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Can we build a warp drive? · Daniel and Kelly’s Extraordinary Universe

• 0:08
  Speaker 1: Traveling to the stars always seems so exciting in the movies.
• 0:12
  Speaker 1: At least it involves lots of dramatic wooshing noises. There's
• 0:16
  Speaker 1: some strengths of light, exotic planets to visit, probably dramatic
• 0:20
  Speaker 1: meetings with aliens. You also noticed in those movies everybody
• 0:24
  Speaker 1: is always well rested. They walk everywhere with a purpose,
• 0:28
  Speaker 1: and they're wearing a well fitting uniform, and everybody seems
• 0:31
  Speaker 1: to be in great shape. I don't know about you,
• 0:34
  Speaker 1: but that's not like any travel experience that I've ever had. Realistically,
• 0:38
  Speaker 1: a trip to the stars is more likely to involve
• 0:41
  Speaker 1: tired people eating junk food and shopping at duty free stores.
• 0:45
  Speaker 1: It probably resembles the experience of a cruise ship more
• 0:48
  Speaker 1: than a trip on the Star Trek Enterprise. So load
• 0:51
  Speaker 1: up on the buffet because we're going to Alpha Centauri. Hi.
• 1:11
  Speaker 1: I'm Daniel. I'm a particle physicist, and you're listening to
• 1:15
  Speaker 1: the podcast Daniel and Jorge Explain the Universe, brought to
• 1:19
  Speaker 1: you by My Heart Radio. Jorge is still away. He's
• 1:22
  Speaker 1: my friend and collaborator and usual co host of this podcast,
• 1:26
  Speaker 1: in which we zoom all around the universe and try
• 1:29
  Speaker 1: to find interesting, amazing facts and talk to you about
• 1:32
  Speaker 1: them and explain them to you so that you really
• 1:35
  Speaker 1: understand them, so they're not just words that you hear
• 1:37
  Speaker 1: coming out of your mouth to try to impress your friends,
• 1:40
  Speaker 1: but actual concepts in your mind you can manipulate and
• 1:43
  Speaker 1: talk about with intelligence. And today we're gonna do more
• 1:46
  Speaker 1: than just zoom around the universe. We're going to talk
• 1:48
  Speaker 1: about how we're going to zoom around the universe. And
• 1:51
  Speaker 1: if you're like me, you like looking up at the
• 1:53
  Speaker 1: stars and imagining what it's like to be over there.
• 1:57
  Speaker 1: What would it be like to orbit that other star?
• 1:59
  Speaker 1: Are there planning it over there? Could you put your
• 2:01
  Speaker 1: foot on them? And I think there's a natural human
• 2:04
  Speaker 1: desire to explore, to see other parts of the world
• 2:07
  Speaker 1: and other parts of the universe. Well, the problem is
• 2:10
  Speaker 1: that the universe is big, frustratingly big, stubbornly huge. Like
• 2:16
  Speaker 1: the nearest star, the closest one to our sun, is
• 2:20
  Speaker 1: four point two light years away. It's called Proximus Centauri.
• 2:24
  Speaker 1: That's a huge distance by any measure. If you use kilometers,
• 2:28
  Speaker 1: which is sort of absurd, you've got a number like
• 2:30
  Speaker 1: forty trillion kilometers. It's sort of like we're on a
• 2:35
  Speaker 1: little island in the middle of nowhere. If anybody out
• 2:37
  Speaker 1: there has been to like Tahiti or a tiny little
• 2:39
  Speaker 1: dot in the Pacific Ocean, you know, the feeling of
• 2:42
  Speaker 1: standing on an island and being surrounded by water and
• 2:45
  Speaker 1: feeling like maybe there's nothing else out there. That's sort
• 2:48
  Speaker 1: of the way I feel standing on Earth, where in
• 2:51
  Speaker 1: an ocean of space, and everything else out there is
• 2:54
  Speaker 1: super duper far away. These distances, they're sort of hard
• 2:58
  Speaker 1: to grasp. You know. Let's talk about how long would
• 3:01
  Speaker 1: it take to get there. Well, if you travel on
• 3:03
  Speaker 1: speeds that are familiar here on Earth, like if you
• 3:06
  Speaker 1: traveled at the speed of a car, then going forty
• 3:09
  Speaker 1: trillion kilometers would take you about forty five million years.
• 3:13
  Speaker 1: Even if you travel at the speed of an airplane,
• 3:15
  Speaker 1: it would take you five million years. Now, nobody's actually
• 3:19
  Speaker 1: gonna drive to Alpha Centauri or even fly an airplane.
• 3:22
  Speaker 1: You can imagine some technology that might take you there
• 3:25
  Speaker 1: in a spaceship at a respectable fraction in the speed
• 3:28
  Speaker 1: of light, maybe five percent or ten percent. Even those
• 3:31
  Speaker 1: kind of ships would take hundreds of years to get
• 3:34
  Speaker 1: to Alpha Centauri. And who wants to board a ship
• 3:37
  Speaker 1: knowing that they're going to die on it, And who
• 3:39
  Speaker 1: wants to have kids on a ship knowing that those
• 3:41
  Speaker 1: kids will probably never set foot on land, any land,
• 3:45
  Speaker 1: on any planet. This kind of structure, of course, is
• 3:48
  Speaker 1: called a colony ship, where you have generations upon generations
• 3:51
  Speaker 1: of humanity living on board, and then eventually one day
• 3:54
  Speaker 1: some some group of people generations down the road, get
• 3:57
  Speaker 1: to actually land on that planet. That would work. That's
• 4:00
  Speaker 1: one way to explore the universe. But I want more.
• 4:03
  Speaker 1: I'm greedy, and I want to walk on those other
• 4:06
  Speaker 1: planets myself. But even if you traveled like at the
• 4:09
  Speaker 1: speed of light, it would still take you four years
• 4:12
  Speaker 1: to get to proximates centauri. That's a long time to
• 4:15
  Speaker 1: spend eating junk food and shopping duty free, And so
• 4:19
  Speaker 1: it makes you wonder is there any way to get
• 4:22
  Speaker 1: there faster? So today on the podcast, we're asking the
• 4:25
  Speaker 1: question can we build a warp drive to travel the universe?
