(Alpha) General relativity dissatisfies the equivalence principle

I mention it because many people have told me that the theorem proves GR is self-consistent.

I don’t disagree with any of this.

If these are based on local flatness, which I agree is a “fundamental feature of GR”, then they don’t prove that GR doesn’t contradict itself about that. Do you disagree? From what I can tell based on an extensive search, GR is thought to be self-consistent only because it has not been shown to be self-inconsistent, and not because it has been proven to be self-consistent. While a simple theory may be readily shown to be self-consistent, GR is not a simple theory. For example, it took years after GR was published before it was shown that a Schwarzschild radius is not a physical singularity.

It does, and thanks. I’ll be posting another thread about this topic, another attempt to show that GR violates the SEP, that doesn’t have the flaw pointed out by Pete on pg. 2. I hope you will give your input.

 

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Agreed to all.

The spacetime is flat within X. That was amply shown above, with references, esp. on page 1 and 2. Spacetime curvature is synonymous with the tidal force. Then by the definition of an inertial frame given in the OP, the spacetime in X is negligibly curved (all but flat). Three references were given on page 1 and 2 to show that an inertial frame can straddle a horizon.

Agreed.

I disagree that the spacetime curvature in X and Y significantly differ, as noted above.

On page 2, Pete showed that the rope in Y will eventually break regardless of its tensile strength. That refuted the OP’s contention that the rope in Y need not break.

By the definition of an inertial frame, which X is, the tidal force throughout the frame is negligible. So a tidal force will not break the rope. Nevertheless, the rope must break because one end is falling below the horizon (GR’s prediction) whereas the other end is attached to the rocket, which hovers above the horizon.

This would indeed cause the rope to break; I gave a link on page 1 or 2 to show that (from Wikipedia topic “event horizon”). But, as above, the rope in X will break regardless.

The experimenter could be beside and at rest with respect to the rope as they both fall freely across the horizon. Then the experimenter can certainly see the rope fall across the horizon. It is an observer in the rocket who cannot see the rope cross the horizon, but there is no such observer mentioned in the OP; such observer is irrelevant to the conclusions in the OP.

The OP is about GR’s adherence to the SEP, not SR’s. Noting that SR “does not recognize gravitational time dilation” neither shows that there “is no problem with GR” nor shows a problem with the thought experiment in the OP.

 

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The constructive theorems I've mentioned are a part of GR and so depend on various of its axioms including the local flatness axiom. In this precise sense, quoting them does nothing to "prove" the axiom, the axiom is already assumed. My point in mentioning them is that they provide an explicit way to set up nice local coordinate systems near the horizon. Nothing goes wrong with these constructions so the horizon is regular.

The real point of the post was the possibility of imbedding all nice (pseudo-)Riemannian manifolds into (pseudo-)Euclidean spaces. Since the spacetimes which can appear from the GR field equations constitute a subset of the nice pseudo-Riemannian manifolds, and since all such manifolds can be imbedded in pseudo-Euclidean spaces, we expect that all spacetimes in GR are as nice and consistent as pseudo-Euclidean spaces. Since proving a theory is truly self consistent is a very complicated business in mathematics (e.g. Godel's theorems), my argument is probably about the best one can do.

As for the confusing history of the Schwarzschild solution, much of the chaos and misunderstanding results from the over dependence on coordinates. In fact, this is the story in general for GR. Real progress began to be made when people stopped relying on coordinates so much. The Schwarzschild coordinates are bad at the horizon, but that tells you nothing about the actual geometry. I suspect, and this is only meant to be friendly advice, that your own issues with GR stem largely from the fact that you rely too much on coordinates. Coordinates are often extremely misleading; for example, you're using S coordinates when you should use EF or KS coordinates, both of which reveal the benign nature of the horizon.

Well, I'm certain you won't find any violations, but I'll participate if I can.

 

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That's an excellent post full of good info.

The OP relies on GR's predicted "benign nature of the horizon" for an inertial frame falling across it. That might imply a particular global coordinate system, but the OP doesn't need to explicitly mention one.

 

OK, let's address one point at a time.

You say a given event can occur in only one frame. I disagree; I say a given event can occur in multiple frames (i.e. a given point in spacetime exists in multiple frames). None of your four sources limits an event to only one frame. So how do these sources refute me?

