Ep. 606: Time Dilation – Skipping Through Time

Posted on May 24, 2021 in Cosmology, Physics, podcast, Relativity, Science | 0 comments


Have you ever wanted to be a time traveler? Good news! You’re time traveling right now. Into the future at one second per second. Too long? Don’t want to wait? Good news, Einstein’s got you covered. Today, let’s talk about the weird world of time dilation.

Download MP3 | Show Notes | Transcript

Show Notes

What’s Up: Mercury at Sunset and Nova in Cassiopeia (CosmoQuest)

Harvard Science Center (Harvard)

What is relativity? Einstein’s mind-bending theory explained (NBC Mach)

How “Fast” is the Speed of Light? (NASA)

The Theory Behind the Equation (PBS)

Buck Rogers in the 25th Century (IMDb)

How does relativity theory resolve the Twin Paradox? (Scientific American)

Landmark NASA Twins Study Reveals Space Travel’s Effects on the Human Body (Space.com)

International Space Station (NASA)

Speed and Velocity (Math is Fun)

COMIC: Gravity Wells (xkcd)

How to Make Your Own Gravity Well (Saint Mary’s University)

Interstellar (IMDb)

The Expanse (IMDb)

How Fast Do Spacecraft Travel in The Expanse? (Wired)

Momentum (The Physics Classroom)

Transcript

Transcriptions provided by GMR Transcription Services

Fraser Cain:                Astronomy Cast Episode 606: Time Dilation. Welcome to Astronomy Cast, our weekly facts-based journey through the cosmos. Where we help you understand not only what we know, but how we know what we know.

I’m Fraser Cain, publisher of Universe Today. And with me as always is Dr. Pamela Gay. A senior scientist for the Planetary Science Institute and the director of CosmoQuest. Hey, Pamela, how you doing?

Dr. Pamela Gay:         I’m doing well. It is a glorious spring day. And while the stars don’t shine as many hours each night, it is great to have Mercery over on the horizon. Have you gotten out to go look at it yet?

Fraser Cain:                I thought we went through this. I can’t see Mercury. I have no view to the East and I have no view to the West. Mercury is – I’m just gonna have to take it on faith that Mercery even exists.

Dr. Pamela Gay:         Okay. I understand. I am going to have to go to a field somewhere.

Fraser Cain:                Yeah.

Dr. Pamela Gay:         Because I, too, have no horizon. But I have access to cornfields that don’t yet have much corn in them.

Fraser Cain:                The only time I’ve ever seen Mercery I was in Australia. That’s it. And you have the benefit that the ecliptic sort of rise is straight overhead in Australia. So, you know, as opposed to things here being very low down to the horizon.

Dr. Pamela Gay:         Right.

Fraser Cain:                But yeah. And so, someone was like, “Oh, yeah. And there’s Mercery.” And I was just like, “This is the first time I’ve ever seen Mercery.” Too great.

Dr. Pamela Gay:         I think I have seen it from the roof of a building at Harvard. The Science Center in Harvard Yard – or just outside Harvard Yard – has a small telescope on its roof that I used to work with. And light pollution always makes it questionable if you know what you’re actually looking at. Because there just aren’t enough stars. But I think I’ve seen it, but now that I live someplace darker, I’m gonna try again.

Fraser Cain:                All right. So, if people wanna see Mercery and they do have, oh, I dunno, a horizon …where and when should they look?

Dr. Pamela Gay:         So, if you go out right now it is located between the very, very bright Venus and the super-thin crescent moon. The moon’s getting higher and higher, and thicker and thicker each day. But it remains above Venus in the West/Northwest. So, go out –

Fraser Cain:                Just after sunset.

Dr. Pamela Gay:         Yeah.

Fraser Cain:                Okay.

Dr. Pamela Gay:         Venus will pop out brightest and then look up.

Fraser Cain:                Have you ever wanted to be a time traveler? Well, good news. You’re time traveling right now into the future at one second per second. Taking too long? Don’t wanna wait? Good news. Einstein’s got you covered. Today, let’s talk about the weird world of time dilation. All right, Pamela. Time dilation. What?

Dr. Pamela Gay:         So, one of my favorite things that was like this breakthrough understanding for me with relativity. Was the understanding that no matter who you are and what you’re doing the speed of light will appear exactly the same. And in order for that to happen, how you perceive time has to change.

So, the way to think about this is what we’re used to in day-to-day life is …if I’m standing on side of the road in front of my house. And a car zips by, it appears to zip by at 30 miles per hour if they’re following the law. Now, if I’m going down the road at 30 miles per hour, the car in front of me – in theory, if they’re following the law – should appear to be moving zero miles per hour relative to me.

