(Alpha) General relativity dissatisfies the equivalence principle

[Trippy]

I take it back, you finally gave a reason why you disagree with it. But your explanation disagrees with the dictionary definition of “as”, as in “SR works in an inertial frame as it falls through a horizon”. Calling it an argument about semantics does not make you right.

Same reason that I have always transparently stated, as for the rest of your 'point', see below.

From Exploring Black Holes by Taylor and Wheeler, pg. 2-4:

No one can stop us from observing a black hole from an unpowered spaceship that drifts freely toward the black hole from a great distance, then plunges more and more rapidly toward the center. Over a short time the spaceship constitutes a "capsule of flat spacetime" hurtling through curved spacetime. It is a free-float [(inertial)] frame like any other. Special relativity makes extensive use of such frames, and special relativity continues to describe Nature correctly for an astronaut in a local free-float frame, even as she falls through curved spacetime, through the horizon, and into a black hole. Keys, coins, and coffee cups continue to move in straight lines with constant speed in such a local free-float frame. ... Collisions, creations, and annihilations of particles continue to follow the special relativity law of conservation of momentum-energy. What could be simpler?

I quote you, it says through, not at.

I can’t be refuted by unscientific reasoning. You are arguing that the SEP is untestable in regards to the lab’s location in spacetime, in which case it’s not science. I say again: Your logic leaves no room for any theory to contradict the SEP regarding a lab’s location in spacetime. You could not give one example of a hypothetical theory doing that; that would be impossible. What example can you give to refute me on that?

I have offered multiple, alternate scenarios, all of which are valid tests. You claim that my statements preclude the testing of GR. You are simply saying this because in your mind, the results of the tests are a foregone conclusion, this does not make the tests invalid, it simply makes the theorry right.

According to your logic, dropping a hammer and a feather on the moons surface was not a valid test of the various theories of gravity, because their falling at the same rate was a forgone conclusion.

That’s a misconception on your part. Google for “relativistic rocket”.

I'm going to ignore this comment, I find it insulting.

Special relativity deals with a special subset.
General Relativity deals with everything else.

Bell’s spaceship paradox shows that the free end of the rope must accelerate at a greater rate than the rocket end of the rope in X or Y’s frame, otherwise it will break eventually. The reason a rope connecting the rockets in Bell’s spaceship paradox breaks is because the pursuing rocket is accelerating at “only” the same rate as the pursued rocket. The rope continuously length-contracts in the inertial frame but has the same measured length in that frame, in which case it is continuously physically stretching. The only accelerated rope that will not eventually break is one which accelerates at specific various rates, like a rocket undergoing Born acceleration (google for it).

No. It doesn't. I'm more then familiar with Born's notion of rigidity, I even know what an elastic wave is, I've studied Rheology (google it). Bells Paradox deals with two spacecraft joined by a rope, or by a rigid pole. In the example of Y, the far end of the rope is free to move.

By YOUR logic no rigid or non rigid body can accelerate indefinitely (barring energy considerations) because every accelerating body must (eventually) break.

I said irrelevant to the OP. If you must take my words out of context to make your point, that should tell you something.

No part of the SEP is irrlevant to the OP. And please refrain from personal insults. It is against the rules of an Alpha thread (as you have repeatedly pointed out to Ben). I have shown you the curtosey of being polite, and refaining from name calling. I expect the same from you. If you can not refrain from such, then I suggest you revisit classifying this thread as an Alpha thread.

I don’t feel the need to pursue your point any further. You’ve given no support for it but your opinion.

I have endeavoured to, multiple times. I have endeavoured to find literature to support either your point, or my own, but have not been able to do so. until you can demonstrate that the present of a schwarzschild event horizon has no effect on causality, then your point remains refuted.

I have mentioned, and it has been pointed out to you that the definition of locality has nothing to do with distance, but causal structure, which is in turn governed by past and future light cones. I have at seen at least one link posted that clearly demonstrated that the presence of an event horizon, and singularity influences the shape and directionality of at least future light cones. Therefore, your assumption that the far end of the rope can be defined as being local to the experimenter remains disputed.

The OP says: Let “Y” be a copy of X, including its contents, with the sole exception that Y does not straddle a horizon.

Do you disagree that the definition of “sole” is “of which there is only one”? If not, then quote me where you think I changed two variables in the OP.

Then please, demonstrate how your experiment reproduces the force regime on the rope in Y. You can't. By the structure of your logic in the OP, it doesn't.

So easy to be right when you don’t need to give a reason why.

I would suggest being more careful with what you say, especially with some of the comments you have been throwing at Ben. First take the post in conext. Then go back, actually read the thread you started, and find the bits where I've justified my position. No, I'm not arguing that Location in space time has no applicability. Quite the oppisite. And no, you have not adequitely refuted me.

I can’t be refuted by unscientific reasoning. You are arguing that the SEP is untestable in regards to the lab’s location in spacetime, in which case it’s not science. I say again: Your logic leaves no room for any theory to contradict the SEP regarding a lab’s location in spacetime. You could not give one example of a hypothetical theory doing that; that would be impossible. What example can you give to refute me on that?

