Time and Space: What Happens When Two Men Meet in Adjacent Rockets?

[tiny-tim]

… gravitational equivalence principle is infinitesimally local …

when a closed body is in free fall, a person in it will not experience any force and cannot actually make out whether he is accelerating, or he is simply in empty space.

Yes … one person, if he's confined to one corner of the spaceship.

… for example, if a ship you are in accelerates, you can feel it. but if the same ship were in a free fall, acceleration would be undetectable. relative to any detecting machine …

No … you're ignoring the fact that he can detect gravitational potential difference by comparing his own clock to another clock at another corner of the spaceship.

So long as you allow him to put his detecting machine a few feet away from him, he can detect acceleration.

The gravitational equivalence principle is purely local … and "local" means "infinitesimally local", not local as in in-the-same-spaceship.

(btw, if you click on the "QUOTE" button under a post, you can insert the quote properly … or does that not work on your browser?)

 

[ankitpandey]

dear tiny tim.
you had said about the case where two bodies collide and return, that the acceleration is huge.i don't have much knowledge about change in time due to acceleration. but even then i have a doubt. may be sometime long ago before Earth was formed, it had some good acceleration with respect to sun. similiarly, all objects must have had accelations during the big bang. doesn't this suggest an absolute space?

 

[tiny-tim]

No! ​

 

[ankitpandey]

"No … you're ignoring the fact that he can detect gravitational potential difference by comparing his own clock to another clock at another corner of the spaceship.

So long as you allow him to put his detecting machine a few feet away from him, he can detect acceleration.

The gravitational equivalence principle is purely local … and "local" means "infinitesimally local", not local as in in-the-same-spaceship."
hey, in relativity, isn't gravitation simply a space curvature towards an object and not a force or acceleration? then how can one detect an acceleration that never was?
(i wonder if this was a really stupid question)

 

[tiny-tim]

… clocks detect gravitational acceleration indirectly …

hey, in relativity, isn't gravitation simply a space curvature towards an object and not a force or acceleration?

Yes.

then how can one detect an acceleration that never was?

As I said, the two-clock method detects a difference in gravitational potential.

In other words, it detects the geometry (the curvature) of space-time.

Although it does not detect acceleration directly, it does allow us to say "we are feeling no forces, but we know that the space round us is curved, so we know that we must be in gravitational free-fall … in other words, accelerating!"

 

[my_wan]

i didnt understand that. when a closed body is in free fall, a person in it will not experience any force and cannot actually make out whether he is accelerating, or he is simply in empty space. i know that according to relativity, gravity is actually curvature in space, but i am referring to it here in Newtons way. what i want to say is that any acceleration is detectable only if the body which is detecting it is not affected directly. for example, if a ship you are in accelerates, you can feel it. but if the same ship were in a free fall, acceleration would be undetectable. relative to any detecting machine, it would be Earth accelerating with 'g', not the ship. the force experienced by you in the previous case is actually due to inertia, but there is no inertia if the force(like gravity) acts upon you as well.

Yes you have described Einstein's principle of equivalence perfectly. In a gravitational field in free fall you are not accelerating. It is when you are standing on the ground that you are accelerating which is why you feel your weight. This is why gravity is described a a curvature of space-time.

If a body is in free fall there is no acceleration, felt or not. The feeling of acceleration is the acceleration. No feeling of acceleration and there is no acceleration to speak of. Standing on the ground you are being accelerated upward because the ground will not let you free fall. When falling toward he Earth you are simply traveling a straight line in curved space, no acceleration.

 

[aachenmann]

this question forom a student couldn't be answered by professor in class-
imagine 2 men in two rockets adjuscent to one other.you are one of them. rockets begin to move, say for example, revolve around sun. after few fast revolutions, they stop near each other. now you and the other man meet. both expect the time in their own clocks to be lesser than that in other's. you both compare your wrist watches, and therefore you both now see the same time "together".
WHAT do you think should happen? do you really expect your time to be lesser than his?

Just draw world lines for each twin in spacetime diagram, then it's clear what happened

 

[yuiop]

when a closed body is in free fall, a person in it will not experience any force and cannot actually make out whether he is accelerating, or he is simply in empty space.

Yes … one person, if he's confined to one corner of the spaceship.

… for example, if a ship you are in accelerates, you can feel it. but if the same ship were in a free fall, acceleration would be undetectable. relative to any detecting machine …

No … you're ignoring the fact that he can detect gravitational potential difference by comparing his own clock to another clock at another corner of the spaceship.

So long as you allow him to put his detecting machine a few feet away from him, he can detect acceleration.

The gravitational equivalence principle is purely local … and "local" means "infinitesimally local", not local as in in-the-same-spaceship.

I think Tiny-Tim is misunderstanding the question asked by ankitpandey here. Ankit is asking what a free falling observer in an accelerating spaceship would feel and measure. While he is free falling within the accelerating spaceship, the freefalling observer feels no acceleration. Even two significantly "vertically separated" free falling observers would measure their clock rates to remain exactly synchronised with each other and their spatial separation to remain exactly constant (at least until the rear of the spaceship painfully catches up with one of them).

Tiny-Tim seems to be considering the clock rates of the two observers when the observers and their clocks are attached to the spaceship (which is not the question posed by ankitpandey) Under these conditions the two observers would indeed measure their clock rates to be different but they would also feel acceleration and would not even have to consult their clocks to know they are accelerating.

So, in the case of observers free falling in the accelerating rocket, there is no requirement to consider an infinitessimal region for the equivalence principle to hold exactly.

 

[phyti]

My wan

In a gravitational field in free fall you are not accelerating. It is when you are standing on the ground that you are accelerating which is why you feel your weight.

You are always accelerating, gravity is never turned 'off'. You detect it directly when the ground gets in the way, as weight, or indirectly when your direction of motion keeps changing.

kev

Even two significantly "vertically separated" free falling observers would measure their clock rates to remain exactly synchronised with each other and their spatial separation to remain exactly constant...

Gravity varies inversly with the square of the distance to the center of mass. It's only approximately constant over a short distance. The vertical separation increases and the horizontal separation decreases (tidal effect), over a period of time.

 

[Bose]

this question forom a student couldn't be answered by professor in class-
imagine 2 men in two rockets adjuscent to one other.you are one of them. rockets begin to move, say for example, revolve around sun. after few fast revolutions, they stop near each other. now you and the other man meet. both expect the time in their own clocks to be lesser than that in other's. you both compare your wrist watches, and therefore you both now see the same time "together".
WHAT do you think should happen? do you really expect your time to be lesser than his?

This puzzle is a typical case of misunderstanding of time dilation in SR. If you realize how many clocks you need to compare time with a moving clock, then everything fall into place and the puzzle is resolved

 

[ankitpandey]

well thanks to all for helping me with the topic. specially thank tiny tim and my wan(i found that a funny name). thanks a lot to kev,bose and others too. i have understood much about relavity, (though i have a separate theory about it) and i have got the answer to the question i posted here.thanks everyone.