Fraser Cain:                Right.

Dr. Pamela Gay:         And so, we’re used to seeing everything with relative speeds. The faster I’m going, I’ll see people on the side of the road appearing to go in reverse. People around me, I see their motions relative to my own. So, it seems like using that human experience that the faster I go, I should eventually be able to catch up to those photons and perceive them as moving side by side with me.

But the reality is that while some outside observer might somehow perceive me and those light particles going at almost the same speed. I will never go as fast as the light. I will never see that. I will always see light. At the exact same speed relative to me.

Fraser Cain:                And that is such – I mean, when you think about Einstein’s ability to perceive the world in a fascinating way. To have this thought experiment that you’re traveling almost at the speed of light. And then you shine a flashlight, and you watch the flashlight. And in your mind, you be like, “Well, do I see the photons speeding away –

Dr. Pamela Gay:         Right.

Fraser Cain:                – just a little faster than me or do I see the photons speeding away at the speed of light?” And the only way – if you see them at the speed of light – is if time itself is changing.

Dr. Pamela Gay:         And so, this brings up that bizarre reality that Buck Rogers in the 21st century is actually a possible outcome of someone orbiting at a high enough velocity. Now, the fact that orbital mechanics doesn’t allow you to zip around the planet that fast. Let’s say instead they put themselves in this massive orbit at super high speeds.

Fraser Cain:                Yeah.

Dr. Pamela Gay:         That’s more realistic. Orbit around the sun instead. But …well, good ole Buck Rogers perception of time will slow.

Fraser Cain:                Okay. So, then you talk about this idea of speed. So, let’s break down time dilation. And I mean, I wanna ask why is time dilation? But I know the answer. And the answer is because. Right? Relativity. Because that’s how the universe works. So, let’s proceed right past ‘why’ and go straight to ‘how.’ How time dilation? And there’s sort of two factors. Two ways that you can get time dilation. And the one is the speed.

                                    So, let’s break this down in some examples. And now you’re providing this example. The twin paradox is the classic one, right?

Dr. Pamela Gay:         Yes.

Fraser Cain:                We’ve got two people. One here on earth. One gets in the spacecraft. What happens next?

Dr. Pamela Gay:         Well, so we actually got to see this with the Kelly twins. And the reality is that the astronauts on the International Space Station are experiencing time ever so much slower. And the way you figure out who experiences the change in time is you look to see who experienced the force. And who experienced that acceleration that got them to that faster velocity.

                                    So, in this case, you accelerate yourself up to the International Space Station and to a velocity that keeps you circling the planet instead of falling back. And time slows.

Fraser Cain:                Right. And in that sort of very slightly –

Dr. Pamela Gay:         Yes.

Fraser Cain:                And it’s more complicated because of course the International Space Station and the twin who’s on the ground are in a gravity well. But let’s say you have the one who accelerates up to close to the speed of light. Flies for 10 years, and then returns. And then the twins meet up. So, what you’re saying is that it’s not the speed.

Dr. Pamela Gay:         Yes.

Fraser Cain:                It’s the acceleration that you experience to get yourself up to that speed.

Dr. Pamela Gay:         That determines who is the one who is experiencing the time change.

Fraser Cain:                Got it.

Dr. Pamela Gay:         It’s the velocity that you accelerate to that determines how much time slows down.

Fraser Cain:                Right. And so, twin No. 1 is sitting on earth. Twin No. 2 gets in a spacecraft. They accelerate – and that’s the key – to close to the speed of light. Compared to the twin who’s just sitting on the planet.

Dr. Pamela Gay:         Yes.

Fraser Cain:                They then return – it’d take them 10 years. Or I guess the person traveling experiences 10 years and returns home to earth to see that the twin who was on earth has experienced –

Dr. Pamela Gay:         Death

Fraser Cain:                – vastly more time.

Dr. Pamela Gay:         Death.

Fraser Cain:                Right. Right.

Dr. Pamela Gay:         Humans only live so long. The human on earth –

Fraser Cain:                Sure. Right.

Dr. Pamela Gay:         – experienced death.

Fraser Cain:                Right. And so, the twin  – so, I just want to be sure I got this clear. So, the twin who flies on the spacecraft experiences 10 years. The twin who stayed on earth experiences hundreds, maybe thousands, maybe millions of years.

Dr. Pamela Gay:         Essentially, the closer you get to the speed of light. The closer you get to stopping time for yourself while time passes for those on earth.

Fraser Cain:                Right. Because you’re experiencing the acceleration.

