B Light Clock & Length Contraction in GR

[sqljunkey]

Hi, can i use a light clock made out of mirrors a distance appart to measure whether there is length contraction in different regions of spacetime?

If the clock speeds up then the distance between the mirrors decreased. If the clock slows down the distance between mirrors increased.

 

[Nugatory]

... the distance between the mirrors...

The distance measured using which frame?

 

[sqljunkey]

I would measure the initial distance between the two mirrors in my frame, and afterwards I would use time to figure the other distances in other frames, I guess.

We can talk about time-dilation in general relativity right?

 

[Nugatory]

I would measure the initial distance between the two mirrors in my frame, and afterwards I would use time to figure the other distances in other frames, I guess.

As long as you don't mishandle the relativity of simultaneity, yes. But you may be underestimating how easy it is to get that wrong.

We can talk about time-dilation in general relativity right?

Yes, but only if we careful to describe time dilation properly, as a consequence of our choice of simultaneity convention. You do not want to go anywhere near time dilaton in general relativity until you have a solid grasp on how time dilation in special relativity arises from the relativity of simultaneity.

 

[hutchphd]

The light clock you build on your lab bench will behave like any other (albeit rather rapidly ticking) clock in your laboratory. That is the point in fact.
The question is what are you desirous of measuring. Building a clock is just building a clock...

 

[sqljunkey]

hutchphd I want to measure the length between the two mirrors. A light clock is kind of easier to understand since light will travel between those two mirrors at c always.

I'm imagining standing an infinite distance away from a mass, and then letting the clock go and free fall into the curved spacetime, if that clock slows down from where I'm standing that would mean the light has more distance to cover between the mirrors, it would not mean that the light is now moving slower,right?

unlike this post is saying that you can't talk about length contraction in gr.

 

[PeterDonis]

If the clock speeds up

If the clock slows down

How do you know if the clock speeds up or slows down? How are you measuring that?

 

[sqljunkey]

Well if we look at MTW Gravitation, on page 1054, they talk about experiments with elementary particles. So there is certainly an experimental basis on which I can assume time dilation in a curved spacetime. But as to how I would measure the up and down motion between the two mirrors that is free falling against against my own clock I have not worked out yet.

 

[sqljunkey]

But you can imagine me making two clocks right, same height, and I throw one into a black hole and one stops ticking. Then I will know.

 

[PeterDonis]

if we look at MTW Gravitation, on page 1054, they talk about experiments with elementary particles.

These experiments have nothing to do with light clocks, and do not involve the issues that your proposed thought experiments with light clocks are raising.

there is certainly an experimental basis on which I can assume time dilation in a curved spacetime

Only if you understand that a fundamental part of that experimental basis involves how to compare the rates of different clocks that follow different paths through spacetime. There are only two invariant ways to do that:

The first way requires that the clocks are like the twins in the twin paradox: they start out together, separate for a while, and then come back together again so their elapsed times while they were separated can be compared.

The second way allows the clocks to be spatially separated, but requires that they are at rest relative to each other, as determined by the round-trip travel time of light signals between them, as measured by each clock, being unchanging. Then you can compare how much time elapses on each clock during one round-trip light travel time, and compare their rates that way.

So far, you have not specified a way of comparing different clocks in your proposed scenarios that meets either of the above requirements. Until you do, the questions you are asking are not answerable.

you can imagine me making two clocks right, same height, and I throw one into a black hole and one stops ticking

No, it won't.

 

[sqljunkey]

Well does it make any difference which way I pick. What I want to know is does the clock slow down as it gets closer to a mass?

 

[PeterDonis]

does it make any difference which way I pick.

Which way you pick what? So far you haven't picked anything at all. You've just posed ill-defined scenarios and asked unanswerable questions.

What I want to know is does the clock slow down as it gets closer to a mass?

Slow down compared to what? Measured how?

Until you can answer those questions, your question is unanswerable.

 

[Nugatory]

if that clock slows down from where I'm standing...

If the clock is anywhere except where you're standing, whatever you think you're saying about whether it's slowing down or speeding up is just talking about your choice of simultaneity convention.