• 4:35
  Speaker 1: I want to take a step back and talk about
• 4:37
  Speaker 1: how we travel the universe and sort of the size
• 4:39
  Speaker 1: of our horizons. You know, a hundred years ago or
• 4:42
  Speaker 1: five hundred years ago, things on the other side of
• 4:46
  Speaker 1: the Earth seemed unreachable. To travel to China, for example,
• 4:50
  Speaker 1: would take months or years. It's not the kind of
• 4:52
  Speaker 1: thing you could do in an afternoon or even a week. Now,
• 4:55
  Speaker 1: of course, because we have better technology for transportation, it's
• 4:59
  Speaker 1: not a big deal to go to the other side
• 5:00
  Speaker 1: of the planet. You can go there, you can come
• 5:02
  Speaker 1: back a couple of days later. So the scope about
• 5:05
  Speaker 1: the universe that we can explore has expanded and has
• 5:08
  Speaker 1: expanded because our technology has improved. And so the thing
• 5:12
  Speaker 1: to understand is that it's not actually distances that are important.
• 5:15
  Speaker 1: The number, the actual number of kilometers between you and
• 5:20
  Speaker 1: and another location, isn't the thing that determines whether or
• 5:23
  Speaker 1: not it's in sort of your sphere of explorability. What
• 5:27
  Speaker 1: determines that is the maximum speed you can travel. Back
• 5:31
  Speaker 1: when the fastest thing you can do is ride a horse,
• 5:34
  Speaker 1: then going across country was a huge endeavor, not something
• 5:37
  Speaker 1: you can do in days of weeks. Going to the
• 5:40
  Speaker 1: other side of the planet in less than months or
• 5:42
  Speaker 1: years was impossible. Now, of course, the top speed we
• 5:45
  Speaker 1: can travel is much much higher. We have airplanes who
• 5:48
  Speaker 1: can go hundreds of kilometers per hour, and so our
• 5:50
  Speaker 1: sphere of explorability now encompasses essentially the entire Earth, And
• 5:55
  Speaker 1: if you talk to old people who remember the day
• 5:57
  Speaker 1: when when those kind of technologies weren't wide the available
• 6:00
  Speaker 1: to them, the world seems to have suddenly gotten smaller.
• 6:04
  Speaker 1: So you might wonder, like, can science just continue? Can
• 6:08
  Speaker 1: science deliver and engine that brings the stars into our
• 6:11
  Speaker 1: sphere of explorability so that you'll be talking one day
• 6:15
  Speaker 1: to your great great grandkids about how amazing it is
• 6:19
  Speaker 1: that you can go to Alpha Centauri and and come
• 6:21
  Speaker 1: back in the same afternoon. That's the question we're focusing
• 6:25
  Speaker 1: on today. Is it possible for science to bring those
• 6:28
  Speaker 1: stars into our grasp. So before we dig into the question,
• 6:31
  Speaker 1: I of course walked around campus that you see Irvine,
• 6:34
  Speaker 1: and I asked people if they thought that a warp
• 6:36
  Speaker 1: drive is possible. How much faith did they have in
• 6:39
  Speaker 1: science or do they think that we have them already.
• 6:42
  Speaker 1: Before you hear these answers, think to yourself, do you
• 6:45
  Speaker 1: believe a warp drive is possible now or in the future.
• 6:49
  Speaker 1: Here's what people that you see Irhune had to say,
• 6:51
  Speaker 1: I honestly don't know enough about that to even answer it.
• 6:54
  Speaker 1: I don't know what a warp drive is yes, you
• 6:58
  Speaker 1: think like possible in the few you're possible today, uh future,
• 7:02
  Speaker 1: you know, I think so. I remember seeing a guide
• 7:08
  Speaker 1: that proved that it was possible, but you would have
• 7:11
  Speaker 1: to use a lot of energy, and it was changing
• 7:14
  Speaker 1: to spacetime ahead and afterwards maybe like today or in
• 7:21
  Speaker 1: the future or in the future today. Probably not at
• 7:25
  Speaker 1: the most point, I think it can well certainly not now.
• 7:28
  Speaker 1: So if all the questions I've ever asked people on
• 7:31
  Speaker 1: the street, this is the one that maybe got the
• 7:33
  Speaker 1: broadest set of responses. You have people saying I don't
• 7:37
  Speaker 1: know what a warp drive is. You have people saying
• 7:39
  Speaker 1: very confidently, yeah, I'm pretty sure we'll figure it out,
• 7:42
  Speaker 1: to people saying I think people could build them today.
• 7:45
  Speaker 1: It's crazy. And let me clarify again what I mean
• 7:48
  Speaker 1: by a warp drive. I mean an engine that could
• 7:50
  Speaker 1: take a spaceship from here to somewhere else faster than
• 7:54
  Speaker 1: light could get there. That's the goal. We don't want
• 7:56
  Speaker 1: to travel just close to the speed of light, because
• 7:58
  Speaker 1: even that would take us years and years to get anywhere.
• 8:01
  Speaker 1: The nearest stars for light years away, but other stars,
• 8:05
  Speaker 1: many more stars that we would love to visit in
• 8:07
  Speaker 1: our galaxy are hundreds or thousands of light years away.
• 8:11
  Speaker 1: Remember that our galaxy is a hundred thousand light years
• 8:14
  Speaker 1: across and the next galaxy is millions of light years away.
• 8:18
  Speaker 1: So if we want to explore the universe, if we
• 8:20
  Speaker 1: want to find alien life, if we want to see
• 8:23
  Speaker 1: crazy things that would never happen in our neighborhood of
• 8:26
  Speaker 1: the universe, after all, that's what's so amazing about traveling,
• 8:30
  Speaker 1: then we need to develop some sort of technology that
• 8:33
  Speaker 1: lets us get to places faster than lightwood get there.
• 8:36
  Speaker 1: And that's the question we're going to dig into today.
• 8:39
  Speaker 1: But first, let's take a quick break. We're back and
• 8:54
  Speaker 1: we're talking about whether we can build an engine we
• 8:57
  Speaker 1: could put in a starship that would take us somewhere
• 9:00
  Speaker 1: faster than light would get there. So the naturally, the
• 9:03
  Speaker 1: first question you might ask is can we travel faster
• 9:06
  Speaker 1: than light? And here physics is pretty specific. Physics says no,
• 9:11
  Speaker 1: nothing can move through space faster than light moves through space.
• 9:15
  Speaker 1: And there's already a little clue there, there's a little wrinkle,
• 9:19
  Speaker 1: a little loophole you might want to try to take
• 9:22
  Speaker 1: advantage of. Nothing moves through space faster than light moves
• 9:25
  Speaker 1: through that space those of you either who know something
• 9:28
  Speaker 1: about physics and particle physics might have heard of Churenkoff light.