Yes, it does. And once again, I have, several times. Go look for them. They're in this thread, and over in Physorg.

The OP says: Let “Y” be a copy of X, including its contents, with the sole exception that Y does not straddle a horizon.

Do you disagree that the definition of “sole” is “of which there is only one”? If not, then quote me where you think I changed two variables in the OP.

You have changed the location of the end of the rope (relative to the singularity).
The Inverse Square Law predicts that changing the location of the end of the rope will change the force acting on the rope.
Changeing the force acting on the end of the rope changes the outcome of the experiment.
The Inverse Square Law predicts a (potential) change in outcome.
The SEP predicts a (potential) change in outcome (if we assume it's applicable).
General Relativity predicts a (potential) change in outcome.

WHERE is the inconsistencey?

Don’t get too carried away. A Rindler horizon is significantly different than the horizon of a black hole. For one thing, light directed “upwards” below a Rindler horizon rises, whereas it falls below the horizon of a black hole. A Rindler horizon doesn’t prove the existence of black holes.

I never said the Rindler Horizon proved anything, I simply stated that it had many of the same properties as a Schwarzschild Event Horizon. They both also represent an Event Horizon. You also manage to contradict yourself in your own post.

Not only in that frame, but also in the inertial frame X or Y.

I've said it before, and now I'm repeating myself. An Event, by it's very definition occurs in ONE reference frame, and one reference frame only. The Event can be observed from multiple reference frames.

I didn’t ask you the same question a second time; I asked a different follow-on question. You’ll answer it or be in violation of the Alpha rules, esp. if you pursue your point that prompted the question.

Yes, you did, and no, I will not. Not when you qoute my answer in the same post as you say this. This is another place I would recommend treading carefully, after all, you said to ben that:

Don’t be coy; the Alpha rules forbid that.

Which you are being right now, and:

You need to establish relevancy first.

Would you please stop beating around the bush, and being coy, and by your own statement breaking the Alpha rules, and show me the courtosey I have always attempted to show you and make your point, or drop it all together.

Which you have not yet done.

 

[Trippy]

Wikipedia:

After he did this, many people, including himself, tried to find any inconsistencies in the system. Many supposed inconsistencies (or paradoxes) were proposed. Einstein took the job of looking for an explanation for all of them one by one, until another scientist, named Hermann Minkowski, showed that the whole system of special relativity is self-consistent and therefore no real paradox can appear.

then we have verified that general relativity is self-consistent at this confidence level

-Black-hole spectroscopy: testing general relativity through gravitational-wave observations
Olaf Dreyer et al 2004 Class. Quantum Grav. 21 787-803 doi:10.1088/0264-9381/21/4/003[/quote]

 

[zanket]

In physics, one must be picky about the difference.

I think it is very presumtuous for you to tell me anything about physics. Jackass.

This is at least the ninth time you’ve blatantly violated the Alpha rules. Four times you’ve attacked people not the idea, and five times you’ve ignored my direct relevant questions. That’s enough. All you’ve proven in this thread is that you think the rules apply only to others, who are free to take over your arguments.

 

[Physics Monkey]

Hi Zanket,

BenTheMan gave only opinions, none of which proved your point. And note that his reason for GR's consistency is that it is a "purely mathematical theory", whereas you say GR's consistency is proven by theorems. If he was right, the theorems you mention wouldn't be necessary, now would they?

I assume that what Ben meant by "purely mathematical theory" is a theory based on consistent axioms and the rules of logic. I don't wish to assert that this is strictly speaking the only possible sort of "purely mathematical theory," only that this is probably what he was talking about. At least it was what I thought he was talking about, so with this understanding, he was basically saying what I had in mind which is why I regarded his response as adequate.

I repeat a question that you didn’t answer:

I’m not trying to pick on you. I’d really like to see if you can show that GR is consistent, or whether it’s just an opinion that you can’t support.

I assure you there are no ill feelings on my part. I'm happy to be specific if you like. First, I'm not sure why you mentioned Birkhoff's theorem since it has nothing to do with local flatness. Now, to the relevant theorems. Within the confines of Riemannian geometry it is possible to prove that every $$ C^\infty $$ Riemannian manifold may be imbedded isometrically in a Euclidean space of sufficiently high dimension. This theorem is quite important and it does have a name: Nash's imbedding theorem. Now this isn't quite what we want since GR is a kind of pseudo-Riemannian geometry, but it has been proven by Sokolov that the same sort of isometric imbedding of psedo-Riemannian manifolds in pseudo-Euclidean spaces is possible. This basically means that the manifolds in question are as consistent as Euclidean spaces which I think we all agree are consistent (though I freely admit I know of no proof of this). Accepting the consistency of Euclidean spaces we conclude that the axioms of (pseudo-)Riemannian geometry, including the local flatness axiom, are consistent.

