What does everybody think is the twin paradox? What's the REAL twin paradox? How is the paradox resolved, and what does it teach us about synchronicity? I discuss these questions and more in today’s Ask a Spaceman!

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EPISODE TRANSCRIPTION (AUTO-GENERATED)

You ever hear the one about the So-called? A Twin paradox. Let's say it's far, far, far in the future. How far? Well, it doesn't matter as long as it's far enough that our characters have access to whatever technology we need them to have to tell the story story. So anyway, future. Our characters are Alice and Bob. They are twins born less than 10 minutes apart at the start of our story. They have just celebrated their 20th birthday, Happy Birthday, Alice and Bob. But that day, Bob decides to get in a rocket ship and blasts off. Bob quickly approaches a cruising speed of 3/5 the speed of light. He travels to a destination three light years away, or somewhere near Proxima Centauri, perhaps turns around and returns to Earth. He lands a spaceship. According to Alice, Bob has been gone for 10 years, five years to get to his destination wherever the heck that is. You know, somewhere near Proxima, presumably and five years to return.

Alice is now, of course, 30 years old, because 20 plus 10 equals 30. But Bob is only 28 years old. Alice is confused. See, she had a watch on the entire time and kept careful track of the seconds, the minutes, the hours, the days, the weeks, the months, the years She she really missed Bob, but so is Bob. He had a watch on the entire time, and he kept careful. Track of the seconds, the minutes, the hours, the days, the weeks, the months and the years. I mean, he missed Alice, but he was also having a really good time. According to Alice's watch, 10 years have passed, according to Bob's only eight. Indeed, Alice does seem a little bit older now. A few more wrinkles, a little sprinkling of gray hair. What's going on? Is this magic? No. Is this a paradox? No, this is relativity. Relativity is our understanding of the connection between space and time and really the universality of physical laws.

Physicists before Einstein were beginning to approach a theory of special relativity where had already made some steps had already laid out the mathematics. Uh, it's it's very well argued that if Einstein hadn't reached it, somebody else would have, because we were right there on the cusp of something needed to break. Uh, there was a fundamental rift between Newton's understanding of universal space and time and master clocks and master rulers out there in the universe, and then our actual experiences and measurements and observations of electromagnetic radiation. Of Maxwell's theories, there was a rift there. I did a couple of episodes on this back in the day, and the only way to get this to work. Uh, you basically had to pick one. You had to pick Newton or Maxwell. Einstein picked Maxwell as all right thinking people should, And that means you have to abandon universal clocks and universal master rulers. You just have to get rid of them that our conceptions of the passage of time and the length of objects just is is relative.

It depends on how fast you're going. It depends on how closely you're moving, uh, relative to other frames of reference and what is saved, what is rescued in all these shenanigans. We then just do it for fun to make the universe more complicated. Uh, what we realize is that our physical laws, in other words, our experiences of physics have to be universal. If you're on a rocket ship floating around in the middle of space and you perform some experiments, it's the same as if you're on the earth. If you're in a frame of reference where you're cruising along at a fixed speed, uh, you can not perform any experiment to tell you that you're moving. It's It's just one of those things. It's the universality of physics. But in order to get that, you have to give up on universal frames of reference. You can pick one, but not both anyway. Einstein picked universal laws, and it worked out. And now we have this thing called relativity where clocks, rulers.

Nobody can agree. It's all a mad house. It's it's nuts, and movement takes on a new meaning. We learned that, uh, space and time are connected. They're unified into a single fabric, which we call space time. We're all used to this now, but it's 100 years later. 100 years ago, this was radically weird and and radically, uh, well radical it was. It was surprising to think about the universe, this way of this unification between space and time, and we now know that we move through space time if I'm sitting perfectly still. And yes, the Earth is moving and spinning and orbiting around the sun. The sun is orbiting them and, you know, et cetera, et cetera, Take away all that. If I'm sitting perfectly still, I'm still moving But I'm not moving through space right now. I'm moving through time and I'm moving through time at the speed of light. And once, I, uh, pick up and start moving through space I I am stealing a little bit of movement through time and giving it to the space direction I, I I'm always moving through.

