Episode 22 - Time is personal

Tomlin Hawthorne

Two identical twins, born minutes apart. On their thirtieth birthday, one of them boards a spacecraft and flies to a star and back, at very nearly the speed of light. The other stays at home, pays the bills, waters the plants.

Tomlin Hawthorne

The traveller steps off the ship. They embrace.

Tomlin Hawthorne

Are they still the same age?

Tomlin Hawthorne

No. The one who stayed is older. Not by a trick of bookkeeping. Older in the body. More grey hair, more heartbeats used, more birthdays lived through. If the trip was fast enough and far enough, the traveller could come home, still in their thirties, to a twin of eighty. Or to a grave.

Tomlin Hawthorne

This isn't a prediction waiting to be tested. It's been measured, with clocks, with aeroplanes, with particles, thousands of times. Time does not run at one rate for everybody. Today we find out why, and I think you'll be surprised how little it takes.

Tomlin Hawthorne

Last time I left you running at nearly the speed of light, holding up a mirror. Does your reflection disappear? Einstein's answer, and nature's, is no. You see your face perfectly normally. Light leaves your face at the speed of light relative to you, always, however you're moving. Otherwise you could tell you were moving by looking in a mirror, and you never can.

Tomlin Hawthorne

So that's the rule. Everyone, however they're moving, measures the same speed for light. And I said something has to pay for that. Today we send the bill. The question is: can two honest clocks disagree?

Tomlin Hawthorne

I'm going to build you a clock. It's the simplest clock that could possibly exist, and it's the one Einstein's argument really rests on.

Tomlin Hawthorne

Take two mirrors, facing each other, one above the other, a little way apart. And between them, a single pulse of light, bouncing up and down. Up, hit the top mirror, down, hit the bottom mirror, up again.

Tomlin Hawthorne

Each bounce is a tick. That's the clock. Light always travels at the same speed, and the mirrors are a fixed distance apart, so the ticks are perfectly regular. Tick. Tick. Tick.

Tomlin Hawthorne

Now I'm going to give one of these clocks to you, and you're going to hold it on your lap in a train. A very fast, very smooth train. And I'll stand on the platform with an identical clock and watch you go by.

Tomlin Hawthorne

First, your view. You're sitting in the train. The clock's on your lap. The pulse of light goes straight up and straight down. Up, down. Nothing odd at all. By Galileo's principle, there couldn't be: you're in the cabin below decks.

Tomlin Hawthorne

Now my view, from the platform. I'm watching your clock through the window as you rush past, left to right.

Tomlin Hawthorne

The pulse leaves the bottom mirror. But by the time it reaches the top mirror, the top mirror has moved along to the right, with the train. So from where I stand, the light didn't go straight up. It went up and across. On a slant. A diagonal.

Tomlin Hawthorne

Then down again to the bottom mirror, which has moved on further still. Another diagonal.

Tomlin Hawthorne

So I see the light in your clock tracing out a zigzag. A row of tall triangles, as it bounces between the mirrors and the mirrors slide along.

Tomlin Hawthorne

Now. A diagonal is longer than a straight up and down. That's just geometry. The slanted side of a triangle is longer than its height. So according to me, the light in your clock travels further between ticks than the light in mine.

Tomlin Hawthorne

And here's the step. In ordinary physics, before 1905, you'd say: fine, it goes further, but it's also going faster, because it's got the speed of the train added on sideways. So it covers the longer path in the same time, and the clocks agree.

Tomlin Hawthorne

But we're not allowed to say that. The rule is that I measure light at the same speed as you do. Always. No bonus from the train.

Tomlin Hawthorne

So from where I stand, the light in your clock has further to go and no extra speed to do it with. Therefore it takes longer.

Tomlin Hawthorne

Your clock ticks more slowly than mine.

Tomlin Hawthorne

That's it. That's the whole argument. A longer path, at the same speed, takes more time. If you're willing to accept that light has the same speed for everyone, you have to accept that a moving clock runs slow.

Tomlin Hawthorne

Now you'll have objections, and they're the right ones.

Tomlin Hawthorne

First objection. That's just your funny light clock. A proper clock, with gears, wouldn't do that.

Tomlin Hawthorne

Yes it would. Suppose you had a wristwatch on as well, and it kept normal time while the light clock on your lap ran slow. Then you could look from one to the other, see them drifting apart, and say: aha, I must be moving. And you'd have detected your own steady motion from inside the train. Which is forbidden. So the wristwatch has to slow by exactly the same amount. And so does a pendulum. And so does your pulse, and the rate your hair grows, and the speed of your thoughts.