 

Hi Zanket---

In the interest of coninuing in the discussion I will apologize to you. I should have adhered to the rules that you have set out in this discussion, as I would expect the same courtesy from you. I took a loose interpretation of the alpha rules, and apparently overestimated my ability to be sarcastic is a manner which was not interpretted as insulting. In attempting to prove you wrong I have learned a bit about GR that I have not known before, and I should thank you for this.

Either way, I would like to pick up where I left off, in proving you wrong.

Trippy has provided about four definitions which refute your interpretaiton of Wheeler and Taylor's definition of reference frame---namely that "physics" and "measurment" are local ideas. I have showed you that your interpretaiton leads to a logical fallacy, which I will not bother cutting and pasting here again.

 

OK, let’s discuss one point at a time, starting with this one:

The part of the SEP used in the OP refers to “any experiment” in a lab moving in an inertial frame. How did you infer that “any experiment” is limited to an experiment that measures something moving at a constant velocity? The vast majority of experiments conducted throughout recorded history have not been so limited.

Y is a copy of X, including the experiment within X, with the sole exception that Y’s location in spacetime differs from that of X. Both X and Y are inertial frames. Only the outcomes of the experiments in X and Y are compared in the OP. X and the rocket’s frame in Y would be incomparable even if the rocket in Y moved at a constant velocity; those frames are apples and oranges.

 

Yes, and in relativity there are no preferred inertial frames, so the event belongs to John’s frame no more or less than it does to Bill’s frame.

Yes. However, in the OP the rocket + rope is the experiment, so no experiment is conducted in a noninertial frame. Observers in the labs that are in free fall in X and Y, both inertial frames, monitor the rope and record whether or not it breaks.

If you have no more issues with events, then please choose your next point of disagreement with the OP.

 

Using this logic, it is quite easy to construct experiments which violate the SEP! One can take some grossly noninertial experiment and stick it in an inertial reference frame, and be done with the matter.

Here is an example, I think. Let my mass be constant and nonzero (which, I assure you, it is). Now put me on a scale in an inertial frame, and my weight is 0. Now put me on a scale on the Earth, and my weight is mg. No problem, you say, because the Earth is a non-inertial reference frame.

But now, put me on a scale on Earth, but observe my weight from an inertial reference frame. I am behaving in a non-inertial manner, but the experiment is still being conducted in an inertial reference frame. So the contradiction---how can my weight be both zero and non-zero.

Zanket says "Ah ha, the SEP is violated", and I say "Sorry but you'll have to do better".

 

This experiment is okay; it’s within the realm of “any local experiment in a lab moving in an inertial frame” to which the SEP refers.

A local experiment measures something within the lab. You’d need to put the Earth within the lab, but then the curvature of spacetime (the tidal force) caused by the Earth makes the inertial status of the lab’s frame doubtful. A better example of such experiment would be to put you on a scale in a rocket that is noninertially accelerating (thrusting) within the lab.

When testing GR’s adherence to the SEP regarding the lab’s location in spacetime, the same experiment must be conducted in both (or all) inertial frames, like X and Y. Your two experiments differ, hence their outcomes are incomparable. You could show that GR violates the SEP only by showing that the outcome of one experiment or the other differs depending on the lab’s location in spacetime. But I don’t see how you could do that. Presumably the outcome of the first experiment is always the same (always zero) regardless of the lab’s location in spacetime. Presumably the outcome of the second experiment is always the same (always the same nonzero value) regardless of the lab’s location in spacetime.

 

By what logic? They are clearly different experiments. One measures the weight of an inertial observer, the other measures the weight of a noninertial observer. In the OP the experiments in X and Y are identical.

No, because the experiment in X is contained wholly within the lab in X. "Local" in "local experiment" in the SEP means "within the lab, doing good measurements". The experimenter cannot look outside a window of the lab and say "there's a planet out there I didn't see before, therefore the SEP is violated". BenTheMan's experiment involving a scale on Earth would be like that, because you couldn't even see the scale on the Earth unless you looked out the window. The Earth could be included within the lab, but then the lab's inertial status is doubtful.