One can also be more concrete with a number of constructive theorems. Schild's ladder can be used to construct geodesics crossing the horizon, and some sort of orthonormal transport, like Fermi-Walker transport, can be used to carry good local coordinate systems across the horizon. Of course, all this is based on local flatness which is, as I have repeatedly emphasized, a fundamental feature of GR.

Hope this helps.

 

[Trippy]

I assume that what Ben meant by "purely mathematical theory" is a theory based on consistent axioms and the rules of logic.

This is also what I understood, that relativity is completely consistent internally. The corrollary(?) of this is that if there are inconsistencies shown within the structure of relativity (Beyond not fully understanding the consequences of the theory) that the theory itself predicts that it will be completely wrong. This is why so much effort is being spent on finding inconsistencies, and why in the early years, so much effort was spent on dreaming up 'paradoxes' until Minkowski demonstrated that there were none.

 

[BenTheMan]

I assume that what Ben meant by "purely mathematical theory" is a theory based on consistent axioms and the rules of logic.

I'll defer to you

Hope this helps.

Zanket will neither understand nor accept these maths. 10 to 1.

 

[BenTheMan]

This is at least the ninth time you’ve blatantly violated the Alpha rules. Four times you’ve attacked people not the idea, and five times you’ve ignored my direct relevant questions. That’s enough. All you’ve proven in this thread is that you think the rules apply only to others, who are free to take over your arguments

And aparently a consensus is not enough to show that your argument is logically inconsistent, which also violates your hallowed Alpha rules. I'm glad you're keeping count of MY violations.

True or false: you are proposing that one of the most experimentally well-verified theories that man has ever conceived is wrong. I have already linked you to a publication which proves this.

True or false: you have studied physics in any detail, beyond an introductory high school or college course.

True or false: you have shown a robust knowledge of the theory of general relativity.

True or false: you have been accused by others of violating the same rules.

All you’ve proven in this thread is that you think the rules apply only to others, who are free to take over your arguments.

They are free to take over my arguments as I am free to take over theirs, I'm sure.

But I am here for the physics and not the company (Physics Monkey and Trippy excluded of course), so I will re-list my main objections here. I know that you are responding to many objections, so I will pick one and focus on it. I will drop the debate about Lorentz trnasforms because you are not understanding the point, whether it be some failure on my part to explain it coherently or otherwise. I will drop this argument with the caveat that it will probably be used again in the future, because, as it is with physics, many things are tied together. I will focus, at least in the short term, on attacking your definition of reference frame, which is used out of the context of Taylor and Wheeler's original intent, I am sure.

I also don't want to debate about the difference between "negligible" and "non-existant" anymore, unless it is necessary. The two must be the same if you are to do a calculation. Your arguments about "different negligible tidal forces" are amusing, but are not really relevant to the experiment, I feel. If you can show otherwise, we can continue bickering about this.

I have often not answered some of the questions that you have asked because I felt that they had been adequately addressed in other posts, or because I felt that they should be clear to someone who had some knowledge of GR. I will assume neither in the future. If you ask a question, I will either cut and paste a past response from me or someone else, or give an explicit answer.

Your definition of reference frame leads to a contradiction:

1. Your definition of "inertial reference frame".
2. Measurements made at all points in an inertial reference frame must be consistent with measurements made at all other points in an inertial reference frame.
3. Define reference frames X and Y to have similar curvatures, as per your thought experiment.
4. Then, by 1, there is an inertial frame S that contains X and Y.
5. S is an inertial reference frame by definition.
6. If S is an inertial reference frame, then, by 2, measurements made at X and Y must be consistent.
7. Thus, 6 implies that if the rope breaks at X, then it also breaks at Y.

Trippy has pointed out that 4 doesn't follow from 3, for some communications that he has had with you in the past, namely that the rocket in Y is behaving in a non-inertial manner. If this is so, then the SEP is trivially violated, as expected. The rocket is non-inertial, and cannot be considered under the SEP, as only inertial reference frames can be compared. The rocket must be moving with a constant velocity. In essence you are comparing an inertial and a non-inertial reference frame, that is, X and the rocket's frame in Y. (Note that the rocket has a reference frame whether you want it to or not.)

If both X and Y are inertial then I respectfully disagree with Trippy---that is, if the rocket is moving with a constant velocity. If X and Y are inertial then you must accept that your definition of inertial frame implies that some larger frame S contains both X and Y.

 

[BenTheMan]

This is also what I understood, that relativity is completely consistent internally.

This is the way I understand it, too. Like Newtonian mechanics is completely consistent mathematically and only happens to apply to the real world or something.

The only thing that Zanket can possibly argue is that GR violates the SEP in some special limit---like the limit where GR fails to apply anymore. This is like Newtonian mechanics being violated when masses and Compton wavelengths are of similar size. We already have an upper bound for this, called the Planck energy (or legth).

What I understood from Space Monkey's reply is that the existence of a smooth Riemannian manifold is a necessary and sufficient ingredient for GR. (Riemannian means it is smooth and admits a metric.) So Zanket would have to proove that the geometry at the horizon is not described by a Riemannian manifold---that is, that it is either not smooth or doesn't admit a metric. But this contradicts his own statements that the horizon can have a flat geometry, described by the Schwarzchild solution. In other words, the SEP follows from GR, it is not required for GR to be consistent.

