(Alpha) General relativity dissatisfies the equivalence principle

[Trippy]

Physics Monkey:

For the sake of transperancey. I graduated from Otago University with a BSc, I have studied some physics up to second year (in a three year course). This included a paper on Quanta and Uncertainty, that dealt with a large chunk of Relativity. I was going to do a paper on Cosmology (something which I have recently found myself reconsidering) that was third year level, however, I decided that I needed to focus on my Chem.

That to one side.

I understand that for a sufficiently large object, even under Newtonian Mechanics, tidal forces can be negligible, because for a sufficiently large mass, the change in radius represented by any 'suitably' sized object produces a negligible change in force.

Somewhere, I've seen the math, using the Schwarzchild Metric, that predicts the tidal force at any radius.

I also understand that for a sufficiently large blackhole, that an object need not experience any tidal disruption, and that for a free falling rope attached to a freefalling rocket there need be no sizeable forces attached when comparing one part of the rocket to another - IE that although the forces pulling the rocket as a whole towards the singularity, are very large, the difference between the ends of the rocket are negligible.

Third, a rocket ship coasting across the event horizon does NOT constitute a ship "dangling a rope across the horizon," which is a fallacious situation. I explained why in my previous post. I'll repeat it here for clarity: if a rocket ship hovering outside the horizon tried to drop a rope into the horizon, the rope WOULD break BEFORE it reached the horizon. This is because the force needed to remain stationary diverges as an object approaches the horizon.

I get that as well, and I think i've made a very similar argument - the other place i've debated this with Zanket is the physorg forums. I personally believe that Zanket is wrong in multiple ways, leading to a wrong conclusion.

However, I suspect that Zanket's response to that point will be that "by design of the original post, I have defined that the rope has sufficient tensile strength to cross the absolute horizon.

One of the things that has always given me trouble was this idea of switching co-ordinate systems. One thing that I've always been unclear on was what precisely that means. It always seemed a little... Hinky to me, Are we talking something roughly analgous to switching from polar to cartesian? Or something more exotic involving more then 4 variables? This is something I'm willing to take into PM's, as long as it's not too math heavy.

But, all of this aside, even using alternative co-ordinate sets to be rid of the co-ordinate set, does the event horizon not still, at the mathmatical level represent a point of inflection? Or is that something that's largely irrelevant?

 

[Farsight]

...I understand that for a sufficiently large object, even under Newtonian Mechanics, tidal forces can be negligible, because for a sufficiently large mass, the change in radius represented by any 'suitably' sized object produces a negligible change in force...

Somewhere, I've seen the math, using the Schwarzchild Metric, that predicts the tidal force at any radius.

Sorry to butt in, but do make a note of the above Trippy. It's at the heart of the matter.

 

[Trippy]

Sorry to butt in, but do make a note of the above Trippy. It's at the heart of the matter.

Huh? I'm not sure what you're point is here.

 

[Farsight]

Sorry if my note wasn't relevant. But I guess I'd better explain myself:

Consider a very small object travelling in space past the earth, such as a dust mote. The gravity that causes it to fall to earth isn't some magical mysterious action-at-a-distance force pulling at the entire object. It's a local gradient in c that steers it from within, akin to light being refracted. (The lower value of c is why clocks run slower in a "gravitational field"). When people talk about neglible tidal forces they're throwing the whole gravity baby out with their mathematical-approximation bathwater. You interpret the gradient as a tidal force, and it must always be there because it's what the gravity is. The tidal disruption occurs when the gradient across the object is so severe it separates into multiple objects as per the Shoemaker-Levy comet.

Note that time dilation goes to infinity at an event horizon. This means that no collapsing star has finished collapsing yet, and never will. This in turn means there are no singularities. Whilst you can talk about the singularities in the reference frame of the object falling into the black hole, you're really talking about something that is "beyond the end of time".

 

[Trippy]

The gravity that causes it to fall to earth isn't some magical mysterious action-at-a-distance force pulling at the entire object. It's a local gradient in c that steers it from within, akin to light being refracted. (The lower value of c is why clocks run slower in a "gravitational field"). When people talk about neglible tidal forces they're throwing the whole gravity baby out with their mathematical-approximation bathwater. You interpret the gradient as a tidal force, and it must always be there because it's what the gravity is.

Never quite thought of it that way. To used to thinking of the whole thing in terms of Geodisics and isostatic lines (IE a freefalling objects trajectory can be approximated by taking the tangent to... Ugh, I think they get called equipotential lines in physics).

The tidal disruption occurs when the gradient across the object is so severe it separates into multiple objects as per the Shoemaker-Levy comet.

Roche limit, etcetera etcetera.

Note that time dilation goes to infinity at an event horizon. This means that no collapsing star has finished collapsing yet, and never will. This in turn means there are no singularities. Whilst you can talk about the singularities in the reference frame of the object falling into the black hole, you're really talking about something that is "beyond the end of time".

I have my own issues with some of the assumptions that Schwarzschild made to compute his solution, however, I'm willing to admit that they could be founded in a lack of understanding, but they're not for discussion here as that could be construed as hijacking the thread.