(This is easier to see after you understand how in special relativity time dilation emerges from the relativity of simultaneity, which is is why I said above that you don't want to take on time dilation in general relativity until you have a solid understanding of how it works in special relativity).

 

[sqljunkey]

Well okay, let us do like the twins, two clocks; one goes around a very massive object, and comes back to me, I'm very very far away with the other clock. I picked one. Now we know that in all frames c is the speed of light. Now if that clock is off by one millisecond, something happened.

 

[PeterDonis]

one goes around a very massive object

What do you mean by "goes around"? Do you mean it goes around in an orbit that comes back to the starting point, where the other clock is? Or do you mean goes down close to the object, stays there for a while, and then comes back?

 

[Halc]

A clock out at geosync orbit (sufficiently distant from Earth gravity well) will run objectively faster than one on the ground, which means that an observer at either clock will observe time on the high clock gain on the ground one. I think this is the answer you're looking for.

A clock on the ISS will run objectively slower. The gravity potential is higher there, but not much higher. The speed difference at that low orbit wins, so the the dilation due to speed is a greater effect than the negative dilation due to gravitational potential. Out at geosync, the potential wins over the effects from speed.

It's a clock thing, not special to light clocks, which are no different than any other clock. The distance between mirrors is not different out in geosync. Light really does move at a different speed at locations of different potential than it does locally. Speed of light is locally always c.

 

[PeterDonis]

we know that in all frames c is the speed of light.

No, we don't. We only know that in all inertial frames the speed of light is $c$. But in a curved spacetime, there are no global inertial frames, only local ones.

Now if that clock is off by one millisecond, something happened

No, you don't. All you know is that the two clocks took different paths through spacetime that had different lengths.

 

[PeterDonis]

Light really does move at a different speed at locations of different potential than it does locally.

More precisely, it moves at a different coordinate speed, in the coordinates that are usually used in the scenario you describe. But that isn't telling us that anything is changing about the light; it is only telling us about the coordinates.

 

[sqljunkey]

I don't see how this is any harder than it should be, if the clock comes back and is off, that distance changed. Because certainly if I traveled with that clock the whole round trip, inside it, the speed of light would have not changed. If I made the clock big enough.

I didn't say global anything. I have two vars, after the experiment one changed, and one stayed the same.

I hope we are not saying the clock when returned is at the same exact time as it's twin. What does it matter what the clock did when it was out on this trip anyway. The clock isn't mass-less.

 

[PeterDonis]

if the clock comes back and is off, that distance changed

No, that is not correct. If the two clocks show different elapsed times when they come back together, it means that they followed paths through spacetime that were of different timelike lengths. It does not mean anything changed about the distance between the mirrors in either clock.

In fact, the opposite is true: in order for the clocks to work correctly at all, the distance between their mirrors must be fixed. The best way to do this would be mechanical: have some rigid rod that connects the mirrors and keeps them a constant distance apart. Otherwise you don't have a good light clock at all.

 

[PeterDonis]

I have two vars, after the experiment one changed, and one stayed the same.

No, you have two clocks with different elapsed times. You have no way of telling which one "changed" and which one "stayed the same".

 

[PeterDonis]

If I traveled with that clock the whole round trip, inside it, the speed of light would have not changed

This is correct, but it does not have the implications you claim it does.

 

[sqljunkey]

well i feel like in SR we can talk about length contraction okay but in GR it seems like taboo or something. Idk much about the difference between timelike worldlines or spacelike worldlines. But I mean eitherway it sounds like equivalent. But okay I need to go to bed to go to work tomorrow.

 

[PeterDonis]

i feel like in SR we can talk about length contraction okay but in GR it seems like taboo or something

That's because there is no gravitational analogue to SR length contraction.

idk much about the difference between timelike worldlines or spacelike worldlines.

There are no spacelike worldlines. Worldlines are always timelike (except for the worldlines of light rays, which are null.)

I mean eitherway it sounds like equivalent.

I have no idea what you mean by this.

The OP of this thread appears to be based on confusions and misconceptions, and no sound basis for further discussion has appeared. Therefore, this thread is closed.