Is this correct?

A minor point---Riemannian manifolds contain the set of Lorentzian manifolds? Is this true?

 

[BenTheMan]

Oh. I meant Physics Monkey's post.

 

[Trippy]

Minor point.
I was arguing that the rocket in X was non-inertial (and Zanket has agreed to this).
The rocket may be stationary (thus have constant velocity) relative to the blackhole, but, it is under the influence of a G-field, and is, by definition of the experiment, not in free fall. The entire rocket experiences a (fictitious) force.

 

[BenTheMan]

A minor point---Riemannian manifolds contain the set of Lorentzian manifolds? Is this true?

Yes I have checked. This is true... Lorentzian manifolds just have a metric which has a single negative eigenvalue. The Riemannian manifolds have metrics which have real eigenvalues.

 

[BenTheMan]

I was arguing that the rocket in X was non-inertial (and Zanket has agreed to this).

If it is non-inertial how can you use the SEP????

 

[2inquisitive]

“ I was arguing that the rocket in X was non-inertial (and Zanket has agreed to this)."

BenTheMan,
If it is non-inertial how can you use the SEP????

I think some are forgetting the original example by Zanket:

Let a lab be in free fall in an inertial frame “X”. A thrusting rocket moves freely within the lab, dragging a rope behind itself. The rope straddles the horizon of a black hole. The rocket hovers above the horizon. Assume that the rope will break before the rocket cannot withstand the rope pulling on it. Let “Y” be a copy of X, including its contents, with the sole exception that Y does not straddle a horizon.

GR predicts that anything below a horizon must fall. Then the rope in X must break, whereas the rope in Y need not break. X and Y differ only by the location in spacetime of their respective labs. Then in GR the outcome of a local experiment (e.g. a test of whether or not the rope breaks) in a lab moving in an inertial frame is dependent on the lab’s location in spacetime. And so GR violates the equivalence principle.

Neither frame X nor frame Y is the rocket's reference frame. Zanket is using two different inertial frames X and Y, and an accelerating rocket in each, separate, inertial frame. 'Y' inertial frame has within it an accelerating rocket dragging a rope in flat spacetime. 'X' inertial frame has within it an accelerating rocket dragging a rope across an event horizon, not flat spacetime. In both cases, the rocket's frame is non-inertial, while the observer is located in an inertial frame, either X or Y. The two rockets are located in two different non-inertial frames in which the spacetime curvature is different in each frame. The observer in frame Y will not see the rope break unless the acceleration is sufficient to place a great enough stress along the length of the rope to cause it to break. The observer in frame X will not see the rope break unless the tidal forces at the event horizon are great. The only 'problem' I see is if the observer in frame X decides to tell the rocket to 'reel in' a rope that has fallen through an event horizon without breaking when it fell through. As I understand GR, the observer in frame X would never actually see the rope 'fall through' the event horizon in the first place because of gravitational time dilation near the event horizon. Special Theory does not adequately address this scenario because it does not recognize gravitational time dilation. There is no problem with GR. Because of the gravitational time dilation, this thought experiment is outside the bounds of Special Theory.

 

[BenTheMan]

Neither frame X nor frame Y is the rocket's reference frame. Zanket is using two different inertial frames X and Y, and an accelerating rocket in each, separate, inertial frame.

So what? Just because you put a non-inertial experiment in an inertial frame doesn't mean you can suddenly apply special relativity. The experiment is non-inertial, and this is all that matters.

'X' inertial frame has within it an accelerating rocket dragging a rope across an event horizon, not flat spacetime.

Zanket has said that the space-time across the horizon is approximately flat, as it must be for the SEP to apply. If the frame was inertial, and the experiment was also inertial, then the SEP could be applied.

In both cases, the rocket's frame is non-inertial, while the observer is located in an inertial frame, either X or Y.

Yes, so the observations are effectively non-inertial. The rocket's frame is the only one that matters.

The two rockets are located in two different non-inertial frames in which the spacetime curvature is different in each frame.

If this is the case then the SEP definitely doesn't apply.

As I understand GR, the observer in frame X would never actually see the rope 'fall through' the event horizon in the first place

This is exactly correct. That is why the frame that sees the rope cross the horizon must be non-inertial. This has been pointed out to Zanket (by Physics Monkey, I think). (It does, of course, depend on where the observer is located.)

There is no problem with GR.

Good luck convincing Zanket of this!

 

[Trippy]

(Post edited by self as a show of good faith)

 

[BenTheMan]

We should make a list of Zanket quotes. This one is my favorite:

The results of the given experiment will be affected by a negligible tidal force, and affected differently by different negligible tidal forces, but affected only insignificantly in any case;

 

[BenTheMan]

God forbid he give me another infraction.

 

[Trippy]

Infraction or Infarction?

And in case anybody want's to question the relevancy of my last post?

I am establishing two things.

