone. This is another
• 2:12:19
  Speaker 1: reason the invariant speed should be understood through causality, rather
• 2:12:23
  Speaker 1: than through a simple picture of racing objects. Special relativity
• 2:12:28
  Speaker 1: is really describing the structure within which causal relationships are organised.
• 2:12:33
  Speaker 1: Once seen this way, many of its most famous effects
• 2:12:36
  Speaker 1: begin to fit together. Time dilation arises because observers moving
• 2:12:41
  Speaker 1: relative to one another divide spacetime differently. Length contraction arises
• 2:12:45
  Speaker 1: from those same transformations. Relativity of simultaneity appears because there
• 2:12:50
  Speaker 1: is no universal slicing of spacetime into a single shared present.
• 2:12:56
  Speaker 1: Relativistic velocity addition preserves the invariant speed. Relativistic energy and
• 2:13:01
  Speaker 1: momentum prevent massive particles from being accelerated onto light-like paths.
• 2:13:07
  Speaker 1: Like cones, separate events that can be causally connected from
• 2:13:11
  Speaker 1: those that cannot. None of these ideas was added independently.
• 2:13:16
  Speaker 1: They are different consequences of the same geometry. Special relativity
• 2:13:21
  Speaker 1: begins to reach its limits when spacetime itself is curved,
• 2:13:25
  Speaker 1: or when acceleration becomes central to the problem. General relativity
• 2:13:30
  Speaker 1: extends the picture. Quantum physics adds another layer of strangeness.
• 2:13:36
  Speaker 1: cosmology reveals scales on which the expansion of spacetime can
• 2:13:41
  Speaker 1: produce effects that look very different from ordinary motion. But
• 2:13:46
  Speaker 1: through all of these extensions, one principle remains remarkably persistent. Locally,
• 2:13:52
  Speaker 1: the invariant speed continues to define the boundary of causal propagation.
• 2:13:57
  Speaker 1: That is the deeper meaning behind what we casually call
• 2:14:00
  Speaker 1: the speed of light. It is not merely the speed
• 2:14:02
  Speaker 1: of photons, It is not simply the fastest number on
• 2:14:06
  Speaker 1: a cosmic speedometer. It is the constant that helps determine
• 2:14:10
  Speaker 1: how space and time are connected, which paths matter can follow,
• 2:14:15
  Speaker 1: which events can influence one another, and how the causal
• 2:14:18
  Speaker 1: structure of relativistic spacetime is arranged. Light makes that structure
• 2:14:23
  Speaker 1: visible to us, but the structure itself runs much deeper
• 2:14:26
  Speaker 1: than light. So what does the speed of light really mean?
• 2:14:30
  Speaker 1: At first, it seems like a simple measurement. Light travels
• 2:14:34
  Speaker 1: through vacuum at approximately 300,000 km per second. But special
• 2:14:39
  Speaker 1: relativity reveals that this number is not merely a property
• 2:14:42
  Speaker 1: of light. It is the invariant speed built into the
• 2:14:46
  Speaker 1: geometry of spacetime itself. It determines how measurements of space
• 2:14:51
  Speaker 1: and time are related. It helps define which events can
• 2:14:54
  Speaker 1: influence one another. And it appears again and again wherever
• 2:14:58
  Speaker 1: relativistic physics connects motion, energy, momentum … distance, duration and causality.
• 2:15:08
  Speaker 1: The first clues appeared through electromagnetism. In the 19th century,
• 2:15:12
  Speaker 1: James Clerk Maxwell showed that electric and magnetic fields could
• 2:15:17
  Speaker 1: propagate together as electromagnetic waves. His equations predicted a definite
• 2:15:22
  Speaker 1: propagation speed. That speed matched the measured speed of light.
• 2:15:27
  Speaker 1: The implication was extraordinary. Light itself was electromagnetic. But the
• 2:15:33
  Speaker 1: discovery also created a problem. Known waves seemed to travel
• 2:15:38
  Speaker 1: through some kind of medium, so physicists proposed the luminiferous
• 2:15:42
  Speaker 1: ether as the substance through which electromagnetic waves might move.