And so are you, by the way. Always moving through space time at the speed of light. But when I move through space, I take away a little bit from that movement in through time and apply it to movement through space. And so this is why moving clocks run slow because you're simply not moving in the direction of time as quickly as you were before. Once you start moving through space, this gets worse and worse. The closer you get to the speed of light, obviously you can't reach the speed of light. But the closer you get to the speed of light, the faster you're moving through space. The slower. You're moving through time. And this is not just some hypothetical clock, not some theoretical imaginary clock. This is a real clocks. Mechanical clocks, physical clocks, chemical clocks, biological clocks, human clocks, biological processes move slower. Uh, physical interactions operate slower. The closer you get to the speed of light. When Bob comes back to Earth, he is literally two years younger than Alice.

Alice is 30 years old. Bob is 28 and it's just that simple. And and let that sink in just how weird this is. There is no universal master clock. There's no absolute reference frame. Once Alice and Bob separate, and one of them approaches speeds reaching the the speed of light. Their clocks no longer agree. Their perceptions of time no longer agree. This is something that is radically different than our everyday experience. We're so used to everyday experiences being like, OK, I'll I'll meet. I'll meet you for dinner at 6. 30. We both know exactly when 6 30 is gonna happen. You know, the train leaves the station at 11. 05. It's gonna leave at 11 05. And everyone around the world can agree when that train is leaving the station when 11 05 happens. But once you start approaching the speed of light, once you start moving quickly, the differences add up.

And 11 05 to you is not 11 05. To me, a seven o'clock dinner date for you is not a seven o'clock dinner date for me. They become fundamentally different in our experiences in the in the reality of the passage of time changes. That means that measurements of the duration of time, the rate of time, the flow of time are simply going to be different. This is what it means to live live in a relativistic universe. And the big idea here, the big word that I would love for you to remember and once again bust out at the next holiday party is the relativity of simultaneity. That's a mouthful. Unless we are in the exact same reference frame, like literally right next to each other, then you now is never going to be the same as mine. Now they are guaranteed to be different. I'll say that again because it's such a profound insight into our universe.

Unless we are in the exact same reference frame, then your now is never going to be the same as mine. Now they are guaranteed to be different. Full stop. So Alice and Bob are going to disagree about their ages. But this is not the paradox. No, this is just relativity, That is This is just the math of relativity. Clocks are gonna be different. Measurements of the duration of time are gonna gonna be different. The actual passage of time is going to be different. Nows are never gonna be simultaneous. That's not the paradox. The real paradox is that all motion is relative. From Alice's point of view, Bob is the one racing what she's standing here on the earth, counting the seconds go by. She sees the rocket ship, gets smaller and smaller, vanish into a tiny little point and then get bigger and bigger and bigger, and then sees Bob land on the earth. And wait a minute. Now he's two years younger. But from Bob's perspective, from his point of view, he's standing perfectly still in in the entire earth is racing away from him.

If you think this is weird, remember that an inertial reference frame. This is reference frames that are moving with constant velocity. So not accelerating or decelerating. You can't tell if you're moving the the next time you're in an airplane, you're cruising along at altitude. You can take off your seatbelts, close all the windows. Do you know that you are moving? Toss a ball in the air, you catch it. How are you moving from the point of view of the ground? Yes, you are moving. They can watch the plane go by. But from you in the plane you look down on the earth and you see the earth rolling by. You could claim that you are perfectly still and the earth is moving underneath you. Now. We don't usually think that way because, you know, we know that the Earth is solid and very, very large and difficult to move. And so it would. It would seem improbable. But yet there is no physics experiment that you could perform to prove that you were the moving one.