Tomlin Hawthorne

It isn't that clocks go wrong when they move. It's time. Time itself passes more slowly on the train, as measured from the platform.

Tomlin Hawthorne

Second objection. I'd notice.

Tomlin Hawthorne

No. You'd notice nothing at all. Everything on the train slows together, including you. Your clock looks fine to you. A minute feels like a minute. It's only when you compare with someone who's been moving differently that the difference shows.

Tomlin Hawthorne

Third objection. If this were true, we'd have noticed long ago.

Tomlin Hawthorne

Here are the numbers. The effect depends on how your speed compares with the speed of light. A jet airliner flies at about a millionth of the speed of light. At that speed, time on board runs slow by about one part in a trillion. Fly continuously for a lifetime and you'd gain about a thousandth of a second.

Tomlin Hawthorne

But it grows. At half the speed of light, a moving clock loses about thirteen per cent. At eighty-seven per cent of light-speed, it runs at exactly half rate. At ninety-nine and a half per cent, a tenth. And as you approach the speed of light itself, time on board slows toward a standstill.

Tomlin Hawthorne

We never noticed because we're slow. We live in the crawling lane of the universe, where this is too small to see. But it's always there.

Tomlin Hawthorne

It gets stranger. Einstein realised that if time is flexible, then so is the idea of two things happening at the same time.

Tomlin Hawthorne

Here's his own example. A long train is moving along a straight track. Two bolts of lightning strike, one at the front of the train and one at the back, and each leaves a scorch mark on the train and on the ground.

Tomlin Hawthorne

A man is standing on the embankment, exactly halfway between the two scorch marks on the ground. The flashes reach him at the same instant. He was the same distance from each. So he says: the two bolts struck at the same time.

Tomlin Hawthorne

A woman is sitting on the train, exactly halfway along it. Now, while the light from the two flashes is on its way to her, she's moving forward, toward the front flash and away from the back one. So the light from the front reaches her first.

Tomlin Hawthorne

She knows she's in the middle of the train. She knows light travels at the same speed from both ends, relative to her. That's the rule. So she can only conclude one thing: the front bolt struck first.

Tomlin Hawthorne

Who's right?

Tomlin Hawthorne

Both. There's no fact of the matter. For him, the strikes were simultaneous. For her, they weren't. And there's no third, neutral position from which to say whose view is the true one.

Tomlin Hawthorne

I'd like you to notice what's just gone. The idea that there's a single moment, now, that stretches across the whole universe. That you can ask what's happening on Mars right now, or in the Andromeda galaxy right now, and there's a definite answer. There isn't. Now is local. Two people walking past each other in the street have very slightly different nows, and over a great enough distance, the difference becomes days.

Tomlin Hawthorne

And this is what the patent applications were about. Deciding when distant clocks agree. Einstein saw that the question has no absolute answer.

Tomlin Hawthorne

One more casualty, quickly. Lengths. If we disagree about times, and we agree about the speed of light, we'll disagree about distances too. A moving object, measured from the platform, is shorter along its direction of motion than it is when measured by someone riding with it. At eighty-seven per cent of light-speed, your train, to me, is half its normal length. To you, it's perfectly normal, and it's the platform that's squashed.

Tomlin Hawthorne

Right. Evidence. Because I wouldn't believe this on the strength of a drawing of some triangles, and neither should you.

Tomlin Hawthorne

First witness: a particle called the muon. It's a sort of heavy cousin of the electron. Muons are made high up in the atmosphere, about fifteen kilometres above us, when rays from space strike the air. They rain down on us constantly. A hundred or so pass through your body every second.

Tomlin Hawthorne

Now, muons are unstable. They fall apart. A muon lasts, on average, about two millionths of a second. And even at very nearly the speed of light, in two millionths of a second you can only travel about six hundred metres.

Tomlin Hawthorne

So a muon made fifteen kilometres up ought to die in the first half-kilometre. Almost none should reach the ground. And yet the ground is thick with them.

Tomlin Hawthorne

The answer is that the muon's clock is running slow. It's travelling so fast that, by our reckoning, its two-millionths of a second is stretched out twenty or thirty times. That gives it time to reach the surface. This was first measured in 1941, on a mountain in Colorado, by comparing the number of muons at the top with the number at the bottom.

Tomlin Hawthorne

And from the muon's own point of view? Its clock is fine. It lives its ordinary two millionths of a second. But the atmosphere, rushing up toward it at nearly light-speed, is squashed. Fifteen kilometres has become a few hundred metres. So it gets to the ground on time either way. We say its clock ran slow. It says the distance shrank. Both descriptions give the same result, which is the muon in your living room.

