Time & Acceleration: A Relativity Puzzle

[mee]

Why is time relative when an accelerating body could be seen as accelerating away from another body at exactly the same speed as the body from which one is accelerating away from is speeding away from the first body? I. e. the bodies could be seen as accelerating away from each other at the same rate, increasing at whatever rate equally. Is it the increased "gravity" on the ship which would cause a distortion? If the propulsive device is seen as a bomb pushing equally on all sides, that just happens to be attatched to the ship, pressing on ship and planetary influence equally, why does the time not change equally for both bodies? Maybe silly I know. :)

 

[Nenad]

this question has been asked on this forum like 1 million times. The reason for this is simple. It's because one body is in motion, and one body is not. The body which accelerates knows that it is in morion, and time distarts for that body, but the body which does not feel an acceleration does not change, time is the same as usual for him. In actuallity, both observers see the other as having slower time. But who is right depends on who rejoins who's referance frame.

 

[mee]

this question has been asked on this forum like 1 million times. The reason for this is simple. It's because one body is in motion, and one body is not. The body which accelerates knows that it is in morion, and time distarts for that body, but the body which does not feel an acceleration does not change, time is the same as usual for him. In actuallity, both observers see the other as having slower time. But who is right depends on who rejoins who's referance frame.

But it seems to me that both bodies could be seen to be in motion if all motion is relative. That it is merely a useful habit we are into see it otherwise. I'm not sure you have cleared this up. Not to me anyways. :) Thanks though.

 

[mee]

"For one, it isn't the magnitude of gravitational force that causes time dilation, but the difference in gravitational potential"

Found this on another post. Thought it might have something to do with this.

 

[Nenad]

But it seems to me that both bodies could be seen to be in motion if all motion is relative. That it is merely a useful habit we are into see it otherwise. I'm not sure you have cleared this up. Not to me anyways. :) Thanks though.

Both bodies are seen to be in motion by both observers. But one of the is wrong. The on in morion is wrong because he is the one in motion and the stationary body is not. The way a time knows who is in motion or not is through acceleration. One of bodies will need to accelerate in order to get to a high speed. Do you see what I mean. If both of them are going at high speeds, than you would have to dilate both their times.
It all depends on which observer returns to whos frame. If the traveling observer is to return to the stationary frame, then the traveling observers notion that he was stationary is wrong, and his assumptions are wrong. But if the stationary observer suddenly speeds up and joins the oberver in motion, then the motion observer is right. What I mean by right time. Both the traveller and the stationary guy will see themselves as having their time pass by more quickly, but in fact, the traveler is wrong and it his his time which is passing by slower. I am sorry if I confused you, but its not easy to explain. If you have more questions, please ask.

 

[mee]

Both bodies are seen to be in motion by both observers. But one of the is wrong. The on in morion is wrong because he is the one in motion and the stationary body is not. The way a time knows who is in motion or not is through acceleration. One of bodies will need to accelerate in order to get to a high speed. Do you see what I mean. If both of them are going at high speeds, than you would have to dilate both their times.
It all depends on which observer returns to whos frame. If the traveling observer is to return to the stationary frame, then the traveling observers notion that he was stationary is wrong, and his assumptions are wrong. But if the stationary observer suddenly speeds up and joins the oberver in motion, then the motion observer is right. What I mean by right time. Both the traveller and the stationary guy will see themselves as having their time pass by more quickly, but in fact, the traveler is wrong and it his his time which is passing by slower. I am sorry if I confused you, but its not easy to explain. If you have more questions, please ask.

It seems to me that the energy from an asteroid crashing into the Earth at high speed and of the Earth crashing into the asteroid at the same high speed would be the same. The potential energy of both the Earth and the spaceship go up equally as the spaceships propulsion accelerates it? As potential energy is a relative term and stillness is only in relationship to another object, usually the center of mass is seen as the still point or where the observer is or againts an apparently stable reference frame, not nonmoving but apparently stable. Acceleration is seen as moving because of what we are used to. Not because it is absolute? I'm kindof trying to say something like this. A similar analogy would be a moving car. The tires wheels could be seen as moving the Earth and the rest of the universe, while the car remains still, moving the rest of the universe until it is the place one wishes to go. actually, the force is equal on both the car and the rest of the universe and both are moving away from each other equally. Fun to think about for me anyway. Thanks for your interest. :)

 

[pervect]

If you draw a space-time diagram, the obsever that accelerates will always have traveled down two sides of a triangle.

The observer that does not accelrate will move in a straight line.

In Euclidean geometry, the person who travels down two sides of a triangle will always travel a longer distance.

In relativity, the person who travels down two sides of a triangle will always have the least amount of time on his clock.

This difference arises because the sign of the metric for time is the opposite for that of space (if that makes sense, sorry if it's too technical).

The acceleration doesn't directly determine the time difference. The length of the sides of the triangle (i.e the length of the trip) is much more critical. The time dilation factor is also important. The actual acceleration used is usually not a factor unless the trip is very short.