And the earth was the standing still one indeed. From your perspective, you are the still one and it's the earth that's moving. Yes, there are things like air turbulence and the fact that the engines on the plane have to push a little. So you do feel a little bit that that take that away And imagine a perfectly idealized inertial reference frame where you are just cruising along at constant speed. No acceleration, no deceleration. There is nothing you can do to prove that you are moving. Go ahead, try it. I dare you. You won't. So, from Bob's perspective, he's standing perfectly still, and he watches the Earth race away from him, shrink down into a tiny low point and then come back to him. So from Bob's perspective, he's standing perfectly still, and Alice is the one doing the moving, which means Alice should be two years younger than him because she's the one that went close to the speed of light. Not Bob. Bob was still Bob was just right here, hanging out, and it was Alice who was moving close to the speed of light, so he should be 30 years old and she should be 28.

But according to Alice, it was Bob who was moving, and she should be 30 years old, and he should be 28 years old. This is the paradox, the real twin paradox. Who's right. They both have valid points of view. I won't keep you waiting. It's Alice. Her. She She's right. Why? Because they do not have identical experiences Before I continue. I need to let you know that this podcast is sponsored by better help. Online therapy and stress. Man stress really stinks. I get it. It's a stressful world. It's stressful times. It can be a stressful life. Uh, when I get stressed out, there's this thing on my neck that starts to hurt, and it just doesn't go away. And and I actually used therapy to help me understand sources of stress in my life and how to deal with them in a more healthy and appropriate way. And I know a lot of you tune into this show to destress, to disconnect, to, to educate yourself, to feel better about yourself and just explore the wonderful universe that we live in.

And I Maybe it's time to also talk to a professional. Better help is customized online therapy that offers video, phone and even live chat sessions with your therapist so you don't have to see anyone on camera if you don't want to. If you want to wear your pajamas. No one's gonna blame you. It's much more affordable than in person therapy. Give it a try and and just see if it works for you. This podcast is sponsored by Better Help and ask a spaceman. Listeners get 10% off their first month at better. Help dot com slash spaceman. That's BE TT ER HE LP dot com slash spaceman. While Bob is mid flight, he's cruising along, so he's a light year away, flying at 3/5 the speed of light just doing his thing. He does correctly figure that Alice is aging is lower because of time dilation. Uh, while he's doing just fine. According to him on that outbound flight, he's standing perfectly still, and Alice is the one who's moving. His clocks run normally fine, and Alice is the one moving in Slow Motion and Alice on the Earth.

She thinks her clock is moving just fine, and it's Bob who's going slow. Yes, these appear contradictory, but guess what? That's relativity. Nobody agrees. And that's fine. That's fine. All motion is relative. But then Bob does something. He does something special. He slows down. He stops, he turns around. He re accelerates and he goes back to Earth. He changes reference frames as long as he is in an inertial reference frame. When he's just cruising along in that rocket, going at a constant speed, then he will have a different accounting than Ali, and he will have a different view of the flow of the universe than Alice Will. And he will disagree with Alice, and that's OK. But the moment he switches the moment he changes. Then, well, things change. He slows down. He stops, he turns around. He really accelerates. He does all these things in a way that he himself can measure on the Rocket. He feels the acceleration changing.

He feels the Rockets firing. He feels the deck vibrating. He can perform experiments and observations on board the rocket that tell him that he is changing reference frames. This change of reference frame introduces an asymmetry into the experiences. Bob really is doing something differently than Alice in a way that Bob can tell himself. He doesn't need to rely on outside observers to tell him that he is slowing down, stopping, reversing and re accelerating. He he can. He knows all that from Bob's perspective on his way out. Alice does initially age slowly, slower than him. But when he turns around and comes back, she appears to age super speed up. She goes in fast forward, so at the end of the trip, it adds up to 10 years. Alice does indeed spend 10 years to Bob's eight. So how can this happen? How can this work? From Bob's perspective, Remember, in relativity, nothing feels different for you.

