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

[ankitpandey]

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?

 

[neopolitan]

Depends if one is in an orbit or not and then their motion relative to an orbit. You don't provide enough information to provide an answer.

cheers,

neopolitan

 

[my_wan]

What do you mean by stop? The two ships were never in motion relative to each other. No relative motion between them means that wrt each other they were always stopped. No relative motion wrt each other means no relativistic effects wrt each other. Stopping is only more acceleration in the other direction and no different that the acceleration when they started the trip. Stopped in not a definable concept in absolute terms.

 

[tiny-tim]

Hi ankitpandey!

A more interesting example is when they orbit in opposite directions round the earth, so each can genuinely say that the other is moving.

The answer is that an observer on Earth will regard both their watches as going slow, but each will regard the other's watch as correct.

There's nothing strange about this, since both are accelerating (their speeds may be constant, but their velocities are changing).

 

[yuiop]

I agree with Tim. If both rockets accelerate in opposite directions and then switch off their engines so that they orbit naturally at the same altitude, then each time they pass each other their clocks will show the same time as each other. Comparing their clock rates to that of an observer on the surface of the Earth is a little difficult, because the surface observer will be deeper in a gravitational well which will cause some time dilation of the surface observer relative to the rockets at higher altitude.

 

[neopolitan]

tiny-tim,

Actually, I think that if they are in natural orbits (not under any acceleration to keep them in orbit), then both would be following a geodesic.

From what I can work out, if their clocks were synchronised on one pass, then the clocks would remain synchronised just as you say. But I think it has more to do with each following a geodesic than their apparent accelerations.

cheers,

neopolitan

 

[tiny-tim]

… gravity is the gradient of positional time dilation …

Actually, I think that if they are in natural orbits (not under any acceleration to keep them in orbit), then both would be following a geodesic.

Hi neopolitan!

Yes, orbits are geodesics.

But time dilation is not zero along a geodesic.

Time dilation depends on velocity and position.

The velocity dependence comes from the Lorentz formula (of special relativity).

The position dependence comes from general relativity.

The gradient of the positional time dilation manifests itself as the "force of gravity", causing an acceleration towards the centre.

For a circular orbit, time dilation will be constant, but it will be different for different radii. For an elliptic orbit, it won't even be constant.

The gradient of positional time dilation will always be towards the centre (or focus), which is the direcction of the gravitational acceleration.

See, for example, the following quote from:

https://www.physicsforums.com/archive/index.php/t-148410.html​

We see that the rate of change of time dilation with respect to position acts just like a "force" as far as the equations of motion go. If time dilation is not a function of position, bodies following geodesics (i.e. bodies extermizing proper time, which means that they satisfy the Euler-Lagrange equations) do not accelerate. When time dilation is present and varying with position, we can interpret the equations of motion to be the same as if we had an actual force present. We call this force "gravity".

So two spaceships in different orbits have relative time dilation, both due to velocity and to distance from the sun - and these two do not generally cancel.

 

[ankitpandey]

hey...
thanks for trying to answer, but none werte to the point. i think i didnt frame it properly. let me ask it again...(takes me time to type)

 

[ankitpandey]

two ships are moving with respect to each other. remove the sun, the Earth and everything. now you have an open space, that's all. no orbits. i am a man in one of those rockets, and wish to calculate time in another guys watch, who is in the other. according to relativity, no frame is preffered. so why can't i find time in his clock by knowing his velocity relative to me, which is first away, and then towards, and then using the time diliation formula? when we meet, both of us will expect our time to be lesser than the others, won't we?

 

[tiny-tim]

… nothing to orbit round …

two ships are moving with respect to each other. remove the sun, the Earth and everything.

Hi ankitpandey!

You haven't specified how they're moving (it can't be in an orbit (a geodesic), because there's nothing to orbit around)!

At least one of them will have to accelerate and decelerate.

Do you want to specify … ?

 

[ankitpandey]

check this one- i recently found it in a site... it is similar to my question... i am not challenging relativity here, i just want to know if there is some point i am missing somewhere...

"Consider two small planets that are moving apart or toward each other at a constant relative velocity, measured by both as being exactly 0.6c. (c represents the speed of light.) There is a baby boy born on each planet, at a moment that we will say is simultaneous, although that is not important here. (We might say that an observer, who is moving at a velocity exactly halfway between their planets' velocities and happened to be exactly equal distance from both planets at that moment, witnessed both births at what he considered the same moment. A critically important factor in this is that the observer was traveling at a velocity that was exactly halfway between.)
When EACH looks at the other, from their own inertial rest-frame, they each have no sensation of motion. Therefore, they see the expected Special Relativity (SR) effect of Time Dilation, due to what they each see as the OTHER planet moving toward or away from them. For this velocity of 0.6c, we can easily calculate that this is a factor of 0.8 regarding time passage. As each grows up, they therefore EACH see the other as aging more slowly (0.8 times as fast) than they age. We are going to momentarily neglect the fact that the two might see each the other as having been born before or after themselves, and ONLY consider the INTERVAL while they constantly watch each other. During an interval when they each live 30 (Earth) years, they each see that the other has only lived 24 (Earth) years!. This is true of BOTH of them! There can be no doubt of this because EACH of them is in a rest-frame coordinate system which is not accelerating, and which each therefore considers to be "stationary", such as we tend to do here on Earth."

