Time Dilation & Foreshortening: Understanding the Twin Paradox

[Dave1939]

As I understand time dilation, at 90% of the speed of light, a space traveling twin would age at a rate 44% of his/her twin on earth; at 99% it would be 14% and at 99.9% it's 4.5%. And these differences would be permanent. Since relativity explains things in terms of spacetime, does this mean that a rocketship traveling at a constant 90% of the speed of light away from and back to Earth - except during turnaround when the rocketship would travel at non-uniform speeds - would shrink to 44% of its earth-length?

My take away from the twin paradox as to time dilation is that when the traveling twin returns to earth, he/she will be younger by a number of years calculated using the formulas and that this difference in aging would be observed by both twins even though they are currently sharing the same reference framework-lightspeed on earth. What about foreshortening? Would the spaceship on its return to Earth only be 44% of the length it was when it left earth? This seems more strange than the traveling twin being younger on his/her return to Earth even though both would be sharing the same reference framework, but given the unity of spacetime the dilation principle, I assume, should apply to both space and time.

Dave1939

 

[Dale]

While the traveling twin is in motion his clocks are time dilated and his rulers are length contracted relative to the stay-at-home twin's frame. While the traveling twin is at rest his clocks are not time dilated and his rulers are not length contracted.

 

[Dave1939]

Is anyone truly at rest? The Earth is moving. I read somewhere that the closest we can come to a rest state is in freefall like the astronauts in orbit around the earth. While freefalling in an orbit is not uniform motion nor absolute rest, is it not the closest we can come to it?

 

[HallsofIvy]

There is a reason why it is called "relativity"! It makes no sense to talk about "at rest" or "in motion" without saying "relative" to something. Everything is at rest relative to itself!

 

[Dale]

Is anyone truly at rest?

I thought it was clear from the context that "in motion" and "at rest" were both "relative to the stay-at-home twin's frame". I apologize if my brevity interfered with clarity.

 

[phinds]

My take away from the twin paradox as to time dilation is that when the traveling twin returns to earth, he/she will be younger by a number of years calculated using the formulas and that this difference in aging would be observed by both twins even though they are currently sharing the same reference framework-lightspeed on earth. What about foreshortening? Would the spaceship on its return to Earth only be 44% of the length it was when it left earth?

No, the spaceship would be the same size but it would be younger than an equivalent spaceship that stayed home. Length contraction and time dilation are characteristics of what is seen by a remote observer. Aging is due to traveling through different path in spacetime. If you take a wind-up clock on such a trip, it ticks at the same old one second per second but the stay-at-home sees it ticking at a different rate. When it gets back, it's still ticking at one second per second but it has ticked fewer times than a similar clock that stayed home. Apparent physical distortions as "seen"/calculated by the stay-at-home are not physical and have no meaning to the traveling objects.

 

[Dave1939]

I thought it was clear from the context that "in motion" and "at rest" were both "relative to the stay-at-home twin's frame". I apologize if my brevity interfered with clarity.

I'm confused. The stay at home twin is not truly at rest since the Earth is moving; however, he/she is moving at a speed closer to the impossible-to-achieve absolute rest state than his/her traveling twin. So if neither twin is truly at rest, is it not more accurate to say relative to one another, the stay-at-home twin is not at rest in any frame of reference but is simply closer to an absolute rest state than his/her traveling twin?

 

[Dave1939]

There is a reason why it is called "relativity"! It makes no sense to talk about "at rest" or "in motion" without saying "relative" to something. Everything is at rest relative to itself!

If absolute rest is not possible, in what sense is everything at rest relative to itself ? In freefall, I come close to being at rest but otherwise I'm in motion. If in no frame of reference is it possible to be at rest, how can I claim to be at rest relative to my own frame of reference or any other? Is "rest state" physical or conceptual?

 

[jbriggs444]

If absolute rest is not possible, in what sense is everything at rest relative to itself ?

In the trivial sense. If I define a coordinate system so that the (0,0,0) position is always my position then, by definition, my position is always (0,0,0). My velocity is always (0,0,0) and my acceleration is always (0,0,0).

"Absolute" rest is not accepted, not because it is not possible, but because it is ambiguous. The laws of physics give us no basis on which to say "that is the One True Reference Frame against which 'absolute' rest must be measured".

 

[PeterDonis]

If absolute rest is not possible, in what sense is everything at rest relative to itself ?

In the sense that "being at rest relative to yourself" is relative, not absolute.

 

[phinds]

In the sense that "being at rest relative to yourself" is relative, not absolute.

I guess it's just semantics, but I've always thought of being at rest relative to oneself as absolute (but it is LOCALLY absolute not globally)

 

[PeterDonis]

I've always thought of being at rest relative to oneself as absolute (but it is LOCALLY absolute not globally)

I don't think this is likely to be illuminating. For one thing, it says that something with the word "relative" in it is absolute, which doesn't seem to be a very good choice of words. For another, then you have to explain what "locally absolute" means as opposed to "globally absolute". I think it's a lot easier just to accept the obvious implication of the wording "at rest relative to oneself" and say that it's relative.

 

[phinds]

I don't think this is likely to be illuminating. For one thing, it says that something with the word "relative" in it is absolute, which doesn't seem to be a very good choice of words. For another, then you have to explain what "locally absolute" means as opposed to "globally absolute". I think it's a lot easier just to accept the obvious implication of the wording "at rest relative to oneself" and say that it's relative.

Reasonable.

 

[Dale]

I'm confused. The stay at home twin is not truly at rest since the Earth is moving; however, he/she is moving at a speed closer to the impossible-to-achieve absolute rest state than his/her traveling twin. So if neither twin is truly at rest, is it not more accurate to say relative to one another, the stay-at-home twin is not at rest in any frame of reference but is simply closer to an absolute rest state than his/her traveling twin?

There is no such thing as "absolute rest" or "truly at rest". There is no sense in which one twin is closer or further from these non-existent states, and it is not more accurate to say one is closer.

That said, the concepts of moving relative to a specific frame or being at rest relative to a specific frame are both well defined and meaningful.