Clowns in Spacetime

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You're about to listen to a brand new episode of Curious Cases.

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I'm Hannah Fry.

And I'm Dara O'Brien.

And this is Curious Curious Cases.

The show where we take your quirkiest questions, your crunchiest conundrums, and then we solve them.

With the power of science.

I mean, do we always solve them?

I mean, the hit rate's pretty low.

But it is with science.

It is with science.

Dara, you're looking particularly excited about today's episode.

This one is very exciting.

We're doing proper, like proper science.

I'm not dismissing the rest of the series entirely, but this is what I came on board for.

I'm extremely pleased to be able to offer offer this for you.

Okay, well, we have had a question this week into curious cases at bbc.credituk from New Zealand, no less.

Have a listen.

Hi, I'm Saskia.

I'm from Christchurch, New Zealand.

So I was having a coffee break with some friends and we were discussing random things, as you do.

And well, I was making fun of my friend for being older than I am.

So I was wondering if I stayed on Earth and my friend, who's one year older than me, goes to space in a rocket and travels at a certain speed for a certain amount of time.

Could he catch up to me age-wise and we'll have our birthday at the same day?

I haven't got my head around it at all.

I don't know.

It's very confusing.

So I need an expert to help.

Bravo, Saskia.

I mean, Saskia, if she said this without any knowledge at all, that is amazing that she has rediscovered relativity.

Just by accident.

Just on a coffee break.

I suspect he's heard some of it and then wonders how it applies.

But also, how harsh you turn to your colleague and go, hey, old man, you're one year older than I am.

What?

You're 46?

Oh, I'm 45.

Oh, excuse me, dinosaur.

Saskia, come on.

Did you study this at school?

Yeah, you need.

Look, this is a particularly special relativity which they did in second year in my university, but I did a lot of other stuff in second year.

Second year, you know, second year I discovered a whole new social life and

girls, dark women.

Women like, I had discovered girls, but only girls from my school.

And then I discovered that there are girls from all those other schools as well.

Different schools of girls.

And they're all in my university.

Hang on.

Are you saying that was more interesting than special relativity?

I'm just saying in that moment.

I'm just saying now, now is the perfect time to do this again.

But at the time, I was 19, 20, and it was really interesting.

It was very interesting.

And so there may be gaps in my knowledge.

Well luckily for me during my uni days I was interested in nothing more than differential calculus so buckle up.

We are ready to expand your minds and slow down time.

Well, to guide us on this bendy journey through space and time we have Professor Sean Carroll from Johns Hopkins University and the Santa Fe Institute.

And Dr.

Kay Clough from Queen Mary University of London.

You've heard the questions from Saskia and she has stumbled upon something quite massive there.

Yes, that's right.

It's one of the most fundamental parts of physics: special relativity, the fact that space and time are not separate, and so how you move through space actually affects how you move through time.

So, I always say, you know, if you go to the shops and you come back sort of an hour late when you meant to only go for an hour and you go for two hours, then you might give an excuse of, oh, well, I travelled very fast to the shops and therefore time didn't travel in the same way for me.

This is perhaps your way of excusing yourself for being late, late, but you know, for that to have happened, you would have had to travel at 86% of the speed of light.

Just making notes here.

Yeah, next situation.

Well, next time you're up in court.

But Your Honour, 86% of the speed of light.

In terms of the formulation, how we came up with this idea, how we, like the way I've written myself into the narrative here, how we as a species came up to it, a lot of it was because we kept hitting this wall of contradictions because of light and its constant speed.

Yes, that's right.

So actually it's very nice because it's one of the things that you can derive from a very simple observation, which is that we all measure the same speed of light.

So this observation tells you that you can't catch up with light.

You know, if you drive along the motorway driving behind another car, as you get faster, you get closer to that other car.

So the relative speed between you seems to kind of decrease.

But you can actually never do that for light.

So light will always be streaming ahead of you at the speed of light, no matter what speed you're traveling at.

And that obviously seems really counterintuitive because from our everyday experience of driving on the motorway, we expect to be able to kind of catch up with things that are going faster than us.