 

[russ_watters]

If the propulsive device is seen as a bomb pushing equally on all sides, that just happens to be attatched to the ship, pressing on ship and planetary influence equally, why does the time not change equally for both bodies? Maybe silly I know. :)

Well, if you apply the same force to a rocket ship and a planet, the rocket ship is still going to accelerate a lot faster.

 

[mee]

Well, if you apply the same force to a rocket ship and a planet, the rocket ship is still going to accelerate a lot faster.

So you are saying that acceleration and not relative speed is the factor?

 

[Nenad]

relative speed is the factior, but acceleration tells someone who is in relative motion and who isnt.

 

[mee]

relative speed is the factior, but acceleration tells someone who is in relative motion and who isnt.

Thanks for your help! So is it pressure created by acceleration perhaps that causes the effect? Also, could it be theoretically sound that the accelerating object could be seen as a decelerating object, with the rest of the universe seen as remaining at a fixed speed? Would the properties of either situation be the same?

 

[Nenad]

Also, could it be theoretically sound that the accelerating object could be seen as a decelerating object, with the rest of the universe seen as remaining at a fixed speed? Would the properties of either situation be the same?

Im not shure what you mean? Can you rephrase your question.

 

[pervect]

Thanks for your help! So is it pressure created by acceleration perhaps that causes the effect? Also, could it be theoretically sound that the accelerating object could be seen as a decelerating object, with the rest of the universe seen as remaining at a fixed speed? Would the properties of either situation be the same?

Acceleration is what makes world-lines bend. But what actually causes the difference in clock readings is that one world line is straight, while another world-line is bent. Bending the world-line of one observer is necessary to cause a difference in clock readings, but the acceleration is like the radius of curvature of the bend - it's just not very important. The angle of the bend (velocity) and the length of the paths traveled are the really important variables.

 

[jcsd]

The easiest way to illustarte this is to draw a simple displacemnt/time graph:

a) for an object with constant velocity

b) for an acelarting object

 

[mee]

Acceleration is what makes world-lines bend. But what actually causes the difference in clock readings is that one world line is straight, while another world-line is bent. Bending the world-line of one observer is necessary to cause a difference in clock readings, but the acceleration is like the radius of curvature of the bend - it's just not very important. The angle of the bend (velocity) and the length of the paths traveled are the really important variables.

Okay, let's say one is leaving the galaxy. The galaxy appears to be moving quite fast in a certain direction. Let's say a ship decelerates to the point to where it is nolonger moving with the galaxy. To the observers in the galaxy, the ship is now moving (accelerating apparently) away from them. What would the time differential be? The ship appeared to be accelerating away, but from another point of view, it could be seen to be decelerating?

 

[mee]

Okay, let's say one is leaving the galaxy. The galaxy appears to be moving quite fast in a certain direction. Let's say a ship decelerates to the point to where it is nolonger moving with the galaxy. To the observers in the galaxy, the ship is now moving (accelerating apparently) away from them. What would the time differential be? The ship appeared to be accelerating away, but from another point of view, it could be seen to be decelerating?

Also, if there were a white light on the ship, what would the shift in frequency beto someone on a planet in the galaxy?

 

[Nenad]

Okay, let's say one is leaving the galaxy. The galaxy appears to be moving quite fast in a certain direction. Let's say a ship decelerates to the point to where it is nolonger moving with the galaxy. To the observers in the galaxy, the ship is now moving (accelerating apparently) away from them. What would the time differential be? The ship appeared to be accelerating away, but from another point of view, it could be seen to be decelerating?

in this case, the accelerating ships time would dilate in the beginning, when he is accelerationg away from the galaxy, but once he sdecelerates and the galaxy is moving away from him, then the galaxys time which dilates. In this case, both the galaxy and the rocket ship's time dilate, but at different times.

 

[Nenad]

Also, if there were a white light on the ship, what would the shift in frequency beto someone on a planet in the galaxy?

there would be no redshft on the light. The two types of redsift in the universe are caused by gravciataion and the rapid expansion of space, not by the acceleleration of bodies from each other.

 

[mee]

in this case, the accelerating ships time would dilate in the beginning, when he is accelerationg away from the galaxy, but once he sdecelerates and the galaxy is moving away from him, then the galaxys time which dilates. In this case, both the galaxy and the rocket ship's time dilate, but at different times.

Im not sure you understand. He is never accelerating away from the galaxy, he is decelerating away from the galaxy. until he is moving slower than it. Thanks for your help.

 

[Janus]

I'm going to step in here and clear something up. Nenad's explanation of what is happening in this situation is not correct. You cannot say that the ship or galaxy is the one that is "truely" moving at any moment. This would imply that there was a preferred frame of reference, one considered at absolute rest, by which you could measure this movement. Relativity denies the existence of such a reference frame.

The time dilations seen by either as affecting the other are equally real.

The reason the ship experiences less time passage depends upon whether you are on the ship or galaxy.

As far as the galaxy is concerned, the ship time slows down due to time dilation.

As far as the ship is concerned, for some periods the galaxy time slows down and for some periods the galaxy time speeds up.