Tomlin Hawthorne

Second witness. In October 1971, two American physicists, Joseph Hafele and Richard Keating, took four atomic clocks around the world on ordinary commercial airliners. Twice. Once flying east, once flying west. The clocks had their own seats, booked under the name Mr Clock, and were strapped in. The whole experiment cost about eight thousand dollars, most of it air fares.

Tomlin Hawthorne

When they got back, they compared the travelling clocks with identical ones that had stayed in Washington. They no longer agreed. The differences were billionths of a second, and they matched what relativity predicted.

Tomlin Hawthorne

Third witness, and you're carrying it. Satellite navigation. Your phone finds its position by listening to signals from satellites, each of which carries an extremely good clock, and working out how long each signal took to arrive. Light travels thirty centimetres in a billionth of a second, so the timing has to be good to billionths of a second.

Tomlin Hawthorne

Those satellites are moving at fourteen thousand kilometres an hour. So their clocks run slow, by about seven millionths of a second a day. There's a second effect, from gravity, which we'll meet in episode twenty-five, and which goes the other way and is bigger. The engineers correct for both. If they didn't, the position on your map would drift by about ten kilometres every day.

Tomlin Hawthorne

So each time a phone tells you to turn left in three hundred metres, it's relying on the fact that time runs at a different rate up there. Relativity isn't an exotic theory about spaceships. It's in your pocket, keeping you out of the river.

Tomlin Hawthorne

Back to the twins. There's a puzzle in the story that you may have spotted.

Tomlin Hawthorne

I said the traveller's clock runs slow as seen from Earth. But motion is relative. From the traveller's point of view, it's the Earth that rushed away and came back. So shouldn't the traveller say the Earth twin's clock ran slow? Shouldn't each think the other is younger? They can't both be right. When they meet, one of them has more wrinkles.

Tomlin Hawthorne

This is called the twin paradox, and it has a clean answer. The two twins haven't had the same experience. The one at home stayed in steady motion the whole time. The traveller didn't. The traveller had to stop at the far end, turn round and come back. They changed direction. They felt it: they were pressed into their seat. And Galileo's principle, the rule that you can't tell who's moving, only applies to steady motion. The moment you turn round, you know it was you.

Tomlin Hawthorne

So the situation isn't symmetrical, and there's no contradiction. The one who turned round is younger.

Tomlin Hawthorne

And people have really done it, in a small way. The astronauts and cosmonauts who've spent a year or more on a space station, going round the Earth at eight kilometres a second, have come home very slightly younger than they would otherwise have been. The record-holder, a cosmonaut with more than two years in orbit, has travelled about a fiftieth of a second into the future. It's not much. But they've done it.

Tomlin Hawthorne

The myth of the week is in four words: it only seems slower.

Tomlin Hawthorne

People hear all this and conclude it's a kind of optical illusion. That the moving clock looks slow, the way a distant person looks small. It doesn't just look slow. The muons arrive. The atomic clocks, sitting side by side on the bench afterwards, show different times. The twin is younger. These are physical facts you can photograph.

Tomlin Hawthorne

And the question to take away.

Tomlin Hawthorne

There's no universal now. That's what the lightning showed. So think about a sentence like: I wonder what she's doing right now. If she's across the room, fine. If she's on a planet round another star, the phrase right now doesn't pick out anything.

Tomlin Hawthorne

We usually think the past is fixed, the future is open, and the present is the thin moving line between them. But if my present and your present are different slices, if an event that's in my future can be in the past of someone walking by, in what sense is the future open?

Tomlin Hawthorne

Don't answer yet. Next episode makes it sharper.

Tomlin Hawthorne

Your challenge. A drawing, and then a conversation.

Tomlin Hawthorne

Draw the light clock. Two short horizontal lines for mirrors, one above the other, and an arrow going straight up between them. That's the view from the train. Next to it, draw three or four copies of the clock in a row, each shifted to the right, and draw the light as a zigzag from the bottom of the first to the top of the second to the bottom of the third. That's the view from the platform.

Tomlin Hawthorne

Look at the two. Straight line, and slanted line. The slanted one is longer. That's the whole of time dilation.

Tomlin Hawthorne

Then find someone, a friend, a partner, a patient child, and explain it to them with the drawing. You're not allowed to say "Einstein proved." You're only allowed the two mirrors, and the rule that everyone measures the same speed for light. If you can get them to say "so the moving clock has to tick slower," you've understood special relativity. People are awarded degrees for less.

Tomlin Hawthorne

Next time. If my time and your time differ, and my lengths and your lengths differ, is anything left that we agree on? Yes. One thing. And a mathematician who'd once called Einstein a lazy dog is about to stand up in a lecture hall in Cologne and say what it is.