And actually just from that simple observation, you can derive the fact that time must be different for different observers.

So the fact that time is not an absolute thing, but actually must vary depending on how you're moving.

A car is driving on the road, if you see it driving past it, you can measure its speed.

If you're running along, you'd measure a slightly different speed.

If you're on a motorbike going half the speed of the car, you'd measure a slightly different speed.

That all makes perfect sense.

But when you hit this wall, where we suddenly realize if it's light, it's the same speed for each of those people.

It doesn't matter if you're standing still, if you're cycling, if you're running, if you're running really close alongside it, it's always traveling at this speed.

Speed, exactly.

So basically, something had to give.

You know, if speed is absolute and not changing, and that's kind of everyone's scratching their head over, something has to change and it ends up being time.

Time, yeah, which we really is really counterintuitive, right?

It's kind of it really goes against everything you experience and that you kind of believe about the universe because we all have this idea that there's this universal time.

You know, if I go to the shops and come back again and we compare our watches, you know,

if there's no problem with my watch or your watch, they should say the same thing.

But, you know, if I go to the shops very fast and come back very fast, then they would actually say different things.

I would somehow have experienced a different amount of time to you.

And that does seem crazy on the face of it.

Yes, but we know this experimentally, anyway, because people have tried to test this.

Yeah, so there's a very famous experiment called the Hefeler-Keating experiment.

So they actually did this using aeroplanes, and they had very accurate atomic clocks, these cesium atomic clocks that are extremely accurate.

You can tell that it was quite a while ago because it's a bit of a sort of basic experiment where they really just booked a seat for the clock on a transatlantic flight and then put it on the seat.

Mr.

Clock was the name on the ticket.

And then they sat next to it and flew one way round the world.

And then they did the same the other way round the world.

And they compared the times on the clocks when they got back to their original starting point.

And they had a third clock that was just sitting on the surface of the Earth.

And if you do the calculation for how you expect time to have moved differently for those three clocks,

you find that they should have changed by about

something of the order of 100 nanoseconds.

And it matched exactly what they expected.

Did they put these atomic clocks in first class?

That's what I want to know.

In the picture, it looks very fancy.

You know, it's a big seat.

Yeah, you definitely wouldn't get one of these clocks on a budget airline seat.

I want to know what it had for lunch.

Well, the alpha was chicken and fish.

It's always chicken and fish.

I mean, look, your experiment with fancy business class atomic clocks with their cigars and porn is all very well and good.

But the thing is that actually, special relativity, I mean, this thing comes into play all the time for all of us, perhaps without us even realizing it.

Because if you have ever used a map on your phone,

then it is absolutely crucial.

And that is because there are satellites in space whizzing around the planet.

Now, we have got Peter Boast from the European version of GPS, which is called Galileo, and he's got a couple of insights into how this works.

So people do not always realize that they're using Galileo, but we estimate that we have more than four billion users of Galileo.

On your mobile telephone, if you use an application to guide you to your destination, it's also making use of Galileo.

We say the foundation of any navigation system is the high-precision clocks that we have.

We have them on board of the satellites, but also we have them in the ground segment.

Because at the end, it determines the accuracy of your position.

A Galileo satellite moves with a velocity of about 3800 meters per second, 14,000 kilometers per hour.

This results that the onboard clocks tick slower compared to the clocks on Earth.

This effect is measurable and we can say that the onboard clicks slower for about seven microseconds per day and a microsecond is one millionth of a second.

This would result in an error of about two kilometers per day.

The interesting thing is that the DNSS is the very first application where Einstein's theory have to be taken into account to make the system usable.

Indeed, if we did not take this in into account, then we would not be able to navigate using a system like Galileo.

Okay, Sean,

walk me through this.

Why is it that to know where you are, you need to know when it is?

Well, basically, you're figuring out where you are by comparing signals from different satellites with different locations, right?

You're asking how long did it take for this signal that moves at the speed of light to go from a satellite over there to me, a satellite over here to me, and you can triangulate and you can find your position very, very accurately.

But that only works if you know what the time is on these satellites that are traveling at different speeds.