 

[ankitpandey]

i have mentioned address of above data below. you might preffer to read it completely before answering. its really long, that web page.

"The Twins Paradox of Relativity is Certainly Wrong!Even High School students learn about the Twins Paradox of Relativity, where a rapidly traveling twin arrives back younger than his twin brother!
mb-soft.com/public2/twinspar.html - 49k - Cached - Similar pages "
i found it in google

 

[my_wan]

You say your ship are "first away then towards". What you need to define to answer this question is which ship accelerated so that the away motion became a toward motion. What needs to be understood is that motion may be relative but acceleration is not, except to degree of how much. Acceleration is not just changing speed in the common way of thinking of it. It occurs when you change the direction of motion. When you slow down relative to something you have simply changed the direction of relative motion toward the reference.

If you are both in ships and you keep speeding away then slowing down then less time will pass for you each time you meet. If you speed away and he speeds up to catch you his time will be what passed slower since you were last together.

 

[tiny-tim]

no paradox … therefore nothing to explain … !

Hi ankitpandey!

Twins paradoxes are pointless unless the twins start and finish together (or keep passing each other).

In the example you quote, they never turn round, so they meet only once.

There's no paradox, and therefore nothing to explain!

 

[ankitpandey]

dear... um..."my_wan"
you are talking in absolute frame... relatively, two bodies always have same acceleration with respect to one another. with frame of reference of two different bodies, you can never make out which is moving toward and which moing away, as you have written. if you do so, you voilate the basic postulate of relativity, which states that no frame is to be preffered. these statements voilate relativity-
" Acceleration is not just changing speed in the common way of thinking of it. It occurs when you change the direction of motion. When you slow down relative to something you have simply changed the direction of relative motion toward the reference.

If you are both in ships and you keep speeding away then slowing down then less time will pass for you each time you meet. If you speed away and he speeds up to catch you his time will be what passed slower since you were last together."
'speeds away and he speeds towards you' is undefined in relativity. you are considering some frame stationary here... for example, you are considering their motion relative to earth. relatively, all you must use is that they are moving towards each other. please read my last few messages as well before answering.(cont. in page 2)

 

[ankitpandey]

"Twins paradoxes are pointless unless the twins start and finish together (or keep passing each other).

In the example you quote, they never turn round, so they meet only once."
was that meant to be an answer to my question or the other long one from the web?
well... they do turn around... when did i, or the other question, say that they dont? they still have a definite velocity, and time diliation should definitely still be applicable the same way as before they turned. they do meet again the same way.

 

[ankitpandey]

"Twins paradoxes are pointless unless the twins start and finish together (or keep passing each other).

In the example you quote, they never turn round, so they meet only once."
wasthat supposed to be answer to my question, or to the long one from the web?
well... they do turn around... when did i, or that question say that they dont? they still have a definite velocity, and time diliation should definitely still be applicable the same way as before.

 

[tiny-tim]

… accelerating, not just speeding …

If you are both in ships and you keep speeding away then slowing down then less time will pass for you each time you meet. If you speed away and he speeds up to catch you his time will be what passed slower since you were last together."

erm … "less time will pass for you each time you meet" and "his time will be what passed slower since you were last together" … don't make any sense.

'speeds away and he speeds towards you' is undefined in relativity

I see what you mean … an observer can't tell whether he is speeding … but this problem is about accelerating away and accelerating towards you, and any observer can tell whether he is accelerating!

 

[tiny-tim]

when did i, or the other question, say that they dont?

(btw, if you press "edit" you can delete one of the last two almost identical posts)

You didn't say they did. We're not going to read things in unless they're obvious, and that certainly wasn't!

they still have a definite velocity, and time diliation should definitely still be applicable the same way as before they turned. they do meet again the same way.

Yes, but only during steady speed … the acceleration cancels out all the time lost during steady speed!

 

[ankitpandey]

i don't agree. if all the bodies, including the man undergo uniform acceleration, you can define or make out only your acceleration with respect to the other body only. for example, if two bodies of some in space move toward each other due to gravitation, (f=gMm/r)your absolute acceleration be "a" from a non relative frame which was unaffected by gravity. but you will, seeing that body, declare that your acceleration ia more than "a", because it is also moving towards you in the relative frame.

