The Twin Paradox

A lot of people think the “twin paradox” of relativity just means if you fly away in a space ship going close to the speed of light you’ll age more slowly than your twin at home and then you’ll paradoxically have twins two different ages.

While perhaps surprising that isn’t actually paradoxical. And it is wrong.

In fact a fundamental part of “relativity” is that movement is relative.

If you are in a spaceship moving away from earth at near the speed of light then…

By relativity…

It is exactly as correct to say the earth is moving away from your stationary spaceship at near the speed of light.

What is moving and what it “still” is entirely determined by your reference frame, which is always chosen arbitrarily.

There is no “true” or fundamental reference frame.

This isn’t just mathematical mumbo jumbo. The earth really is moving. Relative to the sun it moves in a big circle. Relative to the center of the galaxy it moves on a much bigger circle. And of course the whole galaxy is moving quickly.

The fact that you say the space ship is moving away from earth at some speed is just a convenient way to think about it.

It isn’t the real movement. Or perhaps it is better to say it is the real movement but every other way to think about it is just as real, including the one where the earth is moving at near the speed of light and the ship is still. Or one where they both move away from some other star at different speeds.

This concept is absolutely fundamental to Einstein’s theory.

And by “theory” we mean fact. It has been proven repeatedly.

So that gets us back to the twin paradox.

If moving very very fast makes time slow down…

…but how fast you’re moving or if you’re moving at all is relative, then which twin experiences slowed time?

If the ship is moving at near the speed of light then the Astronaut twin ages more slowly.

But if the earth is the thing moving at near the speed of light then it is the earth-bound twin (and every other human) who is aging slowly.

Because movement is relative to the reference frame and you can choose any reference frame you want.

And therefore…

BOTH ARE TRUE.

Great! Then both age slowly and the twins stay the same age, right?

Heh.

No.

They don’t call it a paradox for nothing.

From the perspective of the twin on the ship, she is aging at a normal rate and her brother on earth is aging slowly. At any given moment she is older than her brother.

But from the perspective of the man on earth, it is his ship-bound sister who is aging slowly. From earth’s perspective the twin in space is always younger.

So we have a scenario where both twins are both older and younger than the other simultaneously.

⁉️

In a relativistic world simultaneity is an illusion. In any two different reference frames the idea of things happening at the same time no longer makes sense.

If they could somehow chat via some magic radio what would they find? How could they possibly be both older and younger than the other and somehow converse about it?

They can’t. This is why we’re reasonably sure it is impossible to communicate (which is to say transfer any information at all) at faster than the speed of light.

If you can, then given the same principles as the twin paradox, you can easily set up a scenario where you cause something to happen backwards. In other words, where the effect happens before the cause.

And we choose to believe in a universe that obeys “causality” over one that obeys simultaneity, or allows faster-than-light communication. It just seems more likely to be true.

I have been thinking about the twin paradox tonight. The strange idea of time passing differently for one person vs another.

It seems like yesterday that I took my kids to Biosphere 2 in Tucson.

Like literally it feels like it happened so recently it may have been this year.

But I just saw the pictures and Isabel looked so young.

It was when she was in middle school.

For me, a heartbeat.

For her, the entire high school experience.

Now neither of us was moving at relativistic speeds relative to the other. But still…

Two people…

Connected by life and love…

Moving through life at different rates.

My frame of reference is no less valid than hers.

And perhaps we can never really bridge the gap in understanding of these years.

But I choose to believe that she and I were there…

And now we are here…

And whatever happened…

However strange the phenomenon that divides our perception…

Causality was preserved.

And despite what it seems, the fabric of our universe is sound.