Physics for a friend....Twins Paradox

[Janx]

I've got a friend who's got a question about the Twins Paradox:

"Why is one twin seen as the traveler, moving away and returning at near lightspeed and aging slower? Everything is relative, is it not? Why isn't this scenario seen as both twins moving away from one another and back at equal velocities, in which case both of their clocks would be equally slowed, and they would meet up again, having aged at the same rate?"

For the rest of us, the Twins Paradox, as I understand is that we have a pair of twins. We launch one twin out at super-fast speed on a looping trip (so he returns). The magic of Einstein says time slows down for the faster twin, and thus when they re-meet the "faster" twin will have aged less.

My querulous friend appears to think that the effect of motion would be relative to each other such that stuff he says might be true.

I told him I'd check with my physics friends, and here we are.

Personally, I suspect the fact that one twin experiences additional acceleration and momentum (the faster twin) is the contributing factor to the time dilation. One twin experienced something sciencey the other did not, therefore there's a difference as yet to be explained by an expert.

Can any of y'all spare a moment to explain it?

Thanks!

 

[Morrus]

One's accelerating; the other is not.

 

[Umbran]

Yes.

Not *this* moment, 'cause I am still at work. But I will take a stab at an explanation later tonight, if possible.

 

[Umbran]

One's accelerating; the other is not.

That's... incorrect. I'm sorry.

 

[Umbran]

Okay, finished a thing. I can take a moment on this.

The trick is to not think of this as "one twin stays at home, and one flies out for a while". Think of it as "one twin stays at home, the other goes to a place and comes back"

Imagine that we have twins. One stays on Earth, and the other is sent to Alpha Centauri, 4 light years away. They will travel at 0.8c. We will assume that the time to reach that speed, and to turn around and re-accelerate toward Earth, are negligible. This is not true, but it is demonstrative. Numbers have been chosen to make them easy to work.

From the point of view of Earth (Earth's rest frame), the ship is traveling a total of 8 light years, at 0.8c, and so will come back in 10 years - everyone on Earth will age 10 years before the ship returns.

(People on Earth expect that time on the ship will be reduced by a factor ϵ = sqrt (1 − v^2 / c^2) . ϵ=0.6, so the ship will experience 6 years of time.)

Now, the rest frame of the ship is *moving* with respect to the rest frame of Earth. And time dilation is not the only effect of travel near the speed of light! We talk about time more, because time is mysterious, but distance along the line of motion is also contracted!

When the ship is flying, it looks to them like the distance to Alpha C. is, compared to that measured on Earth, contracted by the same ϵ=0.6. So, the distance to them is only 2.4 light years each way! And, to travel the round trip of 4.8 light years at 0.8c takes... 6 years!

People on the ship *agree* that they will experience less time on a trip there and back again.

-----------
This is a standard example. It may also be seen on Wikipedia if you want a different statement of it in a larger context.

https://en.wikipedia.org/wiki/Twin_paradox#Specific_example

 

[Janx]

Yes.

Not *this* moment, 'cause I am still at work. But I will take a stab at an explanation later tonight, if possible.

Thanks!

He seems fixated on the relativity concept as the twins stare at each other and it appears they are racing toward each other. He's a simpler version of it as "let's eliminate acceleration, unless you want to take the derivative of Einstein's equation. :-D So, set up the scenario such that the two twins both pass each other in "empty" space with a delta V near lightspeed. V1 could be zero and V2 near lightspeed (the Twins Paradox) or V1 and V2 could be equal. Without a reference point, there's no way to tell which twin (if not both) is traveling fast and ageing slowly."

I think your explanation of the Twins Paradox will cover this second one, which really doesn't consider how we got twins separated to setup the experiment....I think we're stumbling over what relativity really means in physics vs. language usage (kind of like theory vs hypothesis).

 

[Morrus]

That's... incorrect. I'm sorry.

Lucky I’ve got you physicists around!

 

[Umbran]

He seems fixated on the relativity concept as the twins stare at each other and it appears they are racing toward each other.

I understand. One can naively think, 'Well I can use any frame of reference I want. I could use Twin A's frame, or Twin B's frame. Each can think the other is moving."

That's why I introduce a frame that is not dependent on the Twins, and measure *both* of them relative to that. In my example, the reference frame in which Earth is at rest*. It happens that one of my Twins stays at rest relative to Earth, and the other does not.

I could have both twins leave Earth, and zoom around and come back, even passing either other, if you want. Using Earth as the stationary frame of reference, I can tell you which one ages more.

Without a reference point, there's no way to tell which twin (if not both) is traveling fast and ageing slowly."

Yes. Remember that this is (falsely) called a paradox, because at some point, the twins are the same age, and later, they are not. So, for some period of their lives, they have the same clock. You can measure everything with respect to *that* frame, where both have the same clock. Then, either one or both can move, and you have a reference.


*If you want, call it the Sun at rest, allow Earth to orbit, the difference is negligible when the travel is on the order of light years. It all comes out in the wash.

 

[Janx]

Thanks for taking the time to explain this Umbran.

 

[freyar]

Umbran's explanation is spot-on, but I did want to offer a comment on the acceleration part. It's not the acceleration that makes the difference in aging, but it isn't possible for the traveling twin to go away and then come back to the earth to make a comparison to the stay-at-home without accelerating, at least in our universe. There has to be a change in inertial frame somewhere.

On the other hand, you could imagine a universe where one direction is actually a circle that's small enough to travel around. Then the traveling twin could just travel around the whole universe to get back to the earth without accelerating. The earth-bound twin will still be older. But both twins are in supposedly equivalent inertial reference frames the whole time. The key in this example is that special relativity doesn't work across the whole universe when a direction is finite in extent. Basically, there is a preferred reference frame where the circle direction is static.