Who is Older: Spaceships Moving at Close to Speed of Light?

[jeffceth]

I have a question about the famous illustration where a guy leaves Earth in a space-ship and zips around the universe at close to the speed of light relative to the earth, and when he comes back he's only a little older but his twin brother on Earth is an old man.

Hopefully someone can help me with this: relative to the man in the spacecraft , hasn't the earth been zipping around at close to the speed of light and thus when he gets back, shouldn't his brother be the one who's young whereas he would have grown old in all the time he was zipping around the universe?

Or perhaps, to make it a bit simpler, let's say there are two spaceships, and an explosion or something in between them accelerates them apart at close to the speed of light relative to each other. However, because of gravitational influences in the local region of space, they all of a sudden stop flying apart and fly back close together, again at close to the speed of light, and then come to a stop next to each other. Relative to each, the other has been the one zipping around space at close to the speed of light. So when they meet, which one is older? Does each perceive the other as the older/younger one and if so, hasn't reality split in some fundamental way?


I hope someone can help me figure this one out.

sincerely,
jeffceth

 

[Galileo]

I have a question about the famous illustration where a guy leaves Earth in a space-ship and zips around the universe at close to the speed of light relative to the earth, and when he comes back he's only a little older but his twin brother on Earth is an old man.
Hopefully someone can help me with this: relative to the man in the spacecraft , hasn't the earth been zipping around at close to the speed of light and thus when he gets back, shouldn't his brother be the one who's young whereas he would have grown old in all the time he was zipping around the universe?

The position of the brother on the spaceship and the brother on Earth are not interchangeable. Although the constant motion is relative, the guy in the spaceship has to turn around and thus accelerate. Acceleration is not relative.
Imagine, otherwise, that for the guy in the ship, not only does the Earth accelerate, but so do all the stars and the rest of the galaxies. There's no force big enough to do that and that's ofcourse not what happens.

For the guy on earth, has brother's trip simply takes a long time, because he's limited to lightspeed. For the guy on the ship, the traveled distance is contracted so the trip takes much less time for him.

 

[jeffceth]

I understand that acceleration is not supposed to be relative, but it was my understanding that the time dilation did not result from the acceleration but rather from the time spent at close to light speeds. In your interpretation, wouldn't all the time dilation have to occur during the brief periods of acceleration at the end and midpoints of the voyager's journey, and since you can arbitraily extend the periods where no acceleration occurs, wouldn't this affect the dilation even though the periods of acceleration on his trip remain exactly the same?

In any case, what happens to our spaceship friends?

sincerely,
jeffceth

 

[Ich]

Your notion of time dilation is the typical truncated view which almost all poular books deliver. It is only half the truth, you can´t solve the twin paradox whith it. SR works only when you add the relativity of simultaneity.
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html"
gives all sorts of viewpoints.

 

[Garth]

Yes, but the OP was not the standard twin paradox, but the cosmological twin paradox. This has been thoroughly discussed on these Forums, such as here some time ago.


Instead of having two twins, consider two observers with clocks moving at high speed, close to the speed of light, relative to one another.

One observer is on Earth and for the sake of the thought experiment the universe is closed, finite yet unbounded.

After a very long time the other observer has circumnavigated the universe and passes close by the Earth again. Her clock should have recorded a far far shorter duration than the Earth bound clock.

However according to the non-Earth observer, in her frame of reference, it is the Earth that has circumnavigated the universe at high speed and the Earth clock should have recorded the much shorter duration!

Neither observer has accelerated, both have remained in inertial frames of reference throughout.

The universe itself has imparted a preferred frame, the one with the maximum duration between encounters, on the observers.

This is a very important and profound paradox that depends on the geometry of the universe being determined by the matter within it.

The ordinary twin paradox comes from SR, yet once we talk of a finite and closed universe we are in the domain of GR. Does GR cosmology therefore imply a preferred frame in contradiction to its fundamental assumption, the principle of relativity?

Garth

 

[Ich]

I don´t think the OP was about the cosmological twin paradox (it was changes in local gravitation, maybe a star or black hole which one could use for a swing-by-maneuver).
But I´m interested myself: does the cosmological TP imply some kind of rotation?