Zanket has agreed (more then once) the Rocket in X is behaving in a non inertial fashion (And is therefore a non-inertial experiment).
Zanket has argued that saying that you can't apply an inertial principle to a non-inertial experiment is wrong, and irrelevant.

 

[zanket]

I quote you, it says through, not at.

It says “as she falls through”, as in “while she is falling across the horizon, straddling the horizon, her frame is inertial and SR works fine”.

I have offered multiple, alternate scenarios, all of which are valid tests.

You have not done that.

You claim that my statements preclude the testing of GR. You are simply saying this because in your mind, the results of the tests are a foregone conclusion, this does not make the tests invalid, it simply makes the theorry right.

The results of the tests would be irrelevant using your logic. I claim that your logic precludes testing GR’s adherence to the SEP in regards to the lab’s location in spacetime, because for any set of experiments one could always say that the lab was at the same location, using your logic. By your logic “location” is something that can be a constant property of the lab, rather than something that changes when the lab is located differently relative to other objects. The lab can be considered stationary in some cases, but not in reference to the part of the SEP used in the OP (or else the SEP becomes untestable in that regard).

According to your logic, dropping a hammer and a feather on the moons surface was not a valid test of the various theories of gravity, because their falling at the same rate was a forgone conclusion.

No, that’s a test of a part of the SEP that is irrelevant to the OP. More on that below.

Special relativity deals with a special subset.
General Relativity deals with everything else.

SR deals with a subset that includes nongravitational acceleration (like the rocket’s acceleration in the OP), which you’d realize with a simple Google search.

By YOUR logic no rigid or non rigid body can accelerate indefinitely (barring energy considerations) because every accelerating body must (eventually) break.

Yes, this is true, with one exception: an object undergoing Born acceleration; that’s the only type of accelerating object that can avoid being continuously physically stretched. It doesn’t matter that one end of the rope (in X or Y) is free; the rope will still physically stretch because it is not undergoing Born acceleration. Bell’s spaceship paradox shows that the rope physically stretches: if a rocket pushing the “trailing” end of the rope is not enough to keep it from physically stretching, then it will certainly physically stretch when that end is not pushed. Texts on Born acceleration confirm that, by showing that the trailing end of an object must accelerate at a higher rate than the leading end, as measured by onboard accelerometers, or else the object will physically stretch.

No part of the SEP is irrlevant to the OP.

False, as I showed above about ANDed statements. The OP need focus on only one of a set of ANDed statements, because any such statement shown to be false falsifies what the set says as a whole (e.g. the entire SEP is violated if any one of its ANDed statements is violated). You didn’t refute that, so you’re expressing only an unsupported opinion at this point.

And please refrain from personal insults. It is against the rules of an Alpha thread (as you have repeatedly pointed out to Ben). I have shown you the curtosey of being polite, and refaining from name calling. I expect the same from you. If you can not refrain from such, then I suggest you revisit classifying this thread as an Alpha thread.

I was polite. When I say “that should tell you something”, I mean “that should tell you that your point is invalid”. I now understand that you think “No part of the SEP is irrlevant to the OP”, but I had already refuted that by when I replied, so there was no reason for me to assume that’s what you meant. If I refute something and you don’t dispute it, then I assume that you agree that it’s refuted, and I assume that you will not carry on with the refuted point, using it in further arguments.

I have endeavoured to, multiple times. I have endeavoured to find literature to support either your point, or my own, but have not been able to do so. until you can demonstrate that the present of a schwarzschild event horizon has no effect on causality, then your point remains refuted.

The OP implies that a horizon does have an effect on causality (i.e. affects the outcome of an experiment). Then it would make no sense for me to claim the opposite. Your point here essentially restates your belief that changing the lab’s location is tantamount to changing the experiment, invalidating the thought experiment; I’ve refuted that.

I have mentioned, and it has been pointed out to you that the definition of locality has nothing to do with distance, but causal structure, which is in turn governed by past and future light cones. I have at seen at least one link posted that clearly demonstrated that the presence of an event horizon, and singularity influences the shape and directionality of at least future light cones. Therefore, your assumption that the far end of the rope can be defined as being local to the experimenter remains disputed.

Here you’re essentially repeating your claim that an inertial frame cannot straddle a horizon. That’s already been refuted.

Then please, demonstrate how your experiment reproduces the force regime on the rope in Y. You can't. By the structure of your logic in the OP, it doesn't.

Here you’re essentially repeating your claim that any change to the outcome of the experiment that is due to changing the lab’s location in spacetime means that the forces changed, hence the thought experiment is invalid. And I have already noted that such logic implies that the SEP is untestable in regards to the lab’s location in spacetime, hence not falsifiable in that regard, and that is not science.

First take the post in conext. Then go back, actually read the thread you started, and find the bits where I've justified my position. No, I'm not arguing that Location in space time has no applicability. Quite the oppisite. And no, you have not adequitely refuted me.