If you're on a rocket ship cruising close to the speed of light, it's not like you're going in slow motion. No, everything feels normal. Your heart rate's the same. You look at your watch, it looks the same. You sleep for eight hours, you need coffee. In the morning, everything feels the same. Your personal experience doesn't change. So if Alice lives for 10 years, Bob only experiences eight of those years. Where, where did the two years go? And Bob doesn't have a different experience. He feels like the flow of time is totally normal for him. Where, where what happens to those two years? How does this add up? Well, remember, kids, you can't have a space time without patreon patreon dot com slash PM Sutter. If you enjoy this show, the best thing you can do to support it is go to patreon dot com slash PM. That's P, as in Paul M as in Matthew. That's my middle name and Sutter SU TT ER That's That's my last name.

Paul is my first. In case you were wondering PM. Sorry patreon dot com slash PM Sutter. It is seriously your contributions that keep the show going, and I truly, truly do appreciate it. I mean space. You can't have space time without space. You have to have both, and you can't consider one without the other. I opened the show talking about space time, and then this unification and and and moving through space and time when Bob is moving relative to Alice's experience of time will be slow. But according to him, the passage of time is totally normal. So how do you get this difference of two years? Well, I've been focusing on time dilation in this discussion, but the other side of the relativistic coin is length contraction moving clocks run slow moving rulers shrink. Imagine AAA meter stick racing by you at close to the speed of light. It will not look like a meter. It will be less than a meter. It will literally be shorter if you measured it right as it goes by and you reach your hands out and you measure it, it will be less than a meter.

And from the perspective of the meter stick moving close to the speed of light, all other distances in the universe are now shorter. I know this is a slippery concept, II I If you're if you're lost or this is just sounding weird, don't sweat it. Relativity is one of the hardest concepts to grasp in all of physics, seriously, just just keeping track of flows of time and rulers and clocks and perspectives and frames of reference. It is grueling. There's a whole mathematical apparatus behind this that helps physicists, you know, do the accounting. But actually, conceptualizing it is is insanely difficult. So don't sweat it. If this If this is a pretty out there episode, the point of it is nobody agrees on the duration of events, and nobody agrees about the lengths between objects. Nobody agrees on either of those, and it's through this sloshing back and forth between time and space that we end up getting the correct accounting.

Remember in our in our accounting of the Twin paradox, Alice ages 10 years, Bob only, ages eight. We realize that Bob really does have a different experience than Alice. There is no real paradox here because he changes reference frames because he turns around. This introduces an asymmetry. So his experience of of this journey is very different than Alice's and we, and another way to say is when Bob turn stops and turns around, that's when he knows that it really is him that's doing the moving and not the universe. So he knows. But Bob's experience on the rocket ship really only lasts eight years. If he has eight years worth of fuel, he will make it back in time. Think about that. Even though his rocket is gone for 10 years, according to Alice. And according to everybody, if he only packed eight years worth of food and fuel, he will make it back alive. So where do the two years come from? Where where do they go? If Bob says eight has passed and Alice has said 10, how can these two things be reconciled.

Well, in Bob's reference frame, when he's cruising the distance between the earth and his destination is not three light years anymore, it's only 2.4 light years away. I can't say it enough. It really is that much shorter. If you are cruising at 3/5 the speed of light and you are cruising to a destination that is three light years away, it is no longer three light years away for for you it is only 2.4 light years away. He doesn't have to travel three light years to get to his destination. He only has to travel 2.4 light years, so his watch is running the same rate that it was. Everything feels normal using his food using his fuel, but he doesn't have to go as far. So from Alice's perspective, Bob is gone for 10 years and he travels three light years away. Takes him five years to get there. Five years to get back from Bob's perspective. It only takes him eight years, four years to get there and four years to get back. But he doesn't have to go as far. He's only going 2.4 light years.

