(Alpha) General relativity dissatisfies the equivalence principle

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I am anxious to hear Zanket's reply---if this is his view then he is seriously mistaken.

 

Oh yeah---we should probably make it clear to him that "local" must mean causally connected. There is absolutely no way that one can have local events occuring across the horizon of a black hole.

This is also a point that physics monkey made a while back.

 

OK, I’ll take this as your next point to debate.

You need to do more than say this; you need to give some outside reference to support it. You are arguing that some local patches of spacetime have a different “causal structure” than other such patches. GR says that SR applies locally. SR requires an inertial frame. Spacetime is flat (negligibly curved) within an inertial frame, by the definition of an inertial frame. Then a local patch of spacetime must be a patch in which the spacetime is flat (negligibly curved). A frame in free fall within such a patch is an inertial frame. Then you are arguing against a postulate of SR, which says (google for it): “The laws of physics are the same in all inertial frames of reference. In other words, there are no privileged inertial frames of reference.” You are arguing that there are privileged inertial frames.

In X, a message sent from the lowest end of the lab can reach the highest end of the lab. The lab is in free fall; the horizon passes through the lab at the speed of light (GR predicts). A message sent from the lowest end at the moment the lowest end is at the horizon can reach the highest end at the moment the highest end is at the horizon.

The observer who cannot successfully receive a message from someone below the horizon is an observer in the rocket. Although this observer is in X, this observer's frame is not X. Within any inertial frame, a noninertial observer can exist who cannot receive a message from someone else in the frame, because (as Trippy noted above) a Rindler horizon can exist within any inertial frame. But a beam of light emitted by an observer at the dangling end of the rope can be received by an observer at the highest end of the lab. In X it would be received when the highest end of the lab is below the rocket (hopefully the lab has no walls or else the rocket would have crashed into the wall of the lab before then).

I assume by “frame” they mean “inertial frame”. It is true that an inertial frame cannot straddle a black hole such that the hole's central singularity is within the frame. But if by “black hole” they meant only the horizon, they contradict the references I gave on page 1 or 2, including from Taylor and Wheeler, references which say that you need not feel a tidal force as you fall freely across a horizon, in which case an inertial frame can straddle a horizon, by the definition of an inertial frame.

 

I’ll take this as your next point to debate.

Can you provide even one reference that shows that the concept of locality in relativity has to do with something other than proximity? I bet you cannot do that.

Physics does not redefine the dictionary definition of the word “local”. However, I’ll recant something I said above that you quoted (see, I don’t ignore what you quote of mine):

I stand by my comment above that “local” is used in multiple ways in relativity. Here is proof of that: On pg. 1-16 of Exploring Black Holes Taylor and Wheeler say “A free-float [(inertial)] frame is "local" in the sense that it is limited in space and time—and also "local" in the sense that its free-float character can be determined from within, locally”. On the same page they use “local” a third way: “Detect each event locally, using a latticework of clocks: Nature puts an unbreakable speed limit on signals—the speed of light. This speed limit causes problems with the recording of widely separated events, because we do not see a remote event until long after it has occurred. To avoid the light-velocity delay, adopt the strategy of detecting each event using equipment located right next to that event.”

The third use of “local” they mention is covered by any decent book on SR—it has to do with doing good measurements and has nothing to do per se with GR. The first usage of “local” is discussing GR; it limits the size of an inertial frame in curved spacetime.

The third use of “local” they mention means “right next to”. That’s specific. The first use of “local” they mention is arbitrary; they nebulously say “in the sense that it is limited in space and time”. The question is, how limited? If you read further, you see what they mean. An inertial frame is limited in space and time (local) to the extent that the tidal force (synonymous with spacetime curvature) throughout the frame can be neglected for the purposes of a given experiment. For the purposes of a particular experiment, an inertial frame could be two million light years long (proper length), like they have in an example on pg. 1-4. The tidal force throughout such a frame could be less than the tidal force throughout a breadbox. The third use of “local” they mention has nothing to do with the tidal force.

What I recant is the part in bold. Upon further reflection, “local experiment” in the SEP must mean “an experiment wholly within the lab”. An experiment can involve multiple measurements and can span the entire lab, even if it’s two million light years long, so “local” in “local experiment” cannot mean “in close proximity” or “right next to”. Even though the SEP explicitly places the experiment in a lab in an inertial frame, “local” is probably used to emphasize that the experiment cannot look out of the window of the lab. Taylor and Wheeler’s third usage of “local” must go without saying in the SEP.

 

I didn’t ask for such a reference. I asked for a reference to support your contention that “local” in “local experiment” in the SEP has nothing to do with “proximity”. I gave a reference to further support my contention to the contrary.

The second sentence does not follow logically from the first. The SEP refers to “any local experiment”. I showed that “local” has nothing to do with whether or not the experiment involves noninertial objects. If you were right, then “any local experiment” would refer to only a tiny minority of the experiments conducted in recorded history. Almost every type of experiment would be excluded. An experiment that so much as monitored the flight of a moth would be excluded. Even a DNA test requires the DNA to move noninertially in a centrifuge. And if you were right, SR would be invalidated, because SR predicts the outcome of experiments involving a noninertially accelerating rocket, and those results depend on no outside force.

No. I want to address one point at a time.

 

I don't see how you've shown that. I haven't shown in this thread that GR violates the SEP (the OP was refuted on page 2 by Pete). Neither have you, as far as I can tell.

How so?

 

Trippy, I've been busy and have been unable to follow the discussion here. What specifically were you interested in references/info on?

 

If your laboratory is fixed at the event horizon, it should be moving with the speed of light locally. There is no such an inertial frame even in special relativity.

If your lab is in free fall, the EH is moving with the speed of light. So to "hover over" the EH requires the spaceship to move with the speed of light relative to the lab. If you pull a rope with this speed rope will just break apart because the atoms cannot communicate with each other faster than the speed of light.

 

Hi temur, welcome to sciforums. The original post (OP) was refuted on page 2 by Pete. I corrected the problem in this thread. Have a go at that one if you want.