The discussion revolves around the concept of length contraction in General Relativity (GR), particularly as it pertains to free-falling objects near black holes. Participants explore the implications of length contraction, the effects of tidal forces, and the challenges of defining length in curved spacetime.
Participants express differing views on the validity and applicability of length contraction in GR, particularly in curved spacetime. While some agree on the local definition of proper length, others argue that length contraction may not hold meaning outside of approximately flat spacetime. The discussion remains unresolved with multiple competing perspectives.
Participants note that the definition of length and the effects of simultaneity conventions can vary significantly between inertial and non-inertial frames, and that these factors complicate the understanding of length contraction in GR.
Which continues "...from some point B to an infinetesimally close point A..."Demystifier said:Page 234, "Suppose a light signal is directed ...". It describes an experimental procedure for measuring distances.
And later says that it can be integrated to finite distances (provided that metric is time-independent).martinbn said:Which continues "...from some point B to an infinetesimally close point A..."
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.Demystifier said:And later says that it can be integrated to finite distances (provided that metric is time-independent).
https://ui.adsabs.harvard.edu/abs/1959PhRv..116.1041T/abstractPeterDonis said:Where are you getting this from? Do you have a 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.PeterDonis said:Reference?
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.jartsa said: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.