Relativity thought experiment

Let me just clarify that the time-dialation due to gravity is constant

I'm guessing that some one in space experiences around 1.000000001 as much time as we do, so it's not a huge effect (at least for planets)

[PairTheBoard]

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Let me just clarify that the time-dialation due to gravity is constant

I'm guessing that some one in space experiences around 1.000000001 as much time as we do, so it's not a huge effect (at least for planets)

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ok. Then it would not provide a solution for the paradox of one windowless craft accelerating at 1 g out and back while the other stays at home with 1 g supplied by gravity. 1g for the travelling craft will get it going pretty fast in just a few dozen years. Besides, the travelling craft doesn't even need to maintain the 1g the whole time. Once it gets up to speed it can just coast fast as lightning as long as it wants. The stay at home craft would have to go off planet to stay acceleration-equal and then it would have No time dilation due to gravity.

PairTheBoard

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ok. Then it would not provide a solution for the paradox of one windowless craft accelerating at 1 g out and back

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The direction of acceleration is important here I think

[PairTheBoard]

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ok. Then it would not provide a solution for the paradox of one windowless craft accelerating at 1 g out and back

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The direction of acceleration is important here I think

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The stay at home craft could duplicate the g directions the whole way by just moving to one side of the planet and then to the other. Theoretically it could go via a corridor through the center of the planet to keep things simple.

PairTheBoard

[Jim T]

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Whichever twin undergoes more acceleration overall will be the one who has aged less. This statement is not well defined, but under most interpretations this will be true most of the time

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So what if twin A is under a constant 1G acceleration on Earth, while twin B is at a constant 1G acceleration until some point when, let's say, she reached a relative velocity of .25C away from twin A at which point her ship begins coasting at that constant velocity and has 0G acceleration.

Your answer above indicates that it is the Earthbound twin, who is still experiencing acceleration, that ages less.

[runner4life7]

I'm lazy, but did you even state a frame of reference because they can all be different "ages" from different frames of reference. Granted I slept through modern physics, but the little I remember is that A) these are not going fast enough and B) You must state a frame of reference

[usmhot]

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So what if twin A is under a constant 1G acceleration on Earth, while twin B is at a constant 1G acceleration until some point when, let's say, she reached a relative velocity of .25C away from twin A at which point her ship begins coasting at that constant velocity and has 0G acceleration.

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In this case the twin on board the spaceship would age less than the twin on the planet.
During the time when her acceleration is 1G her clock and that of the twin on the planet would pass time at the same rate. However, when the spaceship is coasting - experiencing 0G - her clock would be slower than the planet-bound twin.

Special Relativity is not a factor here as from either one's frame of reference it is the other who is moving. So, when you say [ QUOTE ]
she reached a relative velocity of .25C away from twin A at which point her ship begins coasting at that constant velocity and has 0G acceleration

[/ QUOTE ] you have to account for the appropriate frames of reference. Twin B is traveling at a velocity 0.25G away from the planet as measured by twin A on the planet, BUT twin A is traveling at a velocity of 0.25G away from the spaceship as measured by twin B in the spaceship.

The only factor at this point is the acceleration due to gravity of the planet-bound twin.

And, incidentally, a rotating vs non-rotating planet really have nothing to do with anything.

[PairTheBoard]

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So what if twin A is under a constant 1G acceleration on Earth, while twin B is at a constant 1G acceleration until some point when, let's say, she reached a relative velocity of .25C away from twin A at which point her ship begins coasting at that constant velocity and has 0G acceleration.

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In this case the twin on board the spaceship would age less than the twin on the planet.
During the time when her acceleration is 1G her clock and that of the twin on the planet would pass time at the same rate. However, when the spaceship is coasting - experiencing 0G - her clock would be slower than the planet-bound twin.

Special Relativity is not a factor here as from either one's frame of reference it is the other who is moving. So, when you say [ QUOTE ]
she reached a relative velocity of .25C away from twin A at which point her ship begins coasting at that constant velocity and has 0G acceleration

[/ QUOTE ] you have to account for the appropriate frames of reference. Twin B is traveling at a velocity 0.25G away from the planet as measured by twin A on the planet, BUT twin A is traveling at a velocity of 0.25G away from the spaceship as measured by twin B in the spaceship.

The only factor at this point is the acceleration due to gravity of the planet-bound twin.

And, incidentally, a rotating vs non-rotating planet really have nothing to do with anything.

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That can't be right. I'm thinking the g force has nothing to do with it. It's the speed relative to the initial frame of reference that determines the slow down of the clock. Gotta be.

PairTheBoard

[usmhot]

Nope ... fraid not.

Special Relativity accounts for different frames of reference which are in motion relative to each other. In Special Relativity gravity is not taken into account.
Special Relativity was subjected to a number of thought experiments which highlighted paradoxes - the best known of which is the 'Twin Paradox' which is effectively what the original post of this thread exemplifies.

It wasn't until Einstein formulated General Relativity that these questions were properly addressed. He pointed out that acceleration and gravity were, to all intents and purposes, the same thing. So, if you are in a box and feel a force pulling you to one side of the box (which you can call 'the bottom') then there is absolutely no way of knowing whether the force is gravity or acceleration.
He also showed that time dilation occurs when accelerating - which is the same as saying that time dilation occurs in a gravity field. This has been verified by experiment.


Incidentally, sincere apologies - I got it backwards in my original post - the twin on Earth would age more slowly than her space-faring counterpart. Time slows down in a gravity field relative to another point in space.

[usmhot]

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It's the speed relative to the initial frame of reference that determines the slow down of the clock.

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Incidentally, to answer this point more succinctly ... there is no favoured frame of reference. We often fall into the trap of automatically thinking in terms of our postion (i.e. on planet Earth) as being THE frame of reference to which all others are measured - but that's wrong.
To see this more clearly, take two spaceships, A and B, which are traveling apart at some velocity v. What would you expect to see if you were on ship A? And what would you expect to see if you were on ship B?

Answer in white

<font color="white">If you are on ship A your clocks would measure time as normal, but the clocks on ship B would appear to be slower.
BUT
If you are on ship B your clocks would measure time as normal, but the clocks on ship A would appear to be slower.</font>