This is what reconciles Alice's and Bob's experiences this way. Alice has a normal experience of the flow of time. Bob has a normal experience of the flow of time, and yet they age differently because on the other side of that relativistic coin, they disagree about how far Bob went. According to Alice, Bob traveled 10 light years or sorry, six light years but according to Bobby, only traveled 4.8 light years. This is the wildest stuff, people. This is just crazy. We're talking about space ships going near the speed of light sci-fi stuff. But but relativity is very real. It's not sci-fi. It's sci fact. I mean, yes, if you're not traveling close to the speed of light, the changes in time dilation and length contraction are exceedingly small. But we're very good at measuring small things. In 1971 there is the the and Keating Experiment, where they took atomic clocks and flew them on jet aircraft around the world and compared them to an atomic clock that was saying stationary.

And guess what? When they brought them back together, they were off by, you know, 10 to 100 nanoseconds. The clocks literally had different experiences of flow of time. The planes had different experience of the circumference of the earth. The rate of flow of time was different for the stationary clock and the moving clock, the distance that was traveled. The stationary clock will say that the moving clock moved the entire circumference of the earth. The moving clock said No, no, no, no. It was a little bit shorter. What are you talking about? That's why I got here back. The Earth isn't as big as we thought it was. And I know you're like, how can anyone How can you possibly agree on anything? Well, you can't. This is the point of relativity. We are always going to disagree. The relativity of simultaneity now is not gonna be the same. And there is never going to be the same for different observers. We use the mathematics of relativity to to translate back and forth to reconcile the perspectives to make everything add up to make sure that one perspective maps onto another perspective. But the perspectives are simply going to disagree.

Here's another example. They're muons subatomic particle. Uh, when cosmic rays hit the upper atmosphere. It makes a bunch of muons, and, uh, and and then we can measure them. On the surface, you can build a at home, a little cosmic ray detector, and you see muons produced in our upper atmosphere. Uh, they're pretty fast. They travel at 0.98 the speed of light, 98% the speed of light that that's pretty fast. But their half life is only 1.56 microseconds. They do not last long, so you can measure the distance between the upper atmosphere where they're generated and the surface where they're measured. And with a half life of 1.56 microseconds and the speed of 98% the speed of light that's like 22 half lifes to make it down to the surface. So only for every million muons produced, only 0.3 should make it down to the surface. Less than one should make it to the surface for every million produced, but instead we see thousands of them.

What gives what gives this time dilation? The muons are traveling close to the speed of light, so they're half life, even though it's 1.56 microseconds to us because they're moving so quickly it becomes a little bit longer and from their perspective and, you know, coming down from the outer, a upper atmosphere, all these miles of air. To them, it's It's shorter, It's a shorter hop and so more of a make it to the surface. It's tough to live in a relativistic universe. It really is. It's tough to abandon the concept of a universal clock, a master ruler that we can all agree on. It's tough to admit that measurements of time and space can be different, depending on your reference frame. It's tough to admit that observers throughout the universe will always disagree, are guaranteed to disagree about when events start when they end, how long they last the ordering of events.

It's tough, but it's also real. Thank you to Chris F on email and a rash a on email. We're asking the questions that led to today's episode Thank you to all my patreon contributors. That's patreon dot com slash PM Sutter especially Justin G, Chris L Barbeque Duncan M, Corey D, Justin ZNH, Interf, Aaron S, Scott M, Rob H, LOL Justin Lewis and Paul G. John W Alexis, Aaron J, Jennifer M, Gilbert M, Tom B, Joshua and Kurt M. I really and truly appreciate it. Send me more questions. Hashtag Ask the spaceman. Ask us spaceman at gmail dot com website. Ask us spaceman dot com Sign up for patreon. Go read some books. How to Dine Space. Your Place in the Universe You know the drill. Follow me on social media at Paul, Matt Sutter and Yeah, let's meet for coffee tomorrow at, say, four o'clock. Sounds good. See you next time for more complete knowledge of time and space.

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