• 9:31
  Speaker 1: For example, when a muan moves really fast through ice,
• 9:35
  Speaker 1: it can emit this special kind of radiation of blue
• 9:38
  Speaker 1: glow called turank Off light, and it does that because
• 9:41
  Speaker 1: it's moving faster than the light moves through the ice. Right,
• 9:45
  Speaker 1: So muans can go through ice faster than light goes
• 9:48
  Speaker 1: through ice, and they produced this turank Off radiation sort
• 9:52
  Speaker 1: of for the same reason that a plane produces a
• 9:54
  Speaker 1: sonic boom. The muans are traveling faster than the light
• 9:58
  Speaker 1: they make, and so the light they catch up to
• 10:00
  Speaker 1: the light they make and they're adding to it creates
• 10:03
  Speaker 1: this wake, right, So it's sort of like alluminal bloom,
• 10:06
  Speaker 1: not a sonic boom. But that doesn't mean that you
• 10:10
  Speaker 1: could travel through space faster than light can travel through space.
• 10:14
  Speaker 1: It just means that in some materials, some particles can
• 10:17
  Speaker 1: travel through that material faster than light travels through that material.
• 10:21
  Speaker 1: But the speed of light in a vacuum is still
• 10:24
  Speaker 1: the absolute top speed anything can move through space. It
• 10:28
  Speaker 1: just so happens that ice slows light down more than
• 10:31
  Speaker 1: it slows down muance. For example, so you get this
• 10:34
  Speaker 1: special little loophole. But loopholes are a key. We want
• 10:37
  Speaker 1: to pay very careful attention to exactly what the laws
• 10:41
  Speaker 1: of physics say so we can try to exploit them later.
• 10:45
  Speaker 1: But back to traveling faster than the speed of light.
• 10:48
  Speaker 1: You've probably heard me say it and learned it in
• 10:49
  Speaker 1: lots of other places. Is impossible to travel faster than
• 10:52
  Speaker 1: the speed of light, and not just because it would
• 10:55
  Speaker 1: require you to have infinite mass or anything else, but
• 10:58
  Speaker 1: just because the universe does not out according to special relativity.
• 11:01
  Speaker 1: There is no way to get faster than the speed
• 11:04
  Speaker 1: of light. In fact, you can't even travel at the
• 11:07
  Speaker 1: speed of light if you have any mass at all.
• 11:10
  Speaker 1: Only massless things like photons and gravitons can travel at
• 11:14
  Speaker 1: the speed of light. So unless you have a way
• 11:16
  Speaker 1: to transform your spaceship into light and beam it over there,
• 11:19
  Speaker 1: you can't even travel at the speed of light. And
• 11:22
  Speaker 1: you might ask, okay, but that's the way we think today,
• 11:25
  Speaker 1: that's today's physics idea of the way the universe works.
• 11:29
  Speaker 1: Isn't it possible that we're wrong? And that's a good point,
• 11:32
  Speaker 1: And I'm always saying on this podcast in other places
• 11:35
  Speaker 1: that we have so much to learn about the universe
• 11:37
  Speaker 1: that we've learned approximately zero percent of the physics of
• 11:40
  Speaker 1: the universe. And that might give you hope. It might
• 11:43
  Speaker 1: give you the idea that, well, there could be a
• 11:45
  Speaker 1: crack in that armor, or maybe later we'll learn that
• 11:47
  Speaker 1: that was wrong. And you know, there's always a possibility,
• 11:51
  Speaker 1: there's always a chance that future physics will discover that
• 11:54
  Speaker 1: that was not correct. But I'd be very surprised if
• 11:56
  Speaker 1: that were true. This is the kind of thing that
• 11:58
  Speaker 1: we have tested extensive We've come up with all sorts
• 12:01
  Speaker 1: of scenarios to try this. We've tested it out the wazoo,
• 12:04
  Speaker 1: We've even tested it into the wazoo, And it's the
• 12:07
  Speaker 1: cornerstone of modern quantum field theory. The special relativity and
• 12:12
  Speaker 1: the Lorenz groups that we used to build quantum field
• 12:15
  Speaker 1: theory would be totally broken if special relativity was wrong.
• 12:18
  Speaker 1: And this is the basic assumption of special relativity. So
• 12:22
  Speaker 1: it's one of the most well tested axioms in all
• 12:25
  Speaker 1: of modern physics that nothing can travel faster than the
• 12:28
  Speaker 1: speed of light. So I'd be really shocked if that
• 12:32
  Speaker 1: was cracked. If we found a way to move through
• 12:34
  Speaker 1: space faster than the speed of light. Now, I can't
• 12:36
  Speaker 1: rule it out definitively, because who knows what amazing things
• 12:40
  Speaker 1: the future physics will discover. Maybe we all live in
• 12:43
  Speaker 1: a simulation and there's a way to rewrite the program
• 12:46
  Speaker 1: so that things change, or who knows what. I can't
• 12:49
  Speaker 1: rule it out forever. But I don't think that that's
• 12:50
  Speaker 1: a fruitful path to developing a warp drive. And even
• 12:54
  Speaker 1: if you were to find a crack in that armor,
• 12:56
  Speaker 1: you'd still have all sorts of practical problems, like accelerating
• 12:59
  Speaker 1: to really high speeds. So you want to go a
• 13:02
  Speaker 1: million light years somewhere, traveling through space at those high
• 13:05
  Speaker 1: speeds is difficult because you have to accelerate to those
• 13:08
  Speaker 1: high speeds, which you can take a long long time
• 13:10
  Speaker 1: and a huge amount of energy. So theoretically I think
• 13:14
  Speaker 1: it's very unlikely, and practically I don't think it's a
• 13:17
  Speaker 1: good approach. But I think the lesson to learn from
• 13:19
  Speaker 1: that thought experiment is that we should look for loopholes.
• 13:23
  Speaker 1: After all, what is our goal is our goal to
• 13:26
  Speaker 1: travel faster than light. I don't have an inherent desire
• 13:28
  Speaker 1: to move through space faster than the speed of light.
• 13:32
  Speaker 1: What I want to do is I want to get
• 13:34
  Speaker 1: to some distant star faster than the lightwood get there.