I reviewed your posts. Nowhere have you given an example that would refute my claim that, using your logic, the SEP is untestable in regards to the lab’s location in spacetime. You are indeed arguing that “Location in space time has no applicability”. Obviously it has no applicability when, by your logic, the lab’s location in spacetime can be the same no matter where in spacetime the lab is located, relative to other objects.

Yes, it does. And once again, I have, several times. Go look for them. They're in this thread, and over in Physorg.

Nope. Maybe you’re talking about your claims regarding the other part of the SEP that I say is irrelevant to the OP? Not only have I shown that I am right that it’s irrelevant, but also if you were right then the SEP would contradict itself, as I have already mentioned.

You have changed the location of the end of the rope (relative to the singularity).
The Inverse Square Law predicts that changing the location of the end of the rope will change the force acting on the rope.
Changeing the force acting on the end of the rope changes the outcome of the experiment.
The Inverse Square Law predicts a (potential) change in outcome.
The SEP predicts a (potential) change in outcome (if we assume it's applicable).
General Relativity predicts a (potential) change in outcome.

WHERE is the inconsistencey?

I already covered this above. I disagree that the SEP is untestable in regards to the lab’s location in spacetime; that’s not science. If the forces on the rope change solely by changing the lab’s location in spacetime, that shows that GR does not adhere to the SEP, rather than show a problem with the thought experiment.

I never said the Rindler Horizon proved anything, ...

What you said was “[a Rindler horizon] predicts all of the behaviour (as near as I can tell) associated with the event horizon ...” and that’s what I addressed.

You also manage to contradict yourself in your own post.

You didn’t say why, so I ignore this claim.

I've said it before, and now I'm repeating myself. An Event, by it's very definition occurs in ONE reference frame, and one reference frame only. The Event can be observed from multiple reference frames.

No matter how many times you say it, it’s still incorrect. Nothing in the relativistic definition of “event” specifies that it occurs in only one reference frame. And if you were right, other definitions would be nonsensical. For example, the definition of “proper distance” is “a distance measured between two events in a frame in which those events occur simultaneously”. That definition makes sense only when a given event can occur in multiple frames. Taylor and Wheeler give an example of an event: an exploding firecracker. A given such event can occur in multiple frames; the firecracker might be stationary in my frame and moving in yours.

Yes, you did, and no, I will not. Not when you qoute my answer in the same post as you say this.

I could not have quoted your answer, because you never answered it.

Would you please stop beating around the bush, and being coy, and by your own statement breaking the Alpha rules, and show me the courtosey I have always attempted to show you and make your point, or drop it all together.

I drop it, but you have blatantly violated the Alpha rules, by refusing to answer the question, which for the record is:

In your very specific example, it wouldn't. However, if (as previously stated) the moths are moving sufficiently quickly, or (as previously stated) they (the moths) were in a different inertial environment to the person observing the moths, then any measurements the observer might make of the moths physical parameters (life expectancy, aspect ratio of the wings, etc) needs to take into account the Lorentz transformations.

In the experiment in the international space station that I described above, how would the outcome of 19 be modified or affected by the Lorentz transformations?

Anyone can see that you did not answer the question. You say you answered it in what I quoted of yours here, but you ignore that I showed above that this answer is insufficient, by noting the moths are "in a different inertial environment to the person observing the moths" whenever they move relative to the experimenter, so by your own logic your answer must show how the measurement "needs to take into account the Lorentz transformations". You haven't done that. Then in fact you have not answered the question. Your "answer" translates to this: "In your very specific example, it wouldn't. However, it would, because if (as previously stated) the moths are ..."

Wikipedia:

After he did this, many people, including himself, tried to find any inconsistencies in the system. Many supposed inconsistencies (or paradoxes) were proposed. Einstein took the job of looking for an explanation for all of them one by one, until another scientist, named Hermann Minkowski, showed that the whole system of special relativity is self-consistent and therefore no real paradox can appear.

then we have verified that general relativity is self-consistent at this confidence level

-Black-hole spectroscopy: testing general relativity through gravitational-wave observations
Olaf Dreyer et al 2004 Class. Quantum Grav. 21 787-803 doi:10.1088/0264-9381/21/4/003

I don’t deny that SR is self-consistent; that covers the Wikipedia quote. The second reference does not show that GR is self-consistent at the level referenced in the OP (a rocket hovering about the horizon of a black hole).

This is also what I understood, that relativity is completely consistent internally. The corrollary(?) of this is that if there are inconsistencies shown within the structure of relativity (Beyond not fully understanding the consequences of the theory) that the theory itself predicts that it will be completely wrong. This is why so much effort is being spent on finding inconsistencies, and why in the early years, so much effort was spent on dreaming up 'paradoxes' until Minkowski demonstrated that there were none.

Minkowski did not demonstrate that there are no internal inconsistencies in GR. He did that only for SR.

Minor point.
I was arguing that the rocket in X was non-inertial (and Zanket has agreed to this).
The rocket may be stationary (thus have constant velocity) relative to the blackhole, but, it is under the influence of a G-field, and is, by definition of the experiment, not in free fall. The entire rocket experiences a (fictitious) force.