The same type of experiment can be conducted within the lab without the tidal force created by the Earth being an issue, by putting the scale within a noninertially accelerating (thrusting) rocket within the lab. That would be a local experiment. But then the outcome of that same local experiment must differ in an inertial frame at a different location in spacetime before one can say that GR violates the SEP in regards to the lab's location in spacetime.

If the outcome of a local experiment (an experiment contained wholly within the lab, i.e. without looking out a window, doing good measurements) differs depending on the lab's location in spacetime, then GR violates the SEP, rather than (as you suggest) indicating that whatever caused the outcome to differ must be included within the lab.

 

The experiment in both X and Y determines whether or not the rope breaks, that's all. The rope in both X and Y is noninertially accelerating, due to being attached to a thrusting rocket in both cases.

I didn't agree that "the rocket in Y is behaving inertialy". Quote me.

I edited my post after yours to improve the explanation; take a look. The experimenter in either X or Y must not take into account anything outside of the lab, otherwise it's not a local experiment.

No, the two experiments BenTheMan gave differ. They are apples and oranges.

 

We should be clear---you have not defined your reference frames to be local. That is, they are not defined at one point in space time. Your experiments are non-local anyway. You are sure to run to Wikipedia and cut and paste a definition for me. I have checked Wikipedia and found that there isn't an acceptable definition there. So you'll have to try harder

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Your experiment is non-local for several reasons. The principle of which is that, if the rope crosses the horizon, it is no longer in causal contact with the rest of the rope. The end of the rope cannot "talk" to the beginning of the rope---this much should be clear from the causal structure of the space-time in which the black hole is located.

Not as you've defined "lab". Your labs are not local. See the previous paragraph.

And this is different from your lab containing an event horizon how?

Ah yes but GR tells us the two are the same. But ok---let's use your example.

If my experiments differ then so do yours. If I define a reference frame to contain an accelerating rocket, and observe my weight from an inertial reference frame, do my measurements suddenly become valid? This is, I should stress, what you are proposing. All you have done is defined a frame and placed the rocket there. I have done the same thing. Aparently, the fact that the rocket is non-inertial doesn't matter.

 

In the interest of time, I'll argue only one point of yours at a time.

You've made this argument before but you haven't backed it up. Whereas I gave multiple references from top relativity physicists to show that the inertial frame to which the SEP refers need not be point-sized. Even the SEP itself refers to a lab in an inertial frame. I don't see why you keep bringing this up. You’ve already agreed that the tidal force (spacetime curvature) can be neglected in a frame for the purposes of a given experiment. So why do you think the frame must be point-sized? What would be gained by that? More importantly, when are you going to support your point with some outside reference? I call yours the “not exactly flat” argument, as in “if the spacetime is not exactly flat then it’s not an inertial frame”. I once mentioned to a physics professor that people bring up this argument ad nauseam. He said “Why bother having discussions with people like that?” I don’t say that to be rude. I say it to impress upon you that you’re nitpicking. Einstein's “luckiest thought” that led to the idea of the equivalence principle was this: “For an observer in free fall from the roof of his house there exists no gravitational field—at least in his immediate proximity”. Einstein’s next thought was not “scratch that—it’s a useless idea because it’s true only at a point”.

 

Ok fair enough---maybe I should jump off a building because one physics professor somewhere in the world thinks I don't know what I am talking about

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Look---the point is that your experiment isn't local. This was the point that I have made several times before, and you have refused to acknowledge. One cannot define a local experiment stradling the horizon of a black hole---it is not possible. Defining frames as little patches of space is fine, so long as the little patch of space has the same causal structure, as Phisics Monkey pointed out. Clearly the causal structure in one part of your frame is different from the other part of the frame because one end cannot send a message to the other end. The idea of locality ceases to exist across the horizon of a black hole. Once one part of your reference frame crosses a horizon, it is non-local---that is, a beam of light cannot go from one end of the frame to another. There is no way for the end of your rope to comunicate with the beginning of your rope. This is something that you cannot get around. And I don't know how many ways I can say this.

If you ever talk to that physics prof again, tell him I said that defining your reference frames at a single space-time point can ensure that this doesn't happen. You are automatically granted locality when you do this.

To be fair, I have talked with several physics professors about this conversation (even one of the world experts in black holes) and they have all said the same thing---"Did you tell him that you can't define a frame that straddles a black hole?"