And so Professor Einstein is going to come into play because if you think about it,

a a signal appearing just a tiny fraction of a second later puts you physically at a very different distance because the speed of light is so fast.

So people would have discovered special relativity if they had built GPS before they knew about it.

But happily we knew about relativity first.

Is there every chance we would have wanted to do this and then this error would have crept in and we would have found ourselves going, why?

Why is this going wrong?

What's happening here?

Bar the fact that it was predicted in 1905 by Einstein, who was working as a patent clerk at the time, and who came up with a set of equations that seemed to predict this, which is remarkable.

What kind of ideas was he playing with at the time?

Well, he was a patent clerk at a time when the thing that was most often submitted to be patented were clocks.

Because in 1905, they were building railroads crisscrossing Europe, and every different city had its own time zone, right?

They didn't have standardized time zones.

So you wanted to know what time it was, not only here, but everywhere else.

You wanted accurate clocks working everywhere.

So in Einstein's mind was the idea that time is what you measure.

Time is what is read off on a clock.

It's not some absolute thing.

And that's the fundamental thing that lets you make sense intuitively of relativity, because, like Katie says, we're all surprised by this fact that different clocks read different amounts when you travel in different ways.

But if you think of time as what the clocks are reading, just like an odometer tells you how much distance you've traveled through space, then you begin to realize that time can be individual, time can depend on how you move through the universe, and you become less surprised by the whole thing.

I mean, it does feel like reality is being played with to a certain extent.

If you're saying that just by the sheer act of being accelerated, you now exist in a different reality to this dude.

It's a shiki shortcut.

It's bizarre.

It's always been regarded as this kind of fairly mind-blowing thing.

Go on.

I want it to not blow your mind.

If I have two

points in space, like you have an office and you have a restaurant you want to go to, and you walk from the office to the restaurant, and of course there are different routes you can take when you walk there.

You can go the shortest possible route or you could like take a scenic route that takes you around the block or whatever.

You are 0% surprised that the amount of distance you travel depends on the route you took.

All Einstein is saying is that the amount of time elapsed also depends on the route you take.

And he has a formula for telling you exactly what it will be.

And like Katie says, it's not going to actually show up unless you go pretty close to the speed of light.

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The joy of this for me is an absolute universe of thought experiments and hypothetical experiments.

And it is what your cast is essentially a torch,

some sort of vehicle, a clown, a horse, I don't know, there's always different stuff put into it.

And there are all these, like, well, what if you had a double-sided torch and then you're on a bicycle and then you put the beams out and you put the beams out sideways to the bicycle?

There's so many of these that sometimes help and sometimes don't in explaining this.

It's going to be a different example, Katie, of these kind of, of these kind of...

thought

to explain this.

Yeah, I don't know which ones you're referring to.

I don't know the one with a clown.

Clown is my own one.

I think that might be the one that he made up when he missed that lecture

honestly i was improvising a lottery those examples

like if you fire a clown at nearly the speed of light i mean this yeah it's all of things like you know if you yeah if you're it's always on a train you're always on a train so i think that they don't travel on the trains um in england because the trains in england you're supposed to feel you know when you're on a train you can't measure your own speed this is the the thing that they say oh you can't feel that you're moving but i mean if you're on a train usually you're sort of being bumped around a lot and it definitely feels like you're moving.

So, you have to always imagine that you're on a really smooth train that's moving very smoothly forwards, and then you would be able to drink your tea and it wouldn't spill because you actually don't feel your own

speed.

So, all of these thought experiments usually involve you sitting on a train, and then you think about, well, yeah, what if I have a torch and I beam the torch, you know, out the window, and I think, you know, can I catch up with this beam of light that's that the torch is projecting?

And, you know, when you, if you fired a bullet out the window, you you know, in principle, you'd think that you'd be able to,

well, not catch up with it on our trains, but you know, if you were traveling fast enough, you'd be able to catch up with it.

But with the torch, with the light, you can never catch up with it.

You will always measure it as traveling at the speed of light.

So

I guess this is the kind of thing that you had in mind.

Absolutely.

But by the way, that example works perfectly well if the person on the train is a clown.

There's no reason why I shouldn't be a clown with a gun and a torch.