Basically what you're saying is that you don't think it's valid to assume a strong G-field with negligible tidal forces even though it's possible to define a situation where $$ \frac{dg}{dr} $$ is approximately zero by considering a suitably large mass or a suitably small object?

 

[Trippy]

Ben:

Something occurs to me. You mentioned:
$$ds^2 = \frac{32 G^3M^3}{r} e^{\frac{-r}{2GM}} (-dT^2+dR^2) + r^2 d\Omega$$

Would this be correctly represented as:

$$\frac{ds^2}{d^2r} = \frac{32 G^3M^3}{r} e^{\frac{-r}{2GM}} (-dT^2+dR^2) + r^2 d\Omega$$

Either way it's (let me see if I remember this rightly) It's a second order derivative, and represents the rate of change of the slope of the original equation, or the slope of the first order derivative (no, I wouldn't care to try and calculate the integral, although, in theory I know how, but I imagine it's already been done anyway). Either way, it would tend to suggest that the first order derivative is vertical at the event horizon, which means the 'original' equation probably is as well, which would seem to violate the mathmatical definition of linearity (Which implies flatness? Or is that logic flawed).

Either way, that brings us back to one of my original objections. Is it valid to include a point of inflection in something that is supposed to be flat? Adn brings up the point: Is it valid to include something that appears to be 'vertical' in something that is supposed to be flat?

Admittedly, if we rotate our co-ordinate system by 90 degrees, or look at it from the z dimension y=1 then (can) become horizontal, and thus becomes defined again.

 

[zanket]

I have stated repeatedly elsewhere, and I think I mentioned here, that I believe you are tying to apply part of the SEP in a situation where it can not be applied.

You said:

I have also pointed at that while the experiment might, at first glance seem to violate part the SEP (As defined in Wikipedia) it also adheres to part of the SEP (As defined in Wikipedia) namely that:

"The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution."

I believe the part of the SEP used in the OP is clearly stated and properly used there. Please clarify how you think I am misapplying it. (It is insufficient to allude to a problem without being specific.)

No. You're ignoring my first post on this thread, in which I suggested an alternative wording, and alternative question that I considered would be a fair test of GR and the SEP.

What you replied to here was in response to your suggestion in that post; I didn’t ignore it. You need to establish that the part of the SEP used in the OP is used incorrectly there. As it stands, it is clear that you think the SEP is untestable in regards to what it postulates about the lab’s location in spacetime. You dispute that with “No”, but your explanation leaves no possibility for GR to violate the SEP in that regard. According to your logic, GR could predict anything it wants (e.g. a monster eats anything that crosses a horizon) yet could not violate the SEP in that regard. Do you disagree?

Also, taking 5 minutes out and doing a google search will reveal the current generation of tests of relativities conformation to the SEP (and the validity of the SEP).

None of those tests take place in a lab crossing a horizon. Then the situation described in the OP has not been experimentally tested.

I thought that was obvious, yes, I was referring to the rope in X. I was not necessarily referrng to a tidal force. I was referring to the force of gravity acting on the mass of the rope.

OK. That doesn’t contradict the OP, which says that the rope breaks in X.

So, as I said, while it is possible for an inertial reference frame to exist on either side of the event horizon, and while it is possible for al reference frame to pass from one side, to the other, and as previously stated be inertial on either side. I was suggesting that it is not possible for the reference frame to be considered inertial while it spatialy contains the absolute event horizon.

OK, I understand you. This clearly contradicts the quote I gave from Taylor and Wheeler, which you deny contradicting. T&W say: “... special relativity continues to describe Nature correctly for an astronaut in a local free-float [(inertial)] frame, even as she falls ... through curved spacetime, through the horizon ...” T&W disagree with you, and lots of other sources do too. To pursue your belief here, you should start a new thread, since you are contradicting generally accepted physics.

It has also been pointed out to Zanket that while the tidal forces acting on a freefalling object (the lab) the rocket is in a different reference frame to the lab, with differing forces acting on it.

This however was dismissed as obfuscation, and it was suggested that we could ignore the rockets frame of refference.

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?

 

[zanket]

The SEP also states that the "The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution."

No part of the SEP matters other than the part of the SEP to which the OP refers. You need to establish that I’m misapplying the part of the SEP to which the OP refers.

The SEP also predicts that the laws of physics are the same in any flat space.

This is the part that you are taking issue with.

Yes.

Relativity predicts that in both places, the rope will snap if sufficient force is applied to it.

Therefore Relativity in this respect upholds the SEP.

The question is whether "sufficient force is applied to it" in Y. The OP claimed that the rope in Y need not break. The OP claimed that it is not certain that "sufficient force is applied to it" in Y. On page 2 Pete pointed out that I have not shown that. He showed that rope is stretching in Y, therefore it will break eventually. That refuted the OP.

Relativity happens to predict that in certain parts of space time, that gravity will always supply sufficient force to break the rope.

