Gravity and acceleration

[granpa]

Main Question or Discussion Point

general relativity says that gravity and acceleration produce the same effects but when an object accelerates its possible for distant clocks to appear to move backwards. gravitational time dilation doesnt do that.

 

[yuiop]

general relativity says that gravity and acceleration produce the same effects but when an object accelerates its possible for distant clocks to appear to move backwards. gravitational time dilation doesnt do that.

An observer that is stationary with respect to a gravitational body feels constant proper acceleration over time. YOu would have to show that the effect you describe would be observed by an observer that experiences constant proper acceleration due to artificial acceleration in order to support your argument.

Could you also make it clear if by "clocks appear to move backward" you meant clocks appear to tick backwards showing time reversal or if you meant clocks literally move or recede away from the observer.

 

[granpa]

if you have a long line of synchronized clocks and a stationary observer that begins to accelerate at a constant rate then the clocks will become more and more out of synch. those on one side will move forward while those on the other side will move backward (at the same time all clocks are moving forward at some rate).

 

[yuiop]

if you have a long line of synchronized clocks and a stationary observer that begins to accelerate at a constant rate then the clocks will become more and more out of synch. those on one side will move forward while those on the other side will move backward (at the same time all clocks are moving forward at some rate).

Well the equivalent situation would be a stationary observer in a gravitational field on the top of a tall tower that drops a long rod with clocks attached to it so that the rod is free falling. That is what you would have to analyse.

It is not the usual situation of a stationary observer in gravitational field observing that are stationary with respect to him but at different altitudes.

You will also have to make it clear that whether you mean the observer would literally see one of the clocks running backwards in time or just calculates that the clock is running backwards in time if he could see it.

You should probably draw some sort of Minkowski space/time diagram to illustrate what you mean. It can be shown that observers accelerate in a rocket will see an artificial event horizon behind them and if they "drop" an object it will fall behind the horizon and they will no longer be able to see it until they stop accelerating. It is likely that the observer you describe "sees" some clock as running backwards he will actually see some sort of event horizon where the clocks change from running forward to running backwards so he will not actually be able to see the clcoks running backwards, but only be able to calculate or imagine that they are running backwards.

However, I can show that relativity predicts that a clock low down in a strong gravitational field will be running backwards relative to a clock high up in the gravity field and I am not talking about a massive body that is so dense that it is a black hole. Whether the high observer will actually see the low clock running backwards depends on how light travels in a zone where time is running backwards and also on how mass and gravity behave in a negative time zone. That area is not well explored.

 

[pmb_phy]

general relativity says that gravity and acceleration produce the same effects but when an object accelerates its possible for distant clocks to appear to move backwards.

That's news to me. Where did you get this idea from? I never heard of it before myself. Thanks.

Pete

 

[granpa]

let me rephrase.

you have a stationary observer and a long line of stationary clocks that are all synchronized. as the observer begins to accelerate at a constant rate the clocks which remain stationary will begin to get more and more out of synch from the observers point of view. the clocks in front of the observer will seem to him to tick faster but the clocks behind him will tick slower. clocks that are very far behind him will even seem to him to move backwards even after he corrects for time of flight of the light from the clock.

just wondering what sort of gravity field would produce that effect.

 

[Hurkyl]

just wondering what sort of gravity field would produce that effect.

You are not describing a physical effect; you are describing a coordinate effect. (The fact that you're using the word 'synchronized' should be a big clue)

 

[MeJennifer]

you have a stationary observer and a long line of stationary clocks that are all synchronized. as the observer begins to accelerate at a constant rate the clocks which remain stationary will begin to get more and more out of synch from the observers point of view. the clocks in front of the observer will seem to him to tick faster but the clocks behind him will tick slower. clocks that are very far behind him will even seem to him to move backwards even after he corrects for time of flight of the light from the clock.

just wondering what sort of gravity field would produce that effect.

Earth is a good example, if you are stationary above the Earth then anything above you will appear to run faster and anything below you will appear to run slower.

 

[granpa]

Earth is a good example, if you are stationary above the Earth then anything above you will appear to run faster and anything below you will appear to run slower.

yes. but nothing runs backward. at least not from the point of view of anyone that is moving at a constant velocity.

 

[granpa]

You are not describing a physical effect; you are describing a coordinate effect. (The fact that you're using the word 'synchronized' should be a big clue)

what are you saying? that the clocks dont really run backward in time? well duh!

the effect of gravity is supposed to be indistiguishable from the effect of acceleration. i am just wanting to know how that is.

 

[granpa]

i guess that must be the idea behind an event horizon. its the point at which time stops and beyond which time actually begins to move backward.

i guess so anyway.

 

[granpa]

and they will no longer be able to see it until they stop accelerating.

why? the light from the clock is always moving faster than they are.

 

[MeJennifer]

That's news to me. Where did you get this idea from? I never heard of it before myself. Thanks.

Pete

I think he is simply mistaken, time does obviously not run backward in acceleration scenarios.

 

[Hurkyl]

what are you saying? that the clocks dont really run backward in time? well duh!