Yes, the rocket’s frame is noninertial, and that’s irrelevant. The SEP says “any local experiment”. That includes experiments of objects whose frame is noninertial. For example, it includes experiments of meandering moths. Only the lab’s (the experimenter’s) frame need be inertial.

If it is non-inertial how can you use the SEP????

This is has been one of my MAJOR beef's with the OP the whole time.
This is why I keep bringing up the other part of the SEP.
You can't.

EVERY time I have attempted to bring it up with Zanket, he has skirted around the issue, and obfuscated.

I have not obfuscated about that. I have clearly said that you are wrong and noted that you offer no support for your claim but your opinion. When the SEP says “any local experiment”, it is not up to me to show that some local experiments are excluded. The burden of proof is instead on you to show that.

He seems to think that because the rocket's reference frame X is contained in a larger lab S, and because he has defined the LAB as being an inertial reference frame, because the lab is free falling, that my objection is irrelevant and refuted (thus I am in violation of the alpha rules blah blah blah).

I didn’t say your objection is irrelevant. I say that you have not supported the objection; you have not supported your claim that the experiment is not covered by “any local experiment” in the SEP.

The Rocket (in x's) reference frame is non-inertial, therefore the part of the SEP that he is attempting to apply to the experiment, or the SEP as whole CAN NOT BE APPLIED to the experiment.

You’ve offered nothing but your opinion to support this claim. Your claim contradicts the dictionary definition of “any”, as in “any local experiment”.

Zanket seems to either think that SR trumps GR, or seems to mix up GR and SR (as convenient to him?)

You aren’t specific here, but I gather that you think this because you think SR does not handle acceleration like the rocket’s. Even if you were right about that, it wouldn’t matter, because the experiment would still be in the domain of “any local experiment” to which the SEP refers. But I suggested above that you see for yourself that you’re wrong, by googling for “relativistic rocket”. You found that comment “insulting”, and continued to express your unsupported opinion that contradicts relativity. I can’t force you to google for text like “A noninertial frame can be described in special relativity using the proper mathematical forms for relativistic acceleration”, or “It is a common misconception that Special Relativity cannot handle accelerating objects or accelerating reference frames”.

This made me giggle, even Wikipedia contradicts him here:
...
Here's a special one. Implicit in the statement is Zanket's agreement that the rocket is non-inertial:
...
This next one is one of my favourites:
...
Here's another gem:
...
I thought this was special:

You have again blatantly violated the Alpha rules here. This is all “attacking people”; you suggest that my points are laughable without refuting them scientifically. You also repeat claims which I refuted, while ignoring my refutations (for example, about ANDed statements, and about SR’s ability to handle accelerating objects). You also ignore my repeated questions. I specified in the OP that posters in this thread must adhere to the Alpha rules, and you have repeatedly and blatantly violated those rules. Thus my obligation to respond to your posts ends.

 

[Trippy]

CANGAS and Pete, if you're still watching.
Ben, even though he's not inmpartial.

Would you agree that the bolded part in the following quote:

In your very specific example, it wouldn't. However, if (as previously stated) the moths are moving sufficiently quickly, or (as previously stated) they (the moths) were in a different inertial environment to the person observing the moths, then any measurements the observer might make of the moths physical parameters (life expectancy, aspect ratio of the wings, etc) needs to take into account the Lorentz transformations.

Specifically the italiscized part, adequitely answers the question?

If the experiment in X and Y involved monitoring the behavior of meandering moths, do you think the moths’ noninertial frames (whenever they change direction) would necessarily be relevant to the outcome of the experiment?

Why must that be done? If the experiment in the lab instead measured how many meandering moths find their way through a hole in a wall, do you still think the measurement made by the experimenter “must be Lorentz transformed to comply with” the moths’ frames? How does not doing that lead to an invalid outcome? Let 19 moths find their way through a hole in the wall. How is that measurement invalid when the experimenter does not Lorentz transform the number 19 to comply with the moths’ frames?

Then you think that experiments done in the international space station orbiting Earth must consider the frames of meandering moths, bees, and other test subjects. How would the experimenter do that? Let the experiment in the international space station measure how many moths find their way through a hole in their cage, and let that number be 19. How would the outcome of 19 be modified or affected by the moths’ frames? Describe to me how the experimenter should consider those frames.

Same question. Same answer.

Yes, this is true, with one exception: an object undergoing Born acceleration; that’s the only type of accelerating object that can avoid being continuously physically stretched. It doesn’t matter that one end of the rope (in X or Y) is free; the rope will still physically stretch because it is not undergoing Born acceleration. Bell’s spaceship paradox shows that the rope physically stretches: if a rocket pushing the “trailing” end of the rope is not enough to keep it from physically stretching, then it will certainly physically stretch when that end is not pushed. Texts on Born acceleration confirm that, by showing that the trailing end of an object must accelerate at a higher rate than the leading end, as measured by onboard accelerometers, or else the object will physically stretch.

No, you're wrong, that's not what Bells spaceship paradox deals with.