Dr. Pamela Gay:         Well, and so the key is who is the one whose time stops for?

Fraser Cain:                Right.

Dr. Pamela Gay:         We always see things in our frame of reference. And this is where that car idea is important to think about. So, relative to me standing on the sidewalk and the Uber driver zipping down the street. The Uber driver, if they perceive themselves as not moving. Will see me moving at 30 –

Fraser Cain:                Right.

Dr. Pamela Gay:         – miles per hour. So, if you have two spaceships in space it’s harder to sort out who’s the one moving and not than it is on earth.

Fraser Cain:                Right.

Dr. Pamela Gay:         And clearly, compared to the trees, the ground, and everything else, I’m not moving. But in the vastness of space, you stick two spacecrafts down and throw the rockets on one and don’t tell the people on board who is having the rockets thrown. You might feel it. But you can also say, “Hey, we just spun your spacecraft so you felt gravity.” So, the two could experience the same thing.

Fraser Cain:                All right. So, we talked about speed/velocity as one. And I gotta be careful, right? Because I’m using speed/velocity interchangeably. And that is bad physics, Fraser. Bad. So, velocity. Right? Velocity is speed and direction.

Dr. Pamela Gay:         So, in the equations to figure it out, they use the scalar velocity. Which is the speed.

Fraser Cain:                Okay.

Dr. Pamela Gay:         And so, for figuring out how much time has changed you can just say speed.

Fraser Cain:                Okay. Okay. All right. So, we talked about speed.

Dr. Pamela Gay:         Yes.

Fraser Cain:                And the other way is to be in the presence of a gravity well.

Dr. Pamela Gay:         It’s true. It’s true.

Fraser Cain:                And I think we’re all really fortunate because Interstellar came out a couple of years ago. And they had this happen. And so, we got to see what it did. So, what’s going on with that.

Dr. Pamela Gay:         So, the closer you get to a massive object. The way to think about it here is in a normal situation down on the planet earth, if I throw a ball slightly, I see it moving at one speed. If I throw it really hard I see it moving at another speed. And then, if I go to Jupiter and I use the exact same amount of force to throw the exact same amount of balls. They’re gonna move much slower. Because more –

Fraser Cain:                Right.

Dr. Pamela Gay:         – gravity. Now, for a poor innocent little light particle trying to escape from the super high-mass object, that light particle is experiencing all that gravity. And in order for that light particle to continue always moving at the same speed of light, time is gonna have to change as it escapes from different gravity wells.

Fraser Cain:                Right. Okay. And like we saw – you know I was talking about this idea of watching the movie Interstellar. And we saw how in Interstellar he goes down to the surface of this planet that’s orbiting around this supermassive black hole. He’s there for a day. Comes back out and the rest of the universe – the rest of his family – has experienced 80 years. Or some ridiculous amount of time.

Dr. Pamela Gay:         Yeah.

Fraser Cain:                And so, it was not because of the speed they were doing to go through the wormhole and blah blah blah. It was because they spent this time close to the black hole in the gravity well. And so, I think, going back to that conversation that we had about the acceleration is the key.

Dr. Pamela Gay:         Yeah.

Fraser Cain:                When you’re in a gravity well, you’re experiencing acceleration.

Dr. Pamela Gay:         Yes. It’s the – what is doing the fundamental altering of your movement through space and time. And that gravity well is doing its darndest to keep you attached to it.

Fraser Cain:                Right.

Dr. Pamela Gay:         And to keep that light attached to it.

Fraser Cain:                Yeah.

Dr. Pamela Gay:         And the more the gravity pulls on you and light, the more time has to slow down so that light is always perceived as going at the same tick.

Fraser Cain:                Right. Right. Okay. So, now let’s put this all together. What if you are in a gravity well. Say you’re orbiting a black hole. And you’re also going very quickly compared to somebody who is going – I guess a black hole is a bad idea because you’ll be standing – but let’s say you’re on the earth. Right? I mean, but this is a practical example that we can actually do.

Dr. Pamela Gay:         Yes.

Fraser Cain:                Where you are on the surface of the earth.

Dr. Pamela Gay:         Yes.

Fraser Cain:                And so you’re in the presence of a gravity well.

Dr. Pamela Gay:         Yes.

Fraser Cain:                Or you’ve got your twin who’s flying in space on the International Space Station. They are in less of a gravity well because they’re at a higher orbit. But they’re moving faster.

Dr. Pamela Gay:         Yes. And to be fair, I haven’t redone these calculations in ages.

Fraser Cain:                Yeah, I haven’t either, and I apologize. Because it’s not in my head.