Okay, so

let's go with the clown.

Old Mr.

Sad.

No, he's a happy clown.

He's a scary clown.

Mr.

Happy, he's there with his ginormous shoes and red nose, and he's

sitting on a train.

And he's chucking a ball up and down on the train.

This, I think, was always the thing that really nailed it for me: you can throw a ball up and down while on a moving train and it doesn't hit you in the face, as great as that would be as part of a clown trick.

But it's because if the train isn't accelerating,

then you're in your own little purple, perfect little frame of reference, right?

Yeah, Yeah, exactly, yeah.

Yeah, so I think it is actually very counterintuitive, this idea of no one can measure their own speed.

You know, speed is not something we can measure, we can only measure acceleration.

And as I say, that feels kind of counterintuitive because usually, you know, if you're in a fast car with the window open, you have the wind blowing in your hair and things like that.

And these kind of things give you an idea that you can feel your own speed, but you really can't.

As you said, you know, if you're in a very smooth train that's moving very smoothly, you throw a ball up and down in the air and you wouldn't know that you weren't standing still because because the physics is essentially the same because it would be exactly the same yeah but from the outside of the train then mr happy looks very different absolutely yeah i mean sean if the clown is on a train this is now how we're doing all of this now if the clown is on the train looking at a clock if you're trying if that train starts traveling at the speed of light what happens to the clock well you know i'll tell you honestly i don't like the phrase looking at a clock i mean are you looking at a clock that is stationary with respect to you?

Are you going by a clock?

If you're zooming by the clock, then you have to tell me how far away is it because light is going to take time to get to you and whatever.

It's all much easier if you remember two things.

One is that as long as the clock is with you, if it's literally your wristwatch not moving with respect to you, every such clock ticks off at one second per second.

There's no other speed of time ever.

What could it be?

It can't be two seconds per second.

That would make no sense.

Whatever happens to the clock, the same thing happens to you and your heartbeat and your brain and whatever.

It all seems normal to you.

But then number two, the whole journey, if you go from some place, move off at some velocity, come back, there's no reason why the total elapsed time on two different clocks has to be the same.

One that stayed behind and one that went on the journey.

Just like two people running off in the distance, one goes on a straight line, one goes in a loop-de-loop, they're going to experience different amounts of distance.

And all of these difficult things are because light behaves differently to us.

Why is light so special?

It's not.

The special thing is that there is a speed limit.

There is a maximum velocity that any physical thing in the universe can go.

It just so happens that light achieves that speed limit.

Light is always right at the boundary of traversing the speed limit.

So are gravitons or gravitational waves.

Any massless particle in the universe would move at this speed limit.

The only thing special about light is that it is the most familiar of the things that move at the speed of light.

Okay, I just want to go back to the clown for one second, right?

So let's say that the clown is looking at a clock that is on the side of the tracks, okay, stationary to the earth.

Thank you.

John's already shaking his head.

I'm just trying to define everything.

And the clown is on the train.

If

a particle of light leaves the clock's hands,

and will it ever catch up to the clown's eyes?

If the clown, who I now understand why it's a clown, it makes perfect sense to me.

If the clown is moving away from the clock,

then the clown still sees light move at the speed of light.

So the vision of the clock gets to the clown at the speed of light, but it takes more and more time between ticks of the clock that is remaining behind from the point of view of the clown.

And this is just nothing more mysterious than the Doppler effect, right?

When you're moving far away, the frequency of things goes down.

And so what you thought was tick, tick, tick from the clown's point of view is tick, tick, tick.

But

from the point of view of him looking at his own wristwatch, it's still tick, tick, tick.

That makes sense.

That makes sense.

Yeah.

Now I see you guys.

So for you in motion, the time is moving slower and you can see the time at like a measure of the rate of time for the person not in motion and you can see that happening slower.

Yeah, because your because time in your frame of reference is moving slower than it is for the clock that's stationary.

Right, so now all we've got to do is replace the clown with Saskia,

replace the train with a plane,

replace the train tracks with space, and then and then we're there, right?

Is this possible?

Could she catch up to her friends the extra year on Earth?