• 13:38
  Speaker 1: I want to get to have Proximus Centauri, for example,
• 13:40
  Speaker 1: in less than four years. I'd love to do it
• 13:42
  Speaker 1: in an afternoon. So my goal is not actually to
• 13:46
  Speaker 1: travel through space faster than the speed of light. What
• 13:49
  Speaker 1: I want to do is to get there faster than
• 13:51
  Speaker 1: lightwood get there. And that sounds like it's basically saying
• 13:55
  Speaker 1: the same thing, but there's an important difference because the
• 13:59
  Speaker 1: rule the actual limitation according to special relativity, it's not
• 14:03
  Speaker 1: about arriving somewhere faster than the speed of light would
• 14:06
  Speaker 1: move through that space. It's about moving through space faster
• 14:09
  Speaker 1: than the speed of light. There's an opportunity there. Instead
• 14:13
  Speaker 1: of just moving through space and accepting that the space
• 14:16
  Speaker 1: between here and Proximus Centauri is four million light years,
• 14:19
  Speaker 1: what if we could somehow manipulate that space. What if
• 14:22
  Speaker 1: we could squeeze that space, or twist it or bend it,
• 14:25
  Speaker 1: or do something to it so that we didn't have
• 14:28
  Speaker 1: to move through as much space, so we could keep
• 14:31
  Speaker 1: under that speed limit but still get there in a
• 14:34
  Speaker 1: shorter amount of time. That's the key, and I think
• 14:37
  Speaker 1: there's there's some credit we owe here to science fiction
• 14:40
  Speaker 1: authors because a lot of these ideas, the possibility of
• 14:44
  Speaker 1: getting somewhere faster than life could get there, come originally
• 14:47
  Speaker 1: from science fiction. Those people are thinking about the impact
• 14:51
  Speaker 1: of new technologies and what the future might look like,
• 14:54
  Speaker 1: and so their job is to think most creatively, to
• 14:57
  Speaker 1: think how could we change human society or how human
• 15:01
  Speaker 1: society changed if we had this new technology. So they're
• 15:04
  Speaker 1: unbound by the rules of physics and certainly by the
• 15:07
  Speaker 1: practicalities of the engineering, free to think inventively about how
• 15:12
  Speaker 1: to change our lives and explore the universe. So kudos
• 15:15
  Speaker 1: to them for coming up with the whole concept of
• 15:17
  Speaker 1: a warp drive, and of course I love it in
• 15:19
  Speaker 1: all of those movies. But the next step, once the
• 15:22
  Speaker 1: science fiction authors have come up with the idea is
• 15:25
  Speaker 1: for physicists to figure out how to make it possible
• 15:28
  Speaker 1: to take an idea from woe that would be super awesome.
• 15:31
  Speaker 1: I wish we could do that too, you know, there
• 15:34
  Speaker 1: might be a way that we could do it. And
• 15:36
  Speaker 1: then figuring out how to sort of avoid the physics
• 15:39
  Speaker 1: blockades to work away around the rules of the universe
• 15:43
  Speaker 1: that seemed to be preventing that from being possible, and
• 15:46
  Speaker 1: once the physicists have figured out how to make it
• 15:48
  Speaker 1: sort of theoretically possible, then to hand it off to
• 15:51
  Speaker 1: the next people in the chain, which are of course
• 15:53
  Speaker 1: the engineers, because they have to actually build it, you know,
• 15:56
  Speaker 1: design it and build it and make it practical, build
• 15:59
  Speaker 1: something which less than ten quadrillion dollars or let use,
• 16:02
  Speaker 1: less than the mass of the universe. So that's the
• 16:05
  Speaker 1: sort of progression of how you go from I really
• 16:08
  Speaker 1: want this thing to you know, boarding the next flight
• 16:11
  Speaker 1: to Alpha Centauri at four o'clock. Start with the science fiction,
• 16:14
  Speaker 1: move through the physicists, and get to the engineers. So
• 16:17
  Speaker 1: where are we on that step of the process. Clearly
• 16:20
  Speaker 1: science fiction authors have thought of the idea of warp drive,
• 16:23
  Speaker 1: and now we're in this step where physicists are thinking
• 16:25
  Speaker 1: what could we do, what loopholes could we exploit? And so,
• 16:29
  Speaker 1: as I mentioned a few moments ago, the idea here
• 16:32
  Speaker 1: is not to move through space faster than light can
• 16:35
  Speaker 1: move through space, because that's just forbidden, but instead to
• 16:38
  Speaker 1: try to manipulate space. And if manipulate space sounds weird
• 16:43
  Speaker 1: to you, then get ready for some weirdness, because we're
• 16:45
  Speaker 1: gonna do a lot of this on the podcast, where
• 16:47
  Speaker 1: we use normal sounding words together in a way that
• 16:51
  Speaker 1: might make no sense initially, And that's because we're pushing
• 16:55
  Speaker 1: the boundaries of what we can do and what we
• 16:56
  Speaker 1: can understand, and doing that requires challenging our assumption. And
• 17:00
  Speaker 1: so what does it mean to manipulate space? Well, first
• 17:03
  Speaker 1: you have to let go of maybe your initial concept
• 17:07
  Speaker 1: of space, space being emptiness, space being nothing. If you
• 17:11
  Speaker 1: if I say the words space and you close your eyes,
• 17:14
  Speaker 1: do you imagine twinkling stars out there? Sure? But what's
• 17:17
  Speaker 1: between us and those stars? Maybe you imagine some sort
• 17:20
  Speaker 1: of wire frame grid of emptiness, right, just like the rulers,
• 17:25
  Speaker 1: just like the notches on a ruler between here and there.
• 17:28
  Speaker 1: And you might think, well, that's just sort of human interpretation,
• 17:31
  Speaker 1: is just an overlay we put onto the nothingness that's
• 17:34
  Speaker 1: between here and space. But space is not nothingness. And
• 17:38
  Speaker 1: I'm not talking about the quantum fields that are inside it,
• 17:41
  Speaker 1: or the particles that are zooming around, or the little
• 17:43
  Speaker 1: bits of radiation. I'm not making an argument that space
• 17:46
  Speaker 1: is never actually empty. I'm saying that space is more
• 17:49
  Speaker 1: than just the backdrop. It's not just the stage on
• 17:53
  Speaker 1: which the universe plays out. Space itself is dynamical. It
• 17:57
  Speaker 1: can do things that nothingness can't, like what well space
• 18:02
  Speaker 1: can bend. We've talked on this podcast about what gravity is.