Dr. Pamela Gay:         So, last time I did these calculations, assuming I did them correctly – and I really hope I did. What I figured out was time goes more slowly for the astronaut, because the time dilation effect compared to being on the ground is greater for them. Because of the amount of acceleration that went into getting them where they are. Whereas, if you stopped them in space, this would cause them to fall to the earth. So, don’t do this.

Fraser Cain:                Right.

Dr. Pamela Gay:         And compared the time dilation due to their lesser pull from the center of the earth. But they’re still being pulled on, just less.

Fraser Cain:                Yeah.

Dr. Pamela Gay:         But the dilation caused by the lesser pull at altitude compared to the surface of the planet – that time dilation due to gravity is a smaller effect than the time dilation due to accelerating so they don’t fall.

Fraser Cain:                And there’s gotta be like a perfect balance.

Dr. Pamela Gay:         Yeah.

Fraser Cain:                Where you essentially experience no difference in time compared to the person who’s on the surface of the planet. Because your speed of movement balances perfectly out. The fact that they’re in a greater gravity well. And so you –

Dr. Pamela Gay:         And this would be a great homework problem.

Fraser Cain:                Yeah, there you go.

Dr. Pamela Gay:         And right now everyone is very glad I am not still teaching physics for engineers who get calculus.

Fraser Cain:                You would assign it.

Dr. Pamela Gay:         Because yeah…

Fraser Cain:                Yeah.

Dr. Pamela Gay:         You should be able to totally calculate out what density planet do you need? So, that someone on the surface and someone safely in orbit have the exact same ticking of the clock. Although, you can never sync those clocks. Because it takes time for light to get between the two points. But the ticks are the same duration tick.

Fraser Cain:                All right, so now I wanna blow peoples’ minds. And –

Dr. Pamela Gay:         I love time dilation. I just wanna say that –

Fraser Cain:                Yeah. Yeah. Yeah.

Dr. Pamela Gay:         – I absolutely love this concept.

Fraser Cain:                Yeah. Absolutely. And so, one very popular science fiction show that’s come out in the last little while is The Expanse. And they have these really powerful fusion rocket – Epstein rockets – that are able to take your spacecraft really, really fast. And so, if you could just jam on the engine and you had an unlimited fuel supply somehow. And you just kept accelerating, accelerating, accelerating …what would happen to time for you and the rest of the universe?

Dr. Pamela Gay:         Your time, by your perception, your heart would continue to beat the exact same way. But –

Fraser Cain:                You’d continue to be pressed into the seat at 1g.

Dr. Pamela Gay:         Yeah.

Fraser Cain:                Right?

Dr. Pamela Gay:         Yeah. But the more your velocity increases …and here it’s the absolute value of it, that speed, the nonvector, scalar portion that matters. With each moment of acceleration, the moments that an outside observer sees you experience become fewer and fewer.

Fraser Cain:                Right.

Dr. Pamela Gay:         You will stop aging over time. You will stop breathing to the person watching because everything is slowed down so absolutely much. And in other science fiction series – I’m thinking of Hyperion here. There’s this wonderful example of in the future when high-speed travel between solar systems becomes practical. People of means can deposit their money and invest it in good things. And then skip through time become wealthier and wealthier. And experiencing less and less.

And I mean, imagine just how hard it would be on one hand to pop out of space travel and see all the amazing technological changes that have occurred. But at the same time be like, “And I’m rich now.”

Fraser Cain:                But the part that’s kinda crazy is that you could keep on accelerating and from your perspective you would never reach the speed of light. Because it’s impossible. But you would still be experiencing 1g of acceleration for days, months, years, decades.

Dr. Pamela Gay:         Yeah.

Fraser Cain:                And even though, if you did the math, and you’re like, “I should have gotten faster than the speed of light.” You won’t and yet the distances that you’ll be traveling and the time that the rest of the universe will be experiencing just continue to grow.

Dr. Pamela Gay:         Yeah.

Fraser Cain:                For as long as you can keep this going.

Dr. Pamela Gay:         And crazy things start to happen that we’ve discussed in other episodes many years ago. So, go digging through the archives. The way the equations for relativity work out is your momentum increases in ways that aren’t entirely linearly related to your mass. And the impact of this increase momentum, the faster and faster you go, is that it’s like you were gaining more and more mass.

Now, the reality is the number of atoms in your body will not change unless biological things occur. But your ability to destroy things if you hit them increases because of this apparent change in mass that is due to the relativistic effects on your momentum.