Yeah, sure.

So

it really depends how much time her friend is willing to invest in this enterprise.

So if you actually only go at 10% of the speed of light, which already is pretty fast,

it would take 200 years for Saskia's friend to do that journey and then to come back again and to be technically, you know, would be the same age then, but you know, also technically perhaps dead.

So

perhaps you don't want to go

that slowly.

Maybe not worth it.

Maybe not worth it.

So it starts to get reasonable about 50% of the speed of light.

You get to about sort of six years for the journey.

And as I said, if you go at sort of 86% of the speed of light, it just takes a year for them and two years for you, Saskia, waiting on the earth for her friend to come back.

But that assumes that you can just click your fingers and you're going at precisely that speed.

But if you think about trying to get to 86% of the speed of light, it would actually take you about a year of accelerating at 1G.

So you want to be comfortable during that acceleration.

You don't want to be like a fighter pilot pressed against the back of your rocket.

So it would take you, you know, about a year to accelerate to that speed.

And then, you know, you've got to decelerate, turn around, and come back again.

So, you know, it's kind of a minimum four-year commitment to do this experiment.

Still, before 2030, do you know what I mean?

Yeah, okay.

Well, you may make it the time eventually, and you can catch up with your reading.

By the way, the whole clown thing was just honestly an act of revenge.

It was just because I sat to so many of these hypotheticals in university.

It was nice to have you both, proper, serious academics, have to do it on my terms for once.

Okay, we'll make them all clowns.

I'm not sure we shone any greater light on this topic, but I was just happy to see you both engage exactly with that.

Okay, so just by speed alone, this may be impractical.

However, there is more to this than simply speed.

There is also gravity.

Let's listen to this.

My name is Richard Dyer.

I'm a PhD student at the Institute of Astronomy in Cambridge, and I research perhaps one of the most incredible things in the universe, which are black holes.

The fact that speed can affect low of time is pretty mind-boggling, but the magic thing about physics is that there's always room for things to get weirder.

Einstein made this connection between his theory of special relativity and gravity, and this opened doors to a whole new host of ideas.

Most importantly, for now, gravitational time dilation, which basically says if you're at the top of a tall building, you will age faster than if you live at the bottom.

So whilst it's certainly true, this effect is far too small for us to notice.

To really see time move differently, we need a place where space-time is warped like nothing else in the universe.

A black hole.

There is a supermassive black hole at the center of our galaxy called Sagittarius A star.

And this is millions of times the mass of the Sun.

This is a huge black hole.

And with a few simplifications, you can actually do a nice back-of-the-envelope calculation to work out how much time dilation changes the flow of time for someone close to the black hole compared to someone very far away.

So, if Saskia's friend only wanted to wait for a single day to catch up with Saskia on Earth, who has to wait for a year, they would have to travel about 100 kilometers away from the event horizon.

And then, if they were somehow instantly transported back to Earth, they would now have the same birthday.

I would take being a year different in age over traveling that close to a black hole because I hear they're pretty dangerous.

So, we've managed to get the time required down to one day by the simple addition of a supermassive black hole.

Sean,

gravity, we're sticking gravity in this, which we hadn't until now.

What does gravity do to time?

Well, gravity is the equivalent of stretching and bending space and time.

So exactly as if you walk through space on a curvy path rather than a straight one, you will experience different amounts of distance.

Now that Einstein says with his general theory of relativity in 1915 that space and time are warped and bent, and we experience that warping and bending as gravity, now you're basically walking on a hilly terrain.

And the amount of time that you feel elapsing for you will depend on where you are in the universe.

A black hole is a place where

if you dip down and hang out near the event horizon, then come back, you will not have experienced that much time, even as the people back here on Earth have experienced a lot.

So as a benchmark, essentially the more mass, the more gravitational pull, the more space-time is bent, the less or the slower time moves.

Yes, except I know it's a losing battle, but I am just not going to ever be happy with the language of the slower time moves.

Time moves at one second per second.

Fair enough.

When you walk on a curvy path, you do not go more meters per meter.

You just have traveled further.

And likewise with time.

It's not that time has slowed down.

