Gravity & Acceleration: Is Space Shortening Explained?

[Maartenc]

Hi,
I have been asking friends with physics degrees this question, but they cannot answer it, or give conflicting answers.

When two reference systems move relative to each other, space becomes shorter in them, as seen from the other system.
Gravity and acceleration are indistinguishable.
The gravity field moves at the speed of light.
Therefore the effect of acceleration should also move at the speed of light.
This means that when I start accelerating an object, the part furthest away from the point where I apply the force will start moving slightly later than the part that I'm pushing against.
Is this what causes the spatial contraction?

 

[Dale]

Gravity is only locally equivalent to acceleration, so it isn't a heuristic that you want to apply indiscriminately. Also, you are talking about non inertial frames, so there is a lot of freedom to define things the way you like. Not every way will have gravitational acceleration propagating at c.

Those caveats aside, here is a reference that essentially describes the sort of non inertial frame you are describing.

http://arxiv.org/abs/gr-qc/0104077

 

[pervect]

Hi,
I have been asking friends with physics degrees this question, but they cannot answer it, or give conflicting answers.

When two reference systems move relative to each other, space becomes shorter in them, as seen from the other system.

I wouldn't necessarily word it this way, but yes, there is a phenomenon called Lorentz contraction that is what you're undoubtedly talking about.

Gravity and acceleration are indistinguishable.

This isn't quite right Gravity and acceleration are locally indistinguishable, that much is true. The word "locally" is important.

The gravity field moves at the speed of light. Gravity is locally indistinguishable from acceleration, but

OK, here's where things start to get really confused. You've introduced a notion called "gravity fields", or "gravitational fields". There's a lot of things that this term could mean, but it's not at all clear what you think you mean by the term. For instance, if we start with your - slightly misleading - statement that "gravity is acceleration", then you are saying "acceleration fields move at the speed of light". But this doesn't really make sense, an acceleration isn't a "field", it's just a local phenomenon. So in the sense that gravitation is equivalent to local acceleration, it doesn't propagate.

Given that we know that the sort of local acceleration you're talking about is not a field that can propagate, we still have the question of definiing what it is that you call by the same name is, this something else being different in that it can propagate. Well, this would be a long question, and I'm not sure I have an answer. Rather than get into it, I'll just say that if you use the same word to describe something that propagates, and something that doesn't propaate, you'll get confused, because you're using the same word to talk about two things that are actually different, though they may be closely related.

 

[sandy stone]

This means that when I start accelerating an object, the part furthest away from the point where I apply the force will start moving slightly later than the part that I'm pushing against.
Is this what causes the spatial contraction?

I think the effect of a "push" on an object propagates through it at the speed of sound in that material, not at the speed of light. And if by "spatial contraction" you mean Lorentz contraction, then no, that is a different effect due to relative velocity, not acceleration. The distortion of an object undergoing acceleration is explained by Newtonian physics.

 

[Maartenc]

OK, thanks for the answers. I do understand that Lorentz contraction is caused by velocity, but velocity is caused by acceleration, and acceleration would contract an object if it propagated at a finite speed. I guess I'm just surprised that a simple explanation like that doesn't seem to hold.
Is it really true that acceleration doesn't propagate like gravitation or electromagnetism? Is it really only limited by the fact that real object are never completely rigid?

 

[jbriggs444]

OK, thanks for the answers. I do understand that Lorentz contraction is caused by velocity, but velocity is caused by acceleration, and acceleration would contract an object if it propagated at a finite speed. I guess I'm just surprised that a simple explanation like that doesn't seem to hold.
Is it really true that acceleration doesn't propagate like gravitation or electromagnetism? Is it really only limited by the fact that real object are never completely rigid?

The compression wave from a hammer blow at one end of a near-rigid rod cannot propagate to the other end of the rod faster than the speed of light. This is a limitation on the rigidity of real objects.

 

[Maartenc]

Yep, that's clear. But the same is true for gravity. If the same rod is exposed to a sudden large increase in the gravitational field the compression caused by that would also have a limited speed. But the gravitational field will propagate at the speed of light.

My confusion is a bit more fundamental. I cannot understand the precise difference between the effects of a gravity field and the effects of acceleration. I thought these would be identical, but it seems I'm wrong.

 

[Dale]

velocity is caused by acceleration

Not in general. For example, cosmic ray muon's are created already moving at high velocity and then travel inertially.

 

[Dale]

But the gravitational field will propagate at the speed of light.

You have to be very careful with statements like this. What you were describing as the gravitational field (the thing that is equivalent to acceleration) does not generally propagate at c. What propagates at c is changes in the curvature.

Did you read the link I sent? It shows a non inertial frame carefully built so that the field you are talking about does propagate at c.

 

[Maartenc]

Sorry, the article in the link looks a bit too complicated for me. Perhaps I should give it a try anyway. Thanks.

 

[Dale]

Hmm, then you should probably postpone this question for a bit. The reference is about as basic as they can be for a question like this.

 

[Mister T]

I do understand that Lorentz contraction is caused by velocity, but velocity is caused by acceleration,

Lorentz contraction occurs when reference frames move relative to each other. This is not caused by acceleration in any way. Perhaps you are thinking that objects start out with the same velocity that you have, and the only way to change that is to accelerate them. But many objects were born moving relative to you, and they didn't have to experience any acceleration for that to be the case.

and acceleration would contract an object if it propagated at a finite speed.

Huhh? If an object moves with constant velocity its acceleration is zero.

 

[Maartenc]

Sorry, I should have said 'if the effects of acceleration propagate at a finite speed'

 

[pervect]

If you pick two points on a plane, say A and B, and draw a straight line between them, AB, the line is the shortest curve connecting the two points. If you make a detour to a third point, so you have a triangle with A,B, and C, the sum of AC + CB is longer than the direct path AB - except in the degenerate case where A,B,and C are colinear, in which case the sum of the two sides is equal to the hypotenuse.

If you do the same thing on a space-time diagram, the "lengths" on the space-time diagram are actually elapsed times - sometimes called wristwatch time, or by the more technical name, proper times, on the space-time diagram. And the direct path takes the longest time, rather than the shortest.

The standard twin paradox doesn't have, or need, any like acceleration. It has only the two straight lines on the space-time diagram, and the sum of the times. So an explanation that's entirely based on acceleration is basically not really addressing the problem.

To understand this explanation, you need to be able to draw and interpret space-time diagrams. It's not very hard. If you can draw time on a timeline (say, draw a timeline, plot points on it to represent and organize important dates), you have the tools you need to represent time on a diagram. If you can draw lines on a plane, you have the tools needed to handle two dimensions (x and y, horiziontal and vertical) on a diagram. A space-time diagram just uses one dimension to represent time, the other to represent space (distance).

If you know how to draw space-time diagrams, you realize you can represent different velocities by lines with different slopes on the space-time diagram, and a change in velocity is therefore represented by an angle on the space-time diagram. An acceleration is represented by a curving line on the space-time diagram, rather than a straight one.

This is enough to get started at least - to fully understand why the proper time on a space-time diagram is longer (rather than shorter) is a bit harder. It comes from the fact that the space-time diagrams don't follow the pythagorean theorem. Basically, when you choose natural units, the square of the hypotenuse is the difference of the squares of the other two sides on the space-time diagram, rather than the sum (which is what you're used to on the Euclidean plane).

 

[Maartenc]

Thank you very much, all of you, for taking the time to help me understand these issues. It is a fascinating subject, but it can be difficult to see things in the right context. Your comments have helped a lot.