And this led to a question with which I broke a physicist and never really got a good answer. They sort of ended up walking away mumbling. And the question was if a body of mass goes fast enough so that its equivalent mass via momentum is such that it would be a black hole is it actually a black hole?

Fraser Cain:                Right.

Dr. Pamela Gay:         And the answer I’ve gotten from other theorists was no –

Fraser Cain:                No.

Dr. Pamela Gay:         – that’s crazy talk.

Fraser Cain:                Yeah.

Dr. Pamela Gay:         But I did break one physicist –

Fraser Cain:                Good.

Dr. Pamela Gay:         – this way. I was proud of myself.

Fraser Cain:                So, the part that’s crazy is that if you could keep this acceleration up, you could be going to the point that in like a decade you would cross the Milky Way. In two decades you would go to Andromeda. In three decades you would be billions of lightyears away. And in about less than a human lifetime you would travel more than the distance to the edge of the observable universe.

Dr. Pamela Gay:         But the problem is the amount of energy that it takes –

Fraser Cain:                Of course.

Dr. Pamela Gay:         – to keep accelerating your –

Fraser Cain:                Yeah.

Dr. Pamela Gay:         – increasing effective mass. Not your actual mass increasing.

Fraser Cain:                Yes.

Dr. Pamela Gay:         Your effective mass increasing.

Fraser Cain:                Yeah.

Dr. Pamela Gay:         You would exceed the mass-energy of the universe before you exceeded the speed of light. Which is part of how we never actually go faster than the speed of light.

Fraser Cain:                Yeah. And so for someone watching you. You would just be very close to the speed of light. And you’d be doing that for billions of years.

Dr. Pamela Gay:         Yeah.

Fraser Cain:                From your experience because you’re continuing to accelerate you would be like .999999% the speed of light. And so, it would take you two and a half million years to get to Andromeda. It would take you –

Dr. Pamela Gay:         Right.

Fraser Cain:                – 46 billion years to get to the edge of the –

Dr. Pamela Gay:         But you wouldn’t experience it.

Fraser Cain:                But you wouldn’t experience it. And yet the rest of the universe would. And so you would be – you would have to wait. You know, we’d have to wait 50 billion years for you to reach what was the edge of the observable universe. It’s absolutely mind-bending.

Dr. Pamela Gay:         Yeah.

Fraser Cain:                And awesome. And it’s like this one hope that we can travel vast distances in a single human lifetime. Although, you have to say goodbye to everyone and everything you know.

Dr. Pamela Gay:         Well, just travel with your friends. Travel with your friends.

Fraser Cain:                That’s a good way to do it. All right. Thanks, Pamela.

Dr. Pamela Gay:         Thank you.

Fraser Cain:                Do you have some names for us this week?

Dr. Pamela Gay:         I do. I need to find the right window. I have so many monitors. I love my monitor fort.

Fraser Cain:                Your monitor fort.

Dr. Pamela Gay:         I have a monitor fort.

Fraser Cain:                Yeah. That’s awesome.

Dr. Pamela Gay:         This is what one should build – monitor forts.

Fraser Cain:                Yeah. Yeah. I love it. I’ve never heard it said that way, and I think it’s great.

Dr. Pamela Gay:         So, as always, we are here thanks to you. You out there, thank you. Thank you for supporting us and making everything we do possible. For allowing us to pay Rich, Allie, Beth, Nancy. All the people that keep Fraser and I on the straight and narrow. Because Lord knows we need herded. So, thank you for making this possible. Thank you for paying our server bills …our everything else. Thank you.

And this week in particular I would like to thank Kevin Parker, David Truog, Bill Nash, Helge Bjørkhaug, Richard Hendricks, Janelle Duncan. And it turns out that because it’s the end of the month, those are the only names I’ve got.

Fraser Cain:                Okay.

Dr. Pamela Gay:         So, thank you.

Fraser Cain:                Thanks, everybody. And thank you, Pamela. And we’ll see you next week.

Dr. Pamela Gay:         Buh-Bye, everyone.

Astronomy Cast is a joint product of Universe Today and The Planetary Science Institute. Astronomy Cast is released under a creative commons attribution license. So, love it, share it, and remix it. But, please, credit it to our hosts Fraser Cain and Dr. Pamela Gay. You can get more information on today’s show topic on our website astronomycast.com.

This episode was brought to you thanks to our generous patrons on Patreon. If you want to help keep this show going, please consider joining our community at patreon.com/astronomycast. Not only do you help us pay our producers a fair wage, you will also get special access to content right in your inbox and invites to online events. We are so grateful to all of you who have joined our Patreon community already. Anyways, keep looking up. This has been Astronomy Cast.

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