• 18:06
  Speaker 1: Newton thought about gravity as a force between two objects,
• 18:10
  Speaker 1: pulling them together, but Einstein showed us that it's actually
• 18:13
  Speaker 1: more natural to talk about gravity as the bending of
• 18:17
  Speaker 1: space when the presence of mass and energy. So, for example,
• 18:21
  Speaker 1: you can imagine the Earth moving around the Sun, not
• 18:24
  Speaker 1: as the Sun pulling on the Earth using some force,
• 18:27
  Speaker 1: but the Sun distorting space so that it's most natural
• 18:31
  Speaker 1: for the Earth to move in this orbit, to blend
• 18:33
  Speaker 1: its velocity with the bending of space to come up
• 18:35
  Speaker 1: with a stable motion. So it's actually quite an old
• 18:39
  Speaker 1: idea that you could manipulate space. That space is not nothing,
• 18:43
  Speaker 1: that it can bend. This is an idea from Einstein's
• 18:46
  Speaker 1: theory of relativity that space can bend. So already that
• 18:50
  Speaker 1: breaks the idea that space is nothing, and it opens
• 18:52
  Speaker 1: the door to space doing other things right. Space can bend.
• 18:56
  Speaker 1: It can also ripple. We've seen gravitational waves when huge
• 19:00
  Speaker 1: objects like binary black holes accelerate around each other and
• 19:03
  Speaker 1: collapse into a single black hole. Then you get ripples
• 19:06
  Speaker 1: in space. What does that mean. It doesn't mean anything
• 19:10
  Speaker 1: if space is emptiness. But it means something if space
• 19:14
  Speaker 1: is a thing, if it has properties, if it can
• 19:16
  Speaker 1: do stuff, if it can be distorted and twisted. So
• 19:19
  Speaker 1: we're familiar with space bending due to gravity, were recently
• 19:24
  Speaker 1: aware the space can do things like ripple, and space
• 19:27
  Speaker 1: can also expand we know from the Big Bang, we
• 19:31
  Speaker 1: know from dark energy that space is expanding. Right now.
• 19:35
  Speaker 1: Sixty of all the energy in the universe is devoted
• 19:38
  Speaker 1: to something we call dark energy, which we don't understand.
• 19:41
  Speaker 1: But whatever it is is expanding space all the time.
• 19:45
  Speaker 1: It's creating new space between us and other galaxies. Right now,
• 19:49
  Speaker 1: it's doing it. It's making a new space between you
• 19:51
  Speaker 1: and the person sitting next to you. It's everywhere. So
• 19:55
  Speaker 1: space can do all of these things, and the amazing
• 19:58
  Speaker 1: thing is that they're no limit to it. As far
• 20:01
  Speaker 1: as we know, there's no speed limit to how fast
• 20:05
  Speaker 1: you can shrink or expand space. Take for example, the
• 20:08
  Speaker 1: Big Bang. What happened in the very first moments of
• 20:11
  Speaker 1: the universe. The universe expanded very, very rapidly, much faster
• 20:16
  Speaker 1: than the speed of light, much faster than light could
• 20:19
  Speaker 1: have moved through that space. That's why, for example, the
• 20:22
  Speaker 1: universe now is larger than the speed of light times
• 20:27
  Speaker 1: the age in the universe. How is that possible? If
• 20:29
  Speaker 1: nothing can travel faster than the speed of light, how
• 20:32
  Speaker 1: could stuff get further away from each other than light
• 20:36
  Speaker 1: could have traveled through that space. The answer, of course,
• 20:38
  Speaker 1: is space expanded. Inflation in the Big Bang is more
• 20:42
  Speaker 1: than just stuff moving through space. It's space itself expanding.
• 20:46
  Speaker 1: So this is an idea we're familiar with that space
• 20:48
  Speaker 1: can expand you might almost say the universe warped. You
• 20:52
  Speaker 1: might even think of the Big Bang is a huge
• 20:54
  Speaker 1: warping of space, and dark energy now is the continued
• 20:58
  Speaker 1: warping of space, all right, So that gives us an opportunity.
• 21:02
  Speaker 1: We're talking about how to get somewhere faster than light
• 21:05
  Speaker 1: would get us there. And the idea we're working towards
• 21:08
  Speaker 1: is not to try to move through space using some
• 21:10
  Speaker 1: specially fast Zippi engine, but to change the nature of
• 21:14
  Speaker 1: the problem by shrinking the space. And that's the idea
• 21:18
  Speaker 1: for a warp drive. That's how we might actually make
• 21:21
  Speaker 1: it work. The idea is like this, you want to
• 21:24
  Speaker 1: get from here to Alpha Centauri. How do you do
• 21:27
  Speaker 1: it well, you don't just move through that space. You
• 21:29
  Speaker 1: somehow shrink the space between you and that star. You
• 21:34
  Speaker 1: squeeze it, just the way the Sun changes the shape
• 21:37
  Speaker 1: the whole nature of space in the Solar System. Use
• 21:40
  Speaker 1: some mass and energy, and in a moment we'll talk
• 21:42
  Speaker 1: about the details of what we know about how engineers
• 21:45
  Speaker 1: might actually make that happen. Use mass and energy in
• 21:48
  Speaker 1: some way to squeeze the space so that instead of
• 21:50
  Speaker 1: having four point two light years between you and the star,
• 21:53
  Speaker 1: you have four point two meters. And similarly, you turn
• 21:57
  Speaker 1: around behind you, and instead of having four point two
• 22:01
  Speaker 1: meters between you and and where you've left, you can
• 22:04
  Speaker 1: expand the space behind you. So the idea for a
• 22:08
  Speaker 1: warp drive is something which shrinks the space in front
• 22:10
  Speaker 1: of you and expands the space behind you. In that way,
• 22:14
  Speaker 1: you're sort of inside a little bubble, and inside that
• 22:17
  Speaker 1: bubble you don't even need to move with respect to space.
• 22:21
  Speaker 1: It's sort of like instead of running through the airport,
• 22:26
  Speaker 1: you stand on a moving walkway and the walkway moves
• 22:29
  Speaker 1: for you. That's not perfect analogy, because in that analogy
• 22:32
  Speaker 1: the walkway is still moving. And I'll be talking about
• 22:35
  Speaker 1: like pulling the terminal closer to you instead of running
• 22:38
  Speaker 1: there and stretching the distance behind you. But that's the idea.