I'm saying phrases like:
"distant clocks to appear to move backwards"
"synchronized clocks"
"stationary observer"
"clocks will become more and more out of synch"

have no physical meaning, and there is no such thing as an "observer's point of view". There are only coordinate charts, and how things look relative to a coordinate chart.

the effect of gravity is supposed to be indistiguishable from the effect of acceleration. i am just wanting to know how that is.

That means if your observer uses the same method to 'correct for time of flight of the light from the clock', he will get the same result in either circumstance.


Incidentally, the equivalence principle is only assumed to work on small scales.

 

[pmb_phy]

let me rephrase.

you have a stationary observer and a long line of stationary clocks that are all synchronized. as the observer begins to accelerate at a constant rate the clocks which remain stationary will begin to get more and more out of synch from the observers point of view. the clocks in front of the observer will seem to him to tick faster but the clocks behind him will tick slower. clocks that are very far behind him will even seem to him to move backwards even after he corrects for time of flight of the light from the clock.

Clocks behind him will not run backwards. They will simply run slower, which is quite different.

just wondering what sort of gravity field would produce that effect.

Any gravitational field for which the time-time component of the metric tensor has different values at the different locations.

the effect of gravity is supposed to be indistiguishable from the effect of acceleration. i am just wanting to know how that is.

Nobody knows how that is. The equivalence principle is something that is postulated to be true and as such it cannot be derived from other postulates.

You are not describing a physical effect; you are describing a coordinate effect.

In this case a coordinate effect is a physical effect. I.e. using a coordinate system which corresponds to a non-inertial frame of reference will produce measurements of physical quantities which are frame dependant.

Pete

 

[granpa]

well lets see if i am mistaken. you start with a long line of stationary synchronized clocks and a stationary observer. the stationary observer accelerates almost instantly to a very high speed, say gamma=10. when he is done the clocks will appear to him to be severely out of synch but the clock he is next to will still read nearly the same time that it read before. the clocks on one side of that clock will read something higher than that clock and the clocks on the other side will read something less than that clock and the further away they are the more they differ from that clock. the difference in time being proportional to the distance. so even though all the clocks are moving forward at some rate, eventually if you go far enough away you must come to a clock that is running backward from the point of view of the accelerating observer.

 

[Hurkyl]

I think he is simply mistaken, time does obviously not run backward in acceleration scenarios.

"Time running backwards" refers to the situation when, in a coordinate chart, the reading on a clock runs in the opposite direction than its time coordinate.

One of the conventions¹ in special relativity for choosing a coordinate chart² in which a noninertial observer is stationary has this feature.


1: I emphasize this word for the original poster's sake
2: Actually a mild generalization of the notion of coordinate chart; the convention I'm referring to allows multiple coordinate-tuples to refer to the same event in space-time.

 

[Hurkyl]

I.e. using a coordinate system which corresponds to a non-inertial frame of reference will produce measurements of physical quantities which are frame dependant.

I'm confused; physical quantities are, by definition, frame independent. Time dilation, for example, is not a physical quantity. (Of course, the proper time experienced by an observer between two specified events in space-time is a physical quantity)

 

[Hurkyl]

well lets see if i am mistaken. you start with a long line of stationary synchronized clocks and a stationary observer.

What does "stationary" mean? What does "synchronized" mean?

the clocks will appear to him to be severely out of synch

What does "appear out of sync" mean?


I'm not trying to be argumentative; I really believe that either:
1. You do not know what those terms really mean, and have developed a malformed intuition for them that impairs your understanding
2. You do know what those terms mean, but you are being sloppy and haven't thought it through, and have made mistakes

 

[granpa]

stationary and synchronized within the frame of reference of the observer before he begins to accelerate.

exactly what it usually means.

 

[granpa]

"It can be shown that observers accelerate in a rocket will see an artificial event horizon behind them"


kev, i must say that when i read that i thought it was total crap. but you were right. i assumed that infinite time dilation (stopping a clock completely) would require an infinitely strong gravitational field. it just requires a gravitational field that extends far enough. at least, that is the theory. its certainly true for acceleration. presumably it must be true for gravity too.

"and if they "drop" an object it will fall behind the horizon and they will no longer be able to see it until they stop accelerating."


dont know about the object becoming impossible to see though.

 

[dude222]

Yes, gravity does allow for time to run backwards. You can see this in a new gravity force formula that I posted. Gravity becomes repulsive. It depends on at what location the observer is at in the gravitational field. The point at which this happens is when the gravitational potential equals the local speed of light. By the way, I made a small mistake on the gravitational constant I used. I have been too lazy to fix the posting, but should read G/c instead of G.

 

[yuiop]

Using the interior Schwarzschild solution it can be shown that time runs backwards for a body that is marginally larger (9/8) than the Shwarzschild radius. Unlike the exterior solution no imaginary roots are involved and because such a body is larger that Schwarzschild radius it not a black hole and arguments like the laws of physics do not apply here does not hold.

If time reversal is not allowed then a singularity can not form.