What we learned last time

Hey guys it’s so hot right now. So last time we learned something interesting. If you see a bus going past you on the street… and you watch the people in the bus, you’ll notice that they are AGEING slower than you are! Time is moving slower on the bus, than on the sidewalk… it seems.

Wow. So what’s the problem?

There is no problem with that conclusion. Except that… remember how in part 1, we noted that a person INSIDE the bus will think that everything OUTSIDE the bus is moving?

If I repeat the thought experiment from part 2, i’ll see that someone INSIDE the bus will see time passing slower OUTSIDE the bus.

So if Amin is sitting in the bus, and Pawan is sitting outside the bus. and they both have clocks sitting next to them… If i ask Amin, he will say that Pawan is aging SLOWER; and if I ask Pawan, he will say that Amin’s clock is the one which is slow.

Twin Paradox Redux.

Let me spell out the elements of the twin paradox, for clarity sake.

1. We have a Pair of twins, one named Ben, the other named Liz. They are rocket twins. Lets suppose they live together out in deep space.
2. Ben gets into a rocket ship, and accelerates towards a far-off star. (in the process he achieves a velocity close to the speed of light). The Twins miss each other, and so use powerful telescopes to stay in visual contact over the course of the trip. They can, as a result, take note of how fast each other’s clocks are running.
3. When Ben returns from his trip, he notices that Liz is somehow Several Years Older than his twin.

The overly simple resolution to the paradox:

The simplest explanation says that Liz has noticed that Ben’s Clocks were running slower than her own clocks, because Ben attains a sizable velocity (close to the speed of light). And This, surely, is what has happened.

The Problem with this explanation:

Arguing from the point of relativity, where we’d imagine that Ben would argue “hey, Liz is the one who is moving, not me!”, Ben would see that Liz’s clocks were running more slowly.

The Problem with saying this…

As it happens, arguments about time dilation at constant velocities are not sufficient to explain the twin paradox. One reason has to do with the idea of relativity, which can be restated in the following way:

Relativity is the understanding that there is no such thing as “absolute motion”, or equivalently “absolute rest”. Alternatively, If you were under the impression that you were at rest, and i asked you to close your eyes, and then teleported you onto a spaceship moving at constant velocity; there would be no way for you to tell! (aside from all the beeping). Alternatively, any bland, windowless room moving at a constant velocity is indistinguishable from any other bland, windowless room moving at any other constant velocity.

I’m highlighting the identification of  “rooms moving at constant velocity” as being equivalent because it doesn’t address acceleration! Imagine yourself in an elevator. you can *tell* when the elevator is moving. you can feel yourself accelerating up and down, even if there aren’t any visual cues! There’s NO WAY you could con someone in an elevator into thinking that they weren’t moving up and down.

So, Ben’s experience in his rocket ship Is Not equivalent to Liz’s experience at home. And for that reason we can say that even though Liz will see Ben’s clock running slower; Ben will *not* see Liz’s clock moving slower in an equivalent way!

Liz sees Ben’s Clock running slower, because he is moving, and has Time Dilation happening.

Ben’s notes of what happens to Liz’s clock are *not* equivalent to Liz’s notes; because Ben is Accelerating and Liz isn’t.

Another way to describe the resolution of this problem is to say: If Liz had left on *exactly the same* type of trip (accelerated with the same force at the same times), but in the opposite direction; when they both returned home, they’d be the same age. Get it?

Next time I’ll talk about the final generalization of the Twin paradox. *gravity*!