• 22:42
  Speaker 1: So you'd build the sort of warp drive that shrinks
• 22:45
  Speaker 1: the space in front of you, expands the space behind you,
• 22:48
  Speaker 1: and then you're in this sort of warp bubble, and
• 22:50
  Speaker 1: then you pop out of the bubble right and then
• 22:54
  Speaker 1: you're there. And because there's no limit on how fast
• 22:57
  Speaker 1: you can expand space or how much con shrink space,
• 23:01
  Speaker 1: in theory, there's no limit to how far a warp
• 23:04
  Speaker 1: drive could take you, as long as you have the
• 23:07
  Speaker 1: ability to do this and the energy budget to get
• 23:10
  Speaker 1: it done. So let's talk about how you might actually
• 23:13
  Speaker 1: build a warp drive and how much progress science and
• 23:16
  Speaker 1: engineers and science fiction authors have made towards making it
• 23:20
  Speaker 1: a reality. But first let's take another break. All right,
• 23:35
  Speaker 1: So we're talking about warping through the universe, and the
• 23:38
  Speaker 1: basic idea is to avoid the limit of the speed
• 23:42
  Speaker 1: of light by saying we're not going to move through
• 23:44
  Speaker 1: space faster than the speed of light. Instead, we're gonna
• 23:47
  Speaker 1: somehow change the shape of space. We're gonna build an engine,
• 23:50
  Speaker 1: a warp engine, which changes the nature of the problem
• 23:54
  Speaker 1: it doesn't solve the problem directly, it changes it to
• 23:56
  Speaker 1: another problem. And you know that's a standard and very
• 24:00
  Speaker 1: classic approach, Like it's basically what mathematics is. Somebody asks
• 24:03
  Speaker 1: a mathematician, can you solve this problem? They go, no,
• 24:06
  Speaker 1: that seems hard, But I can solve this other problem,
• 24:10
  Speaker 1: and I can prove that the answer is the same.
• 24:12
  Speaker 1: So instead of solving a hard problem, transform it to
• 24:15
  Speaker 1: an easy problem and then solve that. So in this case,
• 24:18
  Speaker 1: we're taking an impossible problem travel through space faster than
• 24:22
  Speaker 1: the speed of light, and transforming it to an easier problem.
• 24:26
  Speaker 1: Still really hard, maybe not feasible, but not theoretically impossible
• 24:32
  Speaker 1: to get there faster than light would have moved through
• 24:35
  Speaker 1: unaltered space. There, the idea again is to change the space,
• 24:39
  Speaker 1: is to squeeze the space in front of you and
• 24:41
  Speaker 1: expand the space behind you. That's the basic operating principle
• 24:44
  Speaker 1: of a warp drive. So let's talk about how that happens, because,
• 24:48
  Speaker 1: like I said earlier, squeezing space. Those are two words
• 24:52
  Speaker 1: you understand, squeezing and space. But what does it mean
• 24:55
  Speaker 1: to squeeze space? How could you possibly do that? What
• 24:59
  Speaker 1: kind of thing we you building? Your lab? To make
• 25:01
  Speaker 1: that happen. What would a warp drive actually look like? Alright,
• 25:05
  Speaker 1: so there's two components there, right, there's squeezing the space
• 25:08
  Speaker 1: in front of you and expanding the space behind you.
• 25:11
  Speaker 1: Let's do the easy one first. That's squeezing the space
• 25:14
  Speaker 1: in front of you. How can you squeeze space? How
• 25:17
  Speaker 1: can you make it to the shape of space as
• 25:19
  Speaker 1: smaller there's sort of constrained and shrunk a little bit. Well,
• 25:23
  Speaker 1: it turns out that's actually not that hard. You're doing
• 25:26
  Speaker 1: it right now. Everything with mass is changing the shape
• 25:29
  Speaker 1: of space in exactly that way. It's squeezing it, it's constricting,
• 25:33
  Speaker 1: it's constraining it. I don't want to get into the
• 25:35
  Speaker 1: mathematical details of the metric solutions to Einstein's equations, but
• 25:39
  Speaker 1: that's the basic idea. In order to shrink space, all
• 25:43
  Speaker 1: you need is a huge amount of mass or energy density,
• 25:46
  Speaker 1: because space bends in that exact way that you need
• 25:50
  Speaker 1: in the presence of mass and energy. So it basically
• 25:53
  Speaker 1: just becomes an engineering problem. You have positive mass and energy,
• 25:58
  Speaker 1: you can shrink space. How how much mass and energy
• 26:01
  Speaker 1: do you need to shrink space enough to get somewhere
• 26:04
  Speaker 1: interesting in the universe. Well, now it's a problem for
• 26:07
  Speaker 1: the engineers, and a bunch of folks have thought about this,
• 26:10
  Speaker 1: and I've even heard there are people in NASA working
• 26:12
  Speaker 1: on it, and they've done some calculations. And as usual,
• 26:16
  Speaker 1: when you first start out, you make basic assumptions. You
• 26:19
  Speaker 1: try the simplest idea first, and it seems impossible. So
• 26:22
  Speaker 1: the first calculation anybody ever did of how much energy
• 26:25
  Speaker 1: you would take, how much mass it would take in
• 26:28
  Speaker 1: order to bend space to get somewhere, like Proximus Centauri,
• 26:32
  Speaker 1: took more mass than all the stuff available in the
• 26:35
  Speaker 1: observable universe. That's a hundred billion solar systems for galaxy
• 26:39
  Speaker 1: and two trillion galaxies. That's an enormous amount of mass.
• 26:43
  Speaker 1: And there's no way you could ever gather that much
• 26:45
  Speaker 1: energy and use it for a warp drive. And anyway,
• 26:48
  Speaker 1: if you did, you would have already destroyed the universe
• 26:51
  Speaker 1: just trying to get somewhere. So it's a bit of
• 26:53
  Speaker 1: a chicken and egg problem. But this is the progression
• 26:55
  Speaker 1: of engineering, right. First you start out with a simple
• 26:58
  Speaker 1: solution that seems impossible and practical, and then somebody figures
• 27:01
  Speaker 1: out a way to do it with one percent of
• 27:03
  Speaker 1: the energy or costing a hundred times less money. That's
• 27:06
  Speaker 1: the way engineering works, and so people have already figured out,
• 27:10
  Speaker 1: oh wait, if you do do it this way and
• 27:11
  Speaker 1: that way, and you focus that this other direction, then
• 27:14
  Speaker 1: you can build a warp drive to get you to
• 27:16
  Speaker 1: the next star using only the amount of mass in
• 27:19
  Speaker 1: the planet Jupiter. Now, whether that seems like a big
• 27:23
  Speaker 1: number to you or not depends on your reference frame
• 27:26
  Speaker 1: if you start out comparing it to all the stars
• 27:29
  Speaker 1: and Solar system and stuff in the observable universe. Yeah,
• 27:32
  Speaker 1: it's a tiny amount of that, but compared to the
• 27:35
  Speaker 1: energy that any humans ever harnessed for any purpose, it's huge.