 

[Garth]

I don´t think the OP was about the cosmological twin paradox (it was changes in local gravitation, maybe a star or black hole which one could use for a swing-by-maneuver).
But I´m interested myself: does the cosmological TP imply some kind of rotation?

Yes you are right, the OP was a little unclear, I saw "a guy leaves Earth in a space-ship and zips around the universe at close to the speed of light " and wrongly read it as the cosmological twin paradox!

If you are interested you may like to read the Barrow and Levin paper The twin paradox in compact spaces.

Thus in Friedmann–Lemaıtre universes, (i) the expansion of the universe and (ii) the existence of a non–trivial topology for the constant time hypersurfaces both break the Poincare invariance and single out the same “privileged” inertial observer who will age more quickly than any other twin: the one comoving with the cosmic fluid – although aging more quickly than all her traveling sisters may be not a real privilege!

I hope this helps.

Garth

 

[Hooloovoo]

Here's a glib answer:

1) Time does not pass for an object traveling at velocity c.

1a) So as one approaches velocity c, time passes less and less.

.

2) We're talking about actual velocity, not apparent velocity.

2a) For example, a photon travels away from your flashlight at the speed of light. From it's perspective, your flashlight is traveling away from it at the speed of light. But only the photon has the actual velocity here.

2b) By the same token, although it appears to the speedy twin that the earthbound twin is the one moving very fast, it really is only the speedy twin who is traveling close to the speed of light.

.

3) Therefore, it is only the speedy twin who experiences less and less time passing, as he approaches c.

 

[Mulder]

An earlier (and IMO more concise) treatment than Barrow and Levin was done by Tevian Dray (AJP 1989 vol.58 - not free unfortunately), which comes to the usual conclusion of a global preferred frame using the cylindrical (1+1) space-time in a pretty clear way. Maybe some of you are familiar with it?

 

[JesseM]

I understand that acceleration is not supposed to be relative, but it was my understanding that the time dilation did not result from the acceleration but rather from the time spent at close to light speeds. In your interpretation, wouldn't all the time dilation have to occur during the brief periods of acceleration at the end and midpoints of the voyager's journey, and since you can arbitraily extend the periods where no acceleration occurs, wouldn't this affect the dilation even though the periods of acceleration on his trip remain exactly the same?
In any case, what happens to our spaceship friends?

sincerely,
jeffceth

Time dilation does depend on speed rather than acceleration, but the point is it has to be speed relative to a particular inertial reference frame, and no matter which inertial frame you choose, the spaceship traveler will have a greater speed than the Earth guy for at least one leg of the trip. Here was my answer to a similar question on this thread:

No matter which inertial frame you use to analyze this problem, both clocks will be ticking at a constant rate if they are moving at a constant velocity. You'd be free to analyze this problem from a frame where A and B are initially moving at 3/4c, then B comes to rest while A continues to move at 3/4c, then B accelerates to some velocity even higher than 3/4c to catch up with A. From the point of view of this frame, during the first leg of the trip when B was at rest its clock was ticking faster than A, but then during the second leg when it was moving at a greater velocity than A its clock was ticking slower, and then end result will be that this frame will still predict that A's clock will be behind B's when they reunite. No matter which inertial frame you use to analyze the problem, you will always get the same answer to the question of what the two clocks read when they reunite, even though you get different answers to how fast each clock was ticking during the two legs of the trip.

You can think of it in a geometric way...if you draw two points on a piece of paper, and draw two paths between them, one which is just a straight line between the points and one which has a bend in it, then the straight line will always be the shortest distance between the two points. Similarly, the geometry of spacetime is such that if you have two paths/worldlines between two events, one which is straight (no accelerations) and one which has a bend (the turnaround), then the straight path will always have the greatest proper time (time as measured by a clock that travels along that path).

(and because it wasn't totally clear, note that when I talked about a straight vs. bent path, that was referring to the path through spacetime, not through space--see my post #6 on that thread if you're not sure what this means)

 

[jeffceth]

Thank you all very much for your help. My original confusion is in my own mind fully resolved if one accepts the bounds of special relativity. I am, however, interested in the implications via GR and the cosmological twin paradox and also what happens when we consider the possibility that acceleration is relative. I believe the former has probably been discussed here before. What about the latter?

sincerely,
jeffceth