I Length contraction in General Relativity

[martinbn]

I'm not sure what do you mean by that. If you mean that Eq. (84.6) in LL is local, one can always integrate it $l=\int dl$ to get a global distance. The integral is taken along a geodesic with respect to the spatial metric (84.7).

No, that is still local.

 

[cianfa72]

And, the proper length is defined as the length in a reference frame in which the object is at rest.

The object actually defines a worldtube in spacetime. The reference frame in which it is at rest should have as "grid lines of constant spatial coordinates" the worldlines in the congruence defined from the object's worldtube.

 

[PeterDonis]

I found this: https://www.physicsforums.com/threads/gravitational-length-contraction-and-dilation.404153/. Post# 9. What bearing does this have on the current discussion?

It shows some of the issues involved if you try to give a well-defined meaning to "gravitational length contraction".

 

[Demystifier]

No, that is still local.

Is that a problem?

 

[martinbn]

Is that a problem?

Yes, if the stick is not near you how do you assign length to it? But even if that worked, the main point since post #2 is that whatever conventions there are in the question, they need to be explicitly made. Otherwise the question is ill posed.

 

[Demystifier]

Yes, if the stick is not near you how do you assign length to it?

The reference in post #43 says how.

But even if that worked, the main point since post #2 is that whatever conventions there are in the question, they need to be explicitly made. Otherwise the question is ill posed.

It's explicit in the reference in post #43.

 

[martinbn]

The reference in post #43 says how.It's explicit in the reference in post #43.

No, it is not there. At least I cannot find it. Can you quote it or point out exactly where to look?

 

[Demystifier]

No, it is not there. At least I cannot find it. Can you quote it or point out exactly where to look?

Page 234, "Suppose a light signal is directed ...". It describes an experimental procedure for measuring distances.

 

[ergospherical]

@Demystifier - it's also pointed out in that section that integration of the spatial line element $dl = \sqrt{\gamma_{\alpha \beta} dx^{\alpha} dx^{\beta}}$ over a finite domain is only meaningful in static spacetimes, for otherwise the metric is time-dependent and the integral is worldline-dependent.

 

[cianfa72]

for otherwise the metric is time-dependent and the integral is worldline-dependent.

Btw, even though the spacetime is static you must evaluate the integral in the appropriate coordinate chart -- i.e. in the adapted coordinate chart in which the metric does not depends on timelike coordinate.

 

[martinbn]

Page 234, "Suppose a light signal is directed ...". It describes an experimental procedure for measuring distances.

Which continues "...from some point B to an infinetesimally close point A..."

 

[Demystifier]

Which continues "...from some point B to an infinetesimally close point A..."

And later says that it can be integrated to finite distances (provided that metric is time-independent).

 

[martinbn]

And later says that it can be integrated to finite distances (provided that metric is time-independent).

We are going in circles. This is local. An observer can do that and say what the length of a stick is, if the stick is right next to him. What about a second observe, who is far away? What is he going to do to measure the stick's length? All this requires some conventions to be specified. It seems that the OP is unaware of that.

What exactly is your position? It is unclear to me what your point is.

 

[jartsa]

Where are you getting this from? Do you have a reference?

https://ui.adsabs.harvard.edu/abs/1959PhRv..116.1041T/abstract

Terrell says "Lorentz contraction can't be seen". Well, maybe the important thing in the paper is not that thing, but the rotation that can be seen. Anyway that is were I got the idea that Lorentz contraction can't be seen.

Reference?

Well, my understanding of a Rindler-horizon is that it's a horizon were motion of stuff appears to freeze, as seen from far above the horizon. Now, if a ruler's one end near said horizon appears to be quite motionless, while the other end is still appears to be moving a little bit, then the length of the ruler appears to be decreasing. And here's some kind of reference about the last thing, that a person hovering above a large black hole sees the same effects as the person on an accelerating spaceship.

https://www.physicsforums.com/threa...ple-and-rindler-horizons.1007879/post-6550886

 

[Ibix]

Terrell says "Lorentz contraction can't be seen". Well, maybe the important thing in the paper is not that thing, but the rotation that can be seen. Anyway that is were I got the idea that Lorentz contraction can't be seen.

That depends a bit what you mean by "seen". Get a 1m long strip lamp and a 1m long piece of photo paper facing each other a centimetre or so apart and have a rod of rest length 1m pass between at 0.866c. Blink the light as the rod passes through and the shadow on the photo paper will be 0.5m long. However, if you stand and watch the rod or use a regular camera that we can model as pointlike then the light coming from the far end of the rod is older than the light from the near end, so you don't see the whole rod as it is at one time (per an Einstein frame) and this can sometimes counter the length contraction effect.