• 27:40
  Speaker 1: Remember we're talking about the energy stored in some object
• 27:43
  Speaker 1: that has mass. We're talking about releasing all of its energy.
• 27:47
  Speaker 1: And there's an enormous amount of energy stored in every
• 27:50
  Speaker 1: object that has mass because of E equals mc squared.
• 27:54
  Speaker 1: And the reason there's a huge amount of energy and
• 27:56
  Speaker 1: every piece of mass is because of the C squared bit,
• 28:00
  Speaker 1: see being the speed of light. Speed of light is
• 28:02
  Speaker 1: a really big number, and see squared is a really
• 28:06
  Speaker 1: big number squared. So you take a small amount of
• 28:08
  Speaker 1: mass like a raisin, which weighs maybe one gram. It
• 28:12
  Speaker 1: has an incredible amount of energy in it. It has
• 28:15
  Speaker 1: as much energy as a nuclear explosion. For example, you
• 28:19
  Speaker 1: wanted to build an antimatter weapon, if you had a
• 28:21
  Speaker 1: raisin and an anti raisin, that's all you would need
• 28:25
  Speaker 1: to have a device with as much explosive power as
• 28:28
  Speaker 1: the bombs that were dropped on Hiroshima. So now imagine Jupiter.
• 28:32
  Speaker 1: Jupiter is a lot of raisins, there's a huge amount
• 28:35
  Speaker 1: of energy, is an incredible amount of energy and jubiter.
• 28:37
  Speaker 1: So if somebody tells you I need I have a
• 28:40
  Speaker 1: warp drive, but we gotta refuel, and we gotta stop
• 28:43
  Speaker 1: by Jupiter and suck it all up, has to transform
• 28:46
  Speaker 1: all of Jupiter into energy to build my warp drive,
• 28:49
  Speaker 1: you'd probably say, we don't have the budget for that.
• 28:52
  Speaker 1: It's a huge reduction. But even requiring all the mass
• 28:55
  Speaker 1: of Jupiter to fuel your warp drive is not good enough.
• 28:59
  Speaker 1: All right, But recently I read an article that somebody
• 29:01
  Speaker 1: came up with a clever reduction in the amount of
• 29:04
  Speaker 1: energy required, so that you'd only need something like the
• 29:07
  Speaker 1: energy stored in a school bus or a large car.
• 29:10
  Speaker 1: And again that's another big step down. From all the
• 29:14
  Speaker 1: stuff in the universe down to Jupiter down to the
• 29:16
  Speaker 1: stuff in a car. Requires some real cleverness to focus
• 29:20
  Speaker 1: that energy in a way that's going to squeeze space
• 29:22
  Speaker 1: using only you know, hundreds and hundreds of kilograms of stuff.
• 29:25
  Speaker 1: Remember that's still a huge amount of energy compared to
• 29:29
  Speaker 1: the explosions of nuclear weapons. It's an enormous budget, but
• 29:33
  Speaker 1: it's not totally infeasible. So the engineers have already come
• 29:36
  Speaker 1: up with some sort of calculations to make this possible. No,
• 29:39
  Speaker 1: nobody's actually built a prototype. This is still just in
• 29:41
  Speaker 1: the planning stages that could this ever work stages, But
• 29:46
  Speaker 1: you know, the physicists have shown that to get there
• 29:48
  Speaker 1: you need to squeeze space, and they've pointed to the
• 29:50
  Speaker 1: engineers what we know about squeezing space, which is using
• 29:54
  Speaker 1: mass and energy to do things like gravity does. And
• 29:57
  Speaker 1: the engineers are working on it, they're chugging through it,
• 29:59
  Speaker 1: and there's all the reasons to believe that in a
• 30:02
  Speaker 1: few years, five years, ten years, fifty years, somebody might
• 30:05
  Speaker 1: be able to build something which begins this process. But
• 30:10
  Speaker 1: but to actually have warp drive, you need both sides.
• 30:13
  Speaker 1: You need the thing in front of you that squeezes space,
• 30:16
  Speaker 1: you also need the thing behind you that expands space. Right,
• 30:20
  Speaker 1: you can't have a moving walkway, and the whole walkway
• 30:23
  Speaker 1: isn't moving, So let's talk about that. How do you
• 30:26
  Speaker 1: expand the space behind you? Well, this is much harder.
• 30:30
  Speaker 1: You are not expanding space, right, You have positive mass,
• 30:33
  Speaker 1: and so you are shrinking space. You're doing that thing
• 30:36
  Speaker 1: that's the space that gravity does. But if shrinking space
• 30:40
  Speaker 1: requires having positive mass, you might be tempted to suggest,
• 30:44
  Speaker 1: sort of the first dumb idea for how to expand space,
• 30:48
  Speaker 1: that maybe you could expand space with negative mass. The
• 30:52
  Speaker 1: argument is not very sophisticated. It's really just that it says,
• 30:55
  Speaker 1: we don't know how to expand space, but we know
• 30:57
  Speaker 1: how to sort of shrink it using positive mass. What
• 31:01
  Speaker 1: if we use negative mass to expand it. It's not
• 31:04
  Speaker 1: a terrible argument. The problem is, of course, what does
• 31:08
  Speaker 1: negative mass mean. It's another of these examples. You take
• 31:11
  Speaker 1: two words that makes sense, negative and mass, and you
• 31:14
  Speaker 1: put them together and you go, huh, what is that?
• 31:17
  Speaker 1: Everything you've ever experienced has positive mass. I have positive
• 31:21
  Speaker 1: mass more than i'd like. Raisins of positive mass, hamsters, bananas, everything,
• 31:26
  Speaker 1: has positive mass. We've never seen anything with negative mass.