• 2:15:47
  Speaker 1: If that ether provided a preferred state of rest, Earth's
• 2:15:51
  Speaker 1: motion through it should have produced detectable effects. Experiments such
• 2:15:55
  Speaker 1: as the one performed by Albert Abraham Michelson and Edward
• 2:15:59
  Speaker 1: Williams Morley failed to reveal the expected ether wind. That
• 2:16:03
  Speaker 1: did not instantly settle the matter, but it helped expose
• 2:16:07
  Speaker 1: a deeper conflict between classical mechanics and electromagnetic theory. Albert
• 2:16:12
  Speaker 1: Einstein approached that conflict differently. In 1905, he began from
• 2:16:17
  Speaker 1: two basic principles. The laws of physics take the same
• 2:16:21
  Speaker 1: form in every inertial reference frame, and every inertial observer
• 2:16:25
  Speaker 1: measures the same speed of light in vacuum. Those two
• 2:16:28
  Speaker 1: ideas sound simple. Their consequences are not. If the speed
• 2:16:32
  Speaker 1: of light is invariant, then observers moving relative to one
• 2:16:36
  Speaker 1: another cannot all agree on universal measurements of space and time.
• 2:16:40
  Speaker 1: Something has to change. And what changes is our classical
• 2:16:44
  Speaker 1: idea of where and when. Simultaneity becomes relative. Two events
• 2:16:49
  Speaker 1: judged simultaneous by one observer need not be simultaneous for
• 2:16:53
  Speaker 1: another moving observer. Clocks moving relative to an observer accumulate
• 2:16:58
  Speaker 1: less time. lengths measured along the direction of relative motion
• 2:17:02
  Speaker 1: become shorter. These are not independent curiosities. They are different
• 2:17:07
  Speaker 1: consequences of the same relativistic structure. The light clock makes
• 2:17:12
  Speaker 1: this especially clear. Imagine light bouncing between two mirrors. For
• 2:17:17
  Speaker 1: the person travelling with the clock, the light follows a
• 2:17:20
  Speaker 1: simple path between them. For an observer who sees the
• 2:17:23
  Speaker 1: clock moving sideways, the light travels along a longer diagonal route.
• 2:17:28
  Speaker 1: Yet both observers must measure the same vacuum speed of light.
• 2:17:32
  Speaker 1: The longer path cannot be explained by giving the light
• 2:17:35
  Speaker 1: a greater speed. The measured time must instead be different.
• 2:17:39
  Speaker 1: From that simple geometric requirement, time dilation appears. Hendrik Antun
• 2:17:45
  Speaker 1: Lawrence provided the mathematical relationships that describe how space and
• 2:17:50
  Speaker 1: time coordinates change between inertial frames. Herman Minkowski then showed
• 2:17:56
  Speaker 1: how those relationships could be understood geometrically. Space and time
• 2:18:00
  Speaker 1: were no longer best treated as independent backgrounds. Together they
• 2:18:04
  Speaker 1: formed space-time. Observers could disagree about distances and durations while
• 2:18:09
  Speaker 1: still agreeing on deeper invariant relationships between events. The old
• 2:18:14
  Speaker 1: picture of universal space and universal time gave way to
• 2:18:18
  Speaker 1: an invariant spacetime geometry. The speed of light sits inside
• 2:18:22
  Speaker 1: that geometry. It is also why massive objects cannot simply
• 2:18:26
  Speaker 1: be accelerated through the light speed barrier. A particle with
• 2:18:30
  Speaker 1: non-zero rest mass can move closer and closer to the
• 2:18:34
  Speaker 1: invariant speed. But as it does, its relativistic energy and
• 2:18:38
  Speaker 1: momentum increase dramatically. Reaching the speed of light exactly would
• 2:18:43
  Speaker 1: require an unbounded amount of energy. So massive matter remains
• 2:18:47
  Speaker 1: on time-like paths through space-time. Photons behave differently. They have
• 2:18:53
  Speaker 1: zero rest mass and follow light-like or null paths through vacuum.
• 2:18:57
  Speaker 1: They do not begin below the speed of light and
• 2:18:59
  Speaker 1: accelerate towards it. The invariant speed is simply the speed
• 2:19:03
  Speaker 1: associated with their class of motion. And because there is
• 2:19:07
  Speaker 1: no valid inertial frame moving alongside a photon, there is
• 2:19:11
  Speaker 1: no ordinary scientific meaning to asking what the universe looks
• 2:19:14
  Speaker 1: like from a photon stationary perspective. The proper time along
• 2:19:18
  Speaker 1: an ideal light-like path is zero. But that does not
• 2:19:22
  Speaker 1: create a usable photon rest frame. The distinction matters. The
• 2:19:27
  Speaker 1: speed of light also defines the structure of cause and effect.