It's just that you have taken a shortcut through time.

So for you, it's taken a day while you visited the black hole.

And for your friends back on Earth, it's taken a year.

I'm sure the phrase, you've taken a shortcut through time,

it's not going to

make it more difficult for people to understand.

So,

for example, if you lived at the top of a skyscraper,

Do you age more slowly than somebody living at the bottom of a skyscraper?

Wait, the opposite.

You're older if you're in the skyscraper.

You would experience more in time by being in a weaker gravitational field.

Yeah.

Yeah, take that, rich people.

Hang on.

So

when you meet in the lobby area, you spend a year

in your apartment, when you come down to the lobby area, you have aged more than the person who's in the ground floor.

oh

and you have to spend all that time in the lift yeah oh it's a bad deal all around for them isn't it forget that the view's not worth it god it isn't okay so gravity is also this huge thing, which actually we sort of sidestepped a bit.

And Einstein, actually, as well, we're basically doing the same journey he did to the second because the whole thing was originally set up without including gravity.

Then he brought gravity in and became the general theory of, and then you put the clowns in.

That's, I mean, that's how that's the order of events.

Step one, step two, step three.

Yeah.

All right, so here's our step three because it means we have a slight admission to make.

Because earlier on, when we were talking about the Galileo system, we kind of ignored the effects of gravity.

We did the Einstein thing.

That's that's uh we can't really be blamed for that.

And so actually we said that the system on board runs seven microseconds slower per day, but once you include gravity, that gravitational field actually makes their clocks run faster by 45 microseconds a day.

Take one from the other, 38 microseconds per day faster than clocks on the ground.

I just didn't want any clown fans writing in and complaining.

Yeah.

Would we agree?

And I know I'm preaching to the converted here.

Do we think that this is the coolest theory in all of science?

So I wrote a textbook on general relativity that opens by saying, come on, everyone agrees general relativity is the most beautiful physical theory ever invented.

I mean, there's a lot of good theories, quantum mechanics and field theory and things like this, but they're kind of ugly and hard to understand.

And general relativity is intimidating when you see the notation and everything, and there's a lot of ideas that you don't meet in your everyday life, but when you get it, it just snaps into place in this beautiful logical structure, and there's nothing like it.

But do we also agree that it's slightly better if you put more clowns into it?

You better write this up.

Submit to physical review.

I'm just saying.

I like to see this peer-reviewed, but peer-reviewed by clowns.

Water theory is not improved by the addition of clowns.

Okay, well, thank you very much to our guest there, Jean-Carroll and Katie Clough.

Thank you very much.

Well, that was very straightforward, ultimately.

Yeah, simple.

Just send you a maze on a big rocket, close to a black hole.

Bish bash bosh.

Job done.

Job's good.

Only problem, though, is that if you do do that, Saskia, you'll no longer be able to use the fact that you're a full year younger to your advantage.

Yeah, you're absolutely right.

This is her weapon against this geriatric who she has to work with.

This is her one thing she has over this person.

Yeah, yeah, the advantage of youth.

Don't give it away, Saskia.

Yeah, don't throw away your youth, Saskia.

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Wouldn't it be nice if your cash savings could just grow by itself?

With the Wealthfront cash account, it can, earning 4% annual percentage yield from partner banks on your uninvested cash, nearly 10 times the national average.

Just imagine if other things in your life work the way Wealthfront works.

If your houseplants grew at 10 times the average rate, you'd have 10 times fewer issues with sad, stunted succulents.

Your crocodile ferns would go to the size of crocodiles.

Wealthfront's cash account keeps your money thriving just like that, earning you an industry-leading rate with no account maintenance fees and with free 24-7 instant withdrawals so you can access your money whenever you need it.

Money works better here.

Go to WealthFront.com to start saving.

Cash account offered by Wealthfront Brokerage LLC member FINRA SIPC.

Wealthfront is not a bank.

The APY on cash deposits as of December 27, 2024, is representative, subject to change, and requires no minimum.

Funds in the cash account are swept to partner banks where they earn the variable APY.

The national average interest rate for savings accounts is posted on FDIC.gov as of December 16, 2024.