 

[ankitpandey]

"You didn't say they did. We're not going to read things in unless they're obvious, and that certainly wasn't!"
sorry if i didnt... i am prone to blunders...

 

[ankitpandey]

"Yes, but only during steady speed … the acceleration cancels out all the time lost during steady speed!"
first, i didnt understand that...
second, let's remove acceration this way first...
bodies move away from each other with constant relative velocity, suffer a near elastic collision somewhere away with very huge masses, and start moving towards with a slightly lesser relative velocity than before.using time diliation in both frames, and now that there has been no acceration at all, won't both bodies expect their times to be greater than the other when they meet?

 

[tiny-tim]

… you can always detect acceleration …

sorry if i didnt... i am prone to blunders...

That's ok … me too!

if all the bodies, including the man undergo uniform acceleration, you can define or make out only your acceleration with respect to the other body only.

No … you can always detect acceleration … you can carry out very simple experiments to show it … for example, just letting go of something and seeing if it moves away from you!

for example, if two bodies of some in space move toward each other due to gravitation {snip} you will, seeing that body, declare that your acceleration ia more than "a" {snip}

Same answer … seeing isn't everything … you carry out experiments because you can't always trust your eyes!

 

[tiny-tim]

… suffer a near elastic collision somewhere away with very huge masses … now that there has been no acceration at all …

Sorry … but there has been acceleration, and it was enormous …

 

[ankitpandey]

"No … you can always detect acceleration … you can carry out very simple experiments to show it … for example, just letting go of something and seeing if it moves away from you!"

that is in case only the ship is accelerating. when accelerations like gravity act, they will act on the object i leave as well, and it will also move with me. experiments cannot detect this kind of accelerations.

 

[ankitpandey]

oh! stupid time! i got to go. it was nice debate, n will surely continue,however,goodbye for now. will meet u again

 

[tiny-tim]

… clocks will detect gravitational acceleration …

when accelerations like gravity act, they will act on the object i leave as well, and it will also move with me. experiments cannot detect this kind of accelerations.

Ah … but you're forgetting that a clock at one end of a rocket will run slower than at the other end, so gravitational acceleration is detectable!

(And don't think it's negligible inside a rocket - the Pound-Rebka experiment using the Mossbauer effect detected a time difference over a height of 22.5 metres, which is shorter than the average rocket! … see:

http://en.wikipedia.org/wiki/Pound-Rebka_experiment)​

oh! stupid time!

erm … what's stupid time?

… from stupid clocks … ? ​

 

[my_wan]

dear... um..."my_wan"
you are talking in absolute frame... relatively, two bodies always have same acceleration with respect to one another. with frame of reference of two different bodies, you can never make out which is moving toward and which moing away, as you have written. if you do so, you voilate the basic postulate of relativity, which states that no frame is to be preffered. these statements voilate relativity-
" Acceleration is not just changing speed in the common way of thinking of it. It occurs when you change the direction of motion. When you slow down relative to something you have simply changed the direction of relative motion toward the reference.

If you are both in ships and you keep speeding away then slowing down then less time will pass for you each time you meet. If you speed away and he speeds up to catch you his time will be what passed slower since you were last together."
'speeds away and he speeds towards you' is undefined in relativity. you are considering some frame stationary here... for example, you are considering their motion relative to earth. relatively, all you must use is that they are moving towards each other. please read my last few messages as well before answering.(cont. in page 2)

I will make another attempt. You assume I'm wrong to your own detriment.

You said, "two bodies always have same acceleration with respect to one another". Acceleration as I said is not relative. You are confusing acceleration and relative motion. Here's why: When you are in a box that you can't see out of you always know when you are accelerated because you will feel a g force pushing you. When you and your friend are moving away from each other the one that feels this force is the one that is accelerating. If you don't accelerate you will not feel this force. That is why acceleration is not relative the way motion is. Two bodies do not always have same acceleration with respect to one another, though they will essentially always have the same relative motion to each other. All observers in the Universe will agree on who is accelerating.

You need to fully understand this before anybody can even think of answering your question.
http://www.madsci.org/posts/archives/2006-01/1137248500.As.r.html

 

[ankitpandey]

"Acceleration as I said is not relative. You are confusing acceleration and relative motion. Here's why: When you are in a box that you can't see out of you always know when you are accelerated because you will feel a g force pushing you. When you and your friend are moving away from each other the one that feels this force is the one that is accelerating. If you don't accelerate you will not feel this force."

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 reffering 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.

 

[ankitpandey]

"All observers in the Universe will agree on who is accelerating."
ok i agree. thanks for correction, mywan.
now back to old debate...

 

[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 reffering 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.