The difference is due to the fact that the while the galaxy remains an inertial frame, the ship does not. The important point is when the ship is accelerating back towards the galaxy.(or decelerating to rest with respect to the galaxy at the far point of separation.) This is the period when the ship will see the galaxy time as running very fast. This is due to the way Relativity deals with measurements made from an accelerated frame. This 'time running fast' period more than compensates for the time when the ship sees the galaxy time as running slow.

IOW, while observers on both the ship and galaxy will agree as to how much time has elapsed for both at the end of the trip, they will not agree as to how this situation came about, and neither's interpretation of events is more vlaid than the other.

 

[mee]

I'm going to step in here and clear something up. Nenad's explanation of what is happening in this situation is not correct. You cannot say that the ship or galaxy is the one that is "truely" moving at any moment. This would imply that there was a preferred frame of reference, one considered at absolute rest, by which you could measure this movement. Relativity denies the existence of such a reference frame.

The time dilations seen by either as affecting the other are equally real.

The reason the ship experiences less time passage depends upon whether you are on the ship or galaxy.

As far as the galaxy is concerned, the ship time slows down due to time dilation.

As far as the ship is concerned, for some periods the galaxy time slows down and for some periods the galaxy time speeds up.

The difference is due to the fact that the while the galaxy remains an inertial frame, the ship does not. The important point is when the ship is accelerating back towards the galaxy.(or decelerating to rest with respect to the galaxy at the far point of separation.) This is the period when the ship will see the galaxy time as running very fast. This is due to the way Relativity deals with measurements made from an accelerated frame. This 'time running fast' period more than compensates for the time when the ship sees the galaxy time as running slow.

IOW, while observers on both the ship and galaxy will agree as to how much time has elapsed for both at the end of the trip, they will not agree as to how this situation came about, and neither's interpretation of events is more vlaid than the other.

Are you saying that the galaxies are relatively still while the space between them increases? If I could take a physics or cosmology class I would. :) Thanks for your help.

 

[pervect]

Okay, let's say one is leaving the galaxy. The galaxy appears to be moving quite fast in a certain direction. Let's say a ship decelerates to the point to where it is nolonger moving with the galaxy. To the observers in the galaxy, the ship is now moving (accelerating apparently) away from them. What would the time differential be? The ship appeared to be accelerating away, but from another point of view, it could be seen to be decelerating?

I was thinking of taking another crack at this, but I think it would overall be best just to refer mee to the sci.physics.faq on the twin paradox

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

It's certainly easier, at any rate :-)

I'm generally fond of the space-time diagram explanation, as I've said several times before, but it doesn't seem to be "clicking" for mee.

No problem, there are _lots_ of different appraoches to the twin "paradox"

Perhaps, if the space-time diagram explanation doesn't "click", the "doppler" explanation might work. (That's my next favorite explanation). This explanation concentrates on what each observer actually *sees* physically.

Note that there is no shortage of appraoches to the twin "paradox", there's even a meta-apology about "too many explanations" in the FAQ.

 

[mee]

I was thinking of taking another crack at this, but I think it would overall be best just to refer mee to the sci.physics.faq on the twin paradox

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

It's certainly easier, at any rate :-)

I'm generally fond of the space-time diagram explanation, as I've said several times before, but it doesn't seem to be "clicking" for mee.

No problem, there are _lots_ of different appraoches to the twin "paradox"

Perhaps, if the space-time diagram explanation doesn't "click", the "doppler" explanation might work. (That's my next favorite explanation). This explanation concentrates on what each observer actually *sees* physically.

Note that there is no shortage of appraoches to the twin "paradox", there's even a meta-apology about "too many explanations" in the FAQ.

I am quite familiar with the twin paradox. I was just wondering what would happen in this new twist on it. Thank you for your help.

 

[pervect]

I am quite familiar with the twin paradox. I was just wondering what would happen in this new twist on it. Thank you for your help.

OK, a few last words, for what they're worth. Trying to work out "when" the time differential occurs is a futile effort. Think of time as an interval, that you measure with a clock. Like a ruler, you have to specify the exact path you traverse in order to measure it.

The main point is very simple - if two clocks start out at the same point in space-time, and are syncrhonized there, and then take different paths through space-time, when the re-unite they will no longer in general be synchronized.

 

[mee]

I was thinking of taking another crack at this, but I think it would overall be best just to refer mee to the sci.physics.faq on the twin paradox

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

It's certainly easier, at any rate :-)

I'm generally fond of the space-time diagram explanation, as I've said several times before, but it doesn't seem to be "clicking" for mee.

No problem, there are _lots_ of different appraoches to the twin "paradox"

Perhaps, if the space-time diagram explanation doesn't "click", the "doppler" explanation might work. (That's my next favorite explanation). This explanation concentrates on what each observer actually *sees* physically.

Note that there is no shortage of appraoches to the twin "paradox", there's even a meta-apology about "too many explanations" in the FAQ.

It doesn't click because I don't know how to draw a space time diagram yet.

 

[pervect]

It doesn't click because I don't know how to draw a space time diagram yet.

You probably do, but just don't know it yet. You take a graph, label one axis "distance", another axis "time", and you draw a curve on it which plots the distance vs the time.