Twin Paradox

[mistermack]

Does anybody understand this?
I started reading the wiki page, and straight away got stuck. Why would the "moving" twin be moving in two different frames? What does that even mean? I thought that any non-accelerating frame was a valid frame, so why would a second frame become involved? It's not explained by wikipedia.
https://en.wikipedia.org/wiki/Twin_paradox

[Rum]

I must admit to getting confused with the notion of one of the twins taking off at 'high speed'. Surely relativity tells us that things only move relative to each other and that the twins are in effect receding from one another.

[jaydot]

it's nonsense.

[mistermack]

I must admit to getting confused with the notion of one of the twins taking off at 'high speed'. Surely relativity tells us that things only move relative to each other and that the twins are in effect receding from one another.

Yes, that's the essence of the paradox. If two are moving relative to each other, SR says that a clock on the moving twin will run slower than a clock on the stationary twin.
But which is actually moving?

Einstein said that if a twin shoots away from the other, and then returns, they are not equivalent in relativity, because one twin undergoes acceleration and retardation, and the other doesn't.
I'm more inclined to go with that, but originally, it was the relative movement, not acceleration, that was supposed to make time go slower or faster. That was why the clocks on the two twins were supposed to run at different speeds. Nothing to do with acceleration.

The effect has been verified using atomic clocks, so it does happen.
But I don't understand the "two frames" business at all. Surely you can describe the motion of both twins in one single frame?

[Rum]

Where's XC when you need him!?

[PsychoSerenity]

I believe the 'moving twin' is the one that's accelerating i.e. having force applied to it's mass.

I've always been rather woolly on the subject though and I don't have time to read into it now so I might be talking bollocks.

[Rum]

There's an explanation of sorts here: Inertia appears to be the key, though I'm not sure I'm that much clearer. Taken from here: http://www.einstein-online.info/spotlights/Twins

"But why can't the travelling twin turn the tables on her sibling? After all, motion is relative. Why can't the twin in the spaceship define herself as being at rest? From that point of view, it would be the Earth that moves away before returning to the spaceship. And if that is so, couldn't the travelling twin apply time dilation ("moving clocks are slower") to everyone who remained on Earth? By that argument, shouldn't it be the humans on Earth that are younger than expected once the twins are reunited? If both twins are on an equal footing, then each one should be allowed to onsider herself at rest and invoke time dilation. But in the end, when the twins meet again, only one of them can be right - then, there cannot be any ambiguity: either the one twin is younger, or the other (or, of course, both twins' arguments are wrong, and they have aged exactly the same). A contradiction - a twin paradox?

The importance of inertial observers

To resolve the contradiction, a closer look at time dilation is needed - in which situations do moving clocks indeed go slower? In the above text, the key criterion was hidden in parentheses: For the dictum "Moving clocks go slower" to hold, you must be an inertial observer. The example of freely floating space stations above gives a flavour of what this qualification means: In an inertial reference frame, all objects are perfectly weightless. For such observers, an object upon which no external forces act (for instance, that is neither pushed nor pulled) either remains at rest or moves with a constant speed along a straight line.

There's the litmus test for each twin: Is she an inertial observer, and thus entitled to apply the time dilation formula, concluding that moving clocks go slower?"

An unfortunate complication: The twin that remains on Earth is no inertial observer. She's in a gravitational field in which objects fall down instead of remaining at rest. There are two possible ways to proceed. Either one can use Einstein's theory of gravity, general relativity, and calculate how the gravitational field influences the twin on Earth. The result is that, in the given situation, the Earth's gravity does not make an appreciable difference. If we ignore Earth's gravity and treat the twin on Earth as an inertial observer, our results regarding the relative aging of the two twins will be correct, give or take a few fractions of a second. If we choose situations in which the twins eventual age difference is counted in years, gravity will not matter.

Alternatively, one could re-define the situation by having the non-travelling twin wait not on Earth, but in a freely floating space station in deep space, far away from any massive objects. That would definitely make her an inertial observer.

[Xamonas Chegwé]

As others have pointed out, acceleration is the key here. THe two twins start in the same frame of reference but the travelling twin MUST accelerate in order to leave that frame and then return to it.

I could go on but my taxi's here! More when I get back from the pub,.

[laklak]

The only twin paradox I'm familiar with happened when I dated a twin, but wasn't interested in shagging the other one. OK, they were fraternal twins and the other one was a dude, but still...

[Rum]

As others have pointed out, acceleration is the key here. THe two twins start in the same frame of reference but the travelling twin MUST accelerate in order to leave that frame and then return to it.

I could go on but my taxi's here! More when I get back from the pub,.

If you are quick - really quick, you could get back here and answer the question before it has been posted!

[mistermack]

As others have pointed out, acceleration is the key here. THe two twins start in the same frame of reference but the travelling twin MUST accelerate in order to leave that frame and then return to it.

I could go on but my taxi's here! More when I get back from the pub,.

I don't really follow this terminology of "leaving" a frame of reference, since a frame is unlimited in spatial extent.
I'm assuming that what is meant, it that it accelerates to a different velocity, so it is STATIONARY in a different frame of reference. So saying that it leaves the frame and then returns to it is exactly the same as saying it accelerates and then accelerates again in the opposite direction.

But surely all of the motion can be described in the original "stationary" frame?

[JimC]

If we replace the human twins by 2 identical sub-atomic particles with a known half-life before decaying, the experiment can actually be done. If one sample is stationary relative to an observer who times the decays, and another sample is accelerated to near light speed in a cyclotron, the stationary observer observes a lengthened decay time of the moving particle by exactly the amount predicted by the Lorenz formula.

[surreptitious57]

In the twin paradox the travelling twin covers more distance in space while the stationary twin experiences more time
But as space and time are not two separate dimensions but one inter connected one then the spacetime distance they
both experience is identical. Einstein states that time as a separate dimension is relative and that space as a separate
dimension is relative too. However when they combine to make the one single dimension of spacetime they cancel out

[mistermack]

I was trying to think of a way of doing away with the acceleration, as it just complicates the matter.

If the twins were atomic stopwatches, and one was passing the stationary one at a high speed, when they were both set to start, then the moving one goes a million miles at high speed, and meets an identical stopwatch moving at the same speed in the opposite direction. At the instant that they pass, the elapsed time is synchronised to the returning stopwatch, using radio.
So now, the second stopwatch returns to the stationary one, and the elapsed time is compared.

So what you have done, is removed any acceleration from the experiment.
Which stopwatch would show the greater elapsed time?

The moving stopwatch should show the time of the outward trip, plus the time of the return trip, which should be identical, and the total should be equal to the elapsed time of a two million mile trip at high speed, with no acceleration involved.
Would it be any different, to the "stationary" stopwatch time?

It sounds complicated, but it would be quite easy to set up, once we are doing regular flights to Mars.
So long as you get two flights that cross, you could easily do it.

[Xamonas Chegwé]

If we replace the human twins by 2 identical sub-atomic particles with a known half-life before decaying, the experiment can actually be done. If one sample is stationary relative to an observer who times the decays, and another sample is accelerated to near light speed in a cyclotron, the stationary observer observes a lengthened decay time of the moving particle by exactly the amount predicted by the Lorenz formula.

Exactly this. They've done it with Muons and other particles.