Two identical spaceships are floating in flat space at relative rest, the one directly in front of the other, and with a cord tied between them, attached at identical points. At the same moment, both ships gradually fire up their identical engines to an identical steady thrust, doing so identically according to identical clocks located at identical places in the ships. They run their engines for long enough to reach half light speed relative to the original rest frame. What happens to the cord? Does it break or does it not?

The consensus is that the cord will snap. Why? Not because any part of the cord is accelerating faster then any other part of the cord. In fact, this consideration can be overcome be replacing the cord with a pole that meets Born's definition for rigidity, and the problem will remain the same.

The cord will snap because the length contraction of the cord tries to pull the two spaceships together, and yet the acceleration profiles are identical, therefore by definition, the distance between any two identical parts of the rocket remains constant, and it is that as measure by a co-moving observer, or the original distance when sationary.

Therefore the distance remains the same, but the rope contracts due to length contraction. The length contraction stretches the rope because the two ends of the rope are being held the same distance apart by the two rockets. This is the source of the force, and happens to be the complete opposite of what you're claiming.

Incidentaly? I covered Bells Spaceship Paradox in my First year of physics at University.

In the situation you are describing, this effect is completely irrelevant.
Assume Y accelerates at a constant rate.
The acceleration initially sets up a series of elastic waves, these elastic waves disperse. Once this happens, the rope can be considered, in some respects, to be a rigid body.
Inertial mass causes the rope to stretch.
Stretching the rope sets up an elastic restoring force.
The forces reach equilibirum.
As long as the acceleration remains constant, the forces acting on it will remain constant (ignoring mass inflation). I'm not sure on the relevance of mass inflation, sure, it applies from the point of view of a stationary observer.

Your line of logic violates GR and the SEP, because it introduces a local experiment an observer can carry out to distinguish between a G-field and an accelerating frame. Hang a rope from the ceiling, if the rope breaks (which by your logic it must) then the frame is accelerating, if not, it's stationary and in a G-field.

You have again blatantly violated the Alpha rules here. This is all “attacking people”; you suggest that my points are laughable without refuting them scientifically. You also repeat claims which I refuted, while ignoring my refutations (for example, about ANDed statements, and about SR’s ability to handle accelerating objects). You also ignore my repeated questions. I specified in the OP that posters in this thread must adhere to the Alpha rules, and you have repeatedly and blatantly violated those rules. Thus my obligation to respond to your posts ends.

I'm sorry if you felt I was attacking you personally. I was not, I was commenting on what I perceived to be the scientific content of the posts. I have given my reasons for regarding the comments as such elsewhere. All were relevant to the topic of discussion. Yes. I have also dropped many lines of logic, however, I have not dropped them because I consider them refuted, I have dropped them because I have come to the logical conclusion that continuing to try to argue them is an act of futility, because you have demonstrated an (apparent) inability to accept that a point might be refuted, and an (apparent) inability to be able to cite sources, as has been requested multiple times.

Physics. in relativity, an occurrence that is sharply localized at a single point in space and instant of time.

4. Physics A phenomenon or occurrence located at a single point in space-time, regarded as the fundamental observational entity in relativity theory

physics single point in space-time: an occurrence defined in the theory of relativity as a single point in space-time

the fundamental entity of observed physical reality represented by a point designated by three coordinates of place and one of time in the space-time continuum postulated by the theory of relativity

So here, I have cited four independent sources ALL of which agree with the definition of an event that I have been using to refute your arguments.

An inertial reference frame is defined as being a region of points in space that meet certain criteria. Well, technically it'd be space and time because it exists in a region of space for a period of time.

You have agreed that the rockets behaviour is non-inertial.
All of the points in space that make up the rocket, are part of a non inertial framework, that of the physicality of the rocket itself. This non inertial framework exists within the inertial framework of the lab.
The rope snapping is an event.
The event occurs, as per the definitions above at a single point in space-time.
The event occurs, as per your explicit agreement, shown in my last post, in a non-inertial frame (the point in space time that the event occurs at is part of a subset of non-inertial points in space time, which is part of a larger set of inertial points in space-time)
THEREFORE the SEP can not be applied to the event in question.
Therefore technically you're arguing (another) logical fallacy.

This is your logic:

1) A applies if B is true.
2) If A applies, A predicts that C=D.
3) C occurs in E
4) In E. B is false.
5) E is a subset of F.
6) Elsewhere in F, B is true.
7) G predicts that in E C<>D
8) Therefore because A predicts that in F A=B, but G predicts that in E A<>B then G contradicts A, therefore G is wrong.

This is a logical fallacy because E is a subset of F, not the other way around.

I don't know how to exaplin it any clearer.

Now, I would appreciate it if you would start abiding by the rules that you have invoked and quoted, and do two things.

1. Demonstrate the relevancy of the moths, and stop being coy about them, and beating around the bushes. (i'm calling you out on them, by the rules you have invoked abnd quoted you MUST respond, or be in violation of them).

2. Cite a reference other then Taylor, Thorne, and Wheeler, that we both agree explicitly states that an inertial frame can include an event horizon.