• 2:19:31
  Speaker 1: Light cones divide space-time into regions. Inside the future light
• 2:19:36
  Speaker 1: cone lie events that can potentially be influenced by a
• 2:19:38
  Speaker 1: signal travelling at or below the invariant speed. Inside the
• 2:19:43
  Speaker 1: past light cone lie events that could have influenced the present.
• 2:19:48
  Speaker 1: Outside those cones lie space-like separated events, too distant from
• 2:19:52
  Speaker 1: one another for even light to connect them in the
• 2:19:54
  Speaker 1: available time. That is why faster-than-light signalling creates such serious
• 2:20:00
  Speaker 1: trouble in special relativity. Once signals are allowed to travel
• 2:20:04
  Speaker 1: outside ordinary light cones, some observers can describe effects occurring
• 2:20:09
  Speaker 1: before their causes. The speed of a light is therefore
• 2:20:13
  Speaker 1: not merely the fastest speed familiar to physics. It is
• 2:20:16
  Speaker 1: part of the boundary that protects causal order. The same
• 2:20:20
  Speaker 1: constant appears yet again when mass and energy are connected.
• 2:20:24
  Speaker 1: Einstein's famous rest-energy relationship can be spoken as energy equals
• 2:20:28
  Speaker 1: mass multiplied by the speed of light multiplied by the
• 2:20:32
  Speaker 1: speed of light. The appearance of the speed of light
• 2:20:35
  Speaker 1: there is not an unrelated coincidence. It reflects the same
• 2:20:39
  Speaker 1: relativistic framework that connects space and time. The constant appears
• 2:20:44
  Speaker 1: in energy. It appears in momentum. It appears in the
• 2:20:48
  Speaker 1: Lorentz transformation. It appears in the geometry of light cones.
• 2:20:52
  Speaker 1: It appears whenever the structure of spacetime becomes impossible to ignore.
• 2:20:57
  Speaker 1: And this is not merely a beautiful theoretical construction. Special
• 2:21:01
  Speaker 1: relativity has been tested repeatedly. Atmospheric muons survive long enough
• 2:21:06
  Speaker 1: to reach Earth's surface because their motion produces the time
• 2:21:09
  Speaker 1: dilation predicted by relativity. Particle accelerators require relativistic energy and
• 2:21:15
  Speaker 1: momentum to describe particles travelling extremely close to the speed
• 2:21:20
  Speaker 1: of light. Precision clocks reveal measurable differences in accumulated time
• 2:21:25
  Speaker 1: when they follow different motions. Experiments continue to test Lorentz
• 2:21:30
  Speaker 1: invariance with extraordinary sensitivity. So far, special relativity continues to
• 2:21:36
  Speaker 1: work across the domains where it applies. That success is
• 2:21:40
  Speaker 1: what gives the theory its authority, not the fame of Einstein,
• 2:21:45
  Speaker 1: not the elegance of the equations, but the repeated agreement
• 2:21:49
  Speaker 1: between prediction and reality. And perhaps the most important lesson
• 2:21:53
  Speaker 1: is that the universe is not simply a collection of
• 2:21:55
  Speaker 1: objects moving through a fixed stage called space, while a
• 2:21:59
  Speaker 1: universal clock ticks somewhere in the background. Space and time
• 2:22:03
  Speaker 1: are intertwined. Motion changes how they are measured. Energy and
• 2:22:07
  Speaker 1: momentum are tied into the same structure. Corsality follows boundaries
• 2:22:12
  Speaker 1: drawn by the invariant speed. Light revealed all of this
• 2:22:17
  Speaker 1: because it refused to behave the way classical intuition expected.
• 2:22:21
  Speaker 1: Its speed did not adjust itself to suit the observer. Instead,
• 2:22:26
  Speaker 1: space and time adjusted their relationship. So the speed of
• 2:22:30
  Speaker 1: light is much more than a very large number. It
• 2:22:34
  Speaker 1: is a window into the hidden geometry beneath motion. A
• 2:22:37
  Speaker 1: constant that links distance with duration. A boundary between different
• 2:22:43
  Speaker 1: kinds of space-time paths. A limit on local causal influence.
• 2:22:49
  Speaker 1: and one of the deepest clues we have to the
• 2:22:52
  Speaker 1: way every event in the universe can be connected to
• 2:22:55
  Speaker 1: every other. What began as the speed of light turns
• 2:22:59
  Speaker 1: out to be something far more fundamental. It is part
• 2:23:02
  Speaker 1: of the structure that holds space, time, motion, energy and
• 2:23:08
  Speaker 1: causality together.