• 31:30
  Speaker 1: We talked about on this podcast for wormholes. You might
• 31:33
  Speaker 1: need negative mass exotic matter particles to stabilize wormholes, but
• 31:38
  Speaker 1: that doesn't mean that they exist. It just means that
• 31:41
  Speaker 1: if you write down the equations, that's the kind of
• 31:43
  Speaker 1: thing which could accomplish it. The things that are in
• 31:46
  Speaker 1: equations aren't necessarily also part of the universe. So we've
• 31:50
  Speaker 1: never seen negative mass, and we don't know how to
• 31:53
  Speaker 1: make negative mass. And also, even if you could make
• 31:56
  Speaker 1: negative mass, could you make a school bus size of
• 31:58
  Speaker 1: it a Jupiter, the planet Jupiter size negative mass? That
• 32:02
  Speaker 1: seems pretty difficult. It might even be a problem engineers
• 32:06
  Speaker 1: couldn't solve. But there is hope. Right, we know that
• 32:09
  Speaker 1: this thing can happen. We know that space can expand.
• 32:13
  Speaker 1: Decades ago, we might have imagined differently. We might have argued, Look,
• 32:16
  Speaker 1: gravity is just an attractive force. All it can do
• 32:20
  Speaker 1: is attract stuff. There's no repulsive side of gravity. Gravity
• 32:23
  Speaker 1: never pushes things apart the way magnetism can, or the
• 32:26
  Speaker 1: strong force can, or even the weak force. All of
• 32:29
  Speaker 1: these things can attract and repel because all those things
• 32:32
  Speaker 1: have both positive and negative charges. For their force. Gravity
• 32:36
  Speaker 1: has only positive charges. This is only positive mass, so
• 32:39
  Speaker 1: we can only attract That's what we think. However, we
• 32:44
  Speaker 1: also know that we don't really understand gravity, and we
• 32:47
  Speaker 1: do know that expansion of space does happen. We don't
• 32:51
  Speaker 1: know how to create negative mass. We don't know if
• 32:53
  Speaker 1: negative mass is the way to expand space, but we
• 32:56
  Speaker 1: do know that space can be expanded because we have
• 32:59
  Speaker 1: seen it happen. We believe that the Big Bang is
• 33:02
  Speaker 1: a huge expansion of space, though we don't know what
• 33:04
  Speaker 1: caused it. We know that dark energy is expanding space,
• 33:08
  Speaker 1: but we don't understand the mechanism. So we know it's possible,
• 33:12
  Speaker 1: but we don't know how to make it happen. We're
• 33:14
  Speaker 1: very far from being able to control it, and we're
• 33:17
  Speaker 1: super far from being able to put it in a
• 33:19
  Speaker 1: warp drive and take you to Alpha Centauri while you
• 33:22
  Speaker 1: stuff your face with junk food. So let's recap. It's
• 33:26
  Speaker 1: impossible to travel to Proximus Centauri or Alpha Centauri or
• 33:30
  Speaker 1: any of the Centauris by moving through space faster than
• 33:34
  Speaker 1: light could do it. You can't build a warp drive
• 33:36
  Speaker 1: that just moves through space. I think the kind of
• 33:38
  Speaker 1: warp drive to have. For example, in star Trek, does
• 33:41
  Speaker 1: that they traveled some factor of the speed of light
• 33:43
  Speaker 1: and they can get there more rapidly than light would
• 33:46
  Speaker 1: get there. That I'm gonna say it's flat out impossible.
• 33:48
  Speaker 1: It is always a possibility that sometimes the future physicists
• 33:52
  Speaker 1: will reveal that it wasn't actually impossible all along in
• 33:54
  Speaker 1: the some condition we assumed dot dot dot. I think
• 33:58
  Speaker 1: that's very unlikely. The more promising way to build a
• 34:01
  Speaker 1: warp drive is to change the problem from I'm gonna
• 34:04
  Speaker 1: move through space faster than the speed of light too,
• 34:07
  Speaker 1: I'm gonna try to squeeze the space. I'm gonna build
• 34:09
  Speaker 1: an engine which changes the nature of the problem. It
• 34:12
  Speaker 1: squeezes the space in front of me and expands the
• 34:14
  Speaker 1: space behind me. Space is not just to ruler you're
• 34:17
  Speaker 1: flying by. It's something we're in. It's like we're fish
• 34:19
  Speaker 1: and we're swimming in water, and to get to the
• 34:22
  Speaker 1: other side of the pond, you want to shrink the
• 34:24
  Speaker 1: amount of water that's between you and the other side
• 34:26
  Speaker 1: of the pond. So theoretically we think that could work.
• 34:30
  Speaker 1: Practically there's some big issues. Shrinking space in front of
• 34:33
  Speaker 1: you is very difficult. Maybe impractical, though theoretically we know,
• 34:38
  Speaker 1: we think we know what's going on, but expanding the
• 34:40
  Speaker 1: space behind you that's much harder. We have no idea
• 34:43
  Speaker 1: how to accomplish the expanding of space, but we think
• 34:46
  Speaker 1: it's probably possible because we see it happening in the universe.
• 34:51
  Speaker 1: We just have no handle on what's doing it or
• 34:54
  Speaker 1: how to make it happen in a controlled way where
• 34:56
  Speaker 1: you'd want to invite your grandmother on a trip to
• 34:58
  Speaker 1: the neighboring star. All right, So that's the explanation of
• 35:01
  Speaker 1: where we stand in terms of building warp drives. There's
• 35:04
  Speaker 1: lots of other really fascinating issues connected to space propulsion,
• 35:08
  Speaker 1: and people have written and asking us to talk about
• 35:10
  Speaker 1: e M drives and all sorts of other stuff. We'll
• 35:13
  Speaker 1: get to that, but until then, thanks very much for
• 35:15
  Speaker 1: all the folks who requested this topic, and thank you
• 35:18
  Speaker 1: in advance to anybody who sends in a request for
• 35:21
  Speaker 1: a future episode. We love hearing what you'd like to
• 35:24
  Speaker 1: hear about. So until Jorge gets back, this is Daniel
• 35:27
  Speaker 1: signing off for Daniel and Jorge explain the universe. Thanks
• 35:31
  Speaker 1: for tuning in. If you still have a question after
• 35:41
  Speaker 1: listening to all these explanations. Please drop us a line.
• 35:44
  Speaker 1: We'd love to hear from you. You can find us
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• 35:54
  Speaker 1: Jorge dot com. Thanks for listening, and remember that Daniel
• 35:57
  Speaker 1: and Jorge Explain the Universe is a production of I
• 36:00
  Speaker 1: Heart Radio. For more podcasts for my heart Radio, visit
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• 36:07
  Speaker 1: listen to your favorite shows. H