There is no gravity in SR, which applies to an inertial frame. Then gravity is irrelevant to an observer whose frame is inertial, like the experimenter’s. Gravity does not explain to this observer why the rope breaks.

This does not attribute any special properties to the location of the rocket. This can be demonstrated by the fact that if you consider the rocket to be 'fixed' and 'stationary' and move the black hole away from the rocket, the exact same change in results is observed, therfore the frame of referece the rocket is in, and the location it exists at, is not preferred or special in any way. Therefore the SEP, once again is upheld.

By this logic, GR’s adherence to the part of the SEP in the OP is untestable. You deny that, but your explanation removes all possibility for such a test. If you think the SEP is untestable in that regard, you should start a new thread; it is assumed in this thread that it is testable.

 

[Trippy]

It's been a long time since I've had a discussion which has had me literally banging my head against a table. Not a personal attack, simply a statement of fact.

I believe the part of the SEP used in the OP is clearly stated and properly used there. Please clarify how you think I am misapplying it. (It is insufficient to allude to a problem without being specific.)

Two reasons. Wikipedia's definition of the SEP uses an And statement and consists of two parts. It is an And statement, but you are treating it as if it is an or statement. It is incorrect to consider one part of an and statement without considering the whole statement. You can only treat an OR statement in this way.
You then go on to argue that because the OP predicts that relativity appears to violate part of the SEP, then Relativity violates the SEP as a whole. This can ONLY be true if the SEP is stated and treated as an AND statement, but as previously stated you are treating the SEP as an OR statement.

I can show this using simple logical statements if you want.

My second point is that you are applying something that can only be explicitly applied to an inertial referrence frame to an object that is behaving in a non inertial fashion. This is, I believe a logical fallacy (which would mean that technically the OP violates the Alpha rules).

What you are saying is more or less akin to saying that: "Apples are green. This Orange is not green, therefore apples are not green."

Here's a third point. Ben and Physics Monkey were able to understand why I thought the SEP was inapplicable, this would seem to indicate that the (communication) problem lies at your end, not mine.

There is no gravity in SR, which applies to an inertial frame. Then gravity is irrelevant to an observer whose frame is inertial, like the experimenter’s. Gravity does not explain to this observer why the rope breaks.

A nitpick. In your previous post you agreed that it was the force of gravity acting on the rope that caused it to snap. Relativity predicts that the fictional force we call gravity is caused by the curvature of time space. Replace "Gravity" with "Space-time curvature". it doesn't matter, my logic still holds.

The inertial Observer sees the rope break in a non-inertial reference frame. The Observer can deduce that this is because of gravity by making observations of and around the event horizon.

OK, I understand you. This clearly contradicts the quote I gave from Taylor and Wheeler, which you deny contradicting. T&W say: “... special relativity continues to describe Nature correctly for an astronaut in a local free-float [(inertial)] frame, even as she falls ... through curved spacetime, through the horizon ...” T&W disagree with you, and lots of other sources do too. To pursue your belief here, you should start a new thread, since you are contradicting generally accepted physics.

I disagree. My statement is not contradictory to my interpretation of what taylor and wheeler have said. Further elucidation is not necessary, because it becomes an argument of semantics, which you are best taking to another thread.

What you replied to here was in response to your suggestion in that post; I didn’t ignore it. You need to establish that the part of the SEP used in the OP is used incorrectly there. As it stands, it is clear that you think the SEP is untestable in regards to what it postulates about the lab’s location in spacetime. You dispute that with “No”, but your explanation leaves no possibility for GR to violate the SEP in that regard. According to your logic, GR could predict anything it wants (e.g. a monster eats anything that crosses a horizon) yet could not violate the SEP in that regard. Do you disagree?

Yes, I disagree. If my logic leaves no room for GR to be shown to contradict the SEP with your OP, then it is not because I am saying that GR is untestable, it I because your suppositions and conclusions are wrong, and your OP fails to demonstrate that GR violates the SEP.

None of those tests take place in a lab crossing a horizon. Then the situation described in the OP has not been experimentally tested.

Prove it. What was it you said on page two? As I recall it as "And to use one of my favourite sentences, you might have crossed an event horizon while reading this..." So by your own statements and logic, some of the experiments might have been conducted near an event horizon, we just didn't notice.

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?

Obviously, yes. If the moths were moving fast enough, or if the moths were in a different reference frame to the observer.

My argument was a simple series of logical statements, made from some basic assumptions.

1. The SEP is testable.
2. I am wrong, and the SEP in it's full form is totally applicable to the experiment.
3. The OP is a valid test of whether or not GR adheres to the SEP.

Therefore under the guidelines of the rules for an Alpha thread, belongs here.

If your interpretation of my statements appears to leave no room for the testing of GR, then it is because GR upholds the SEP.

You are arguing a logical fallacy. You are arguing that a correlation is a cause. Correlation does not imply cause.

Relativity does not predict that the laws of physics changes in etheir X or Y
Relativity does not predict that the refference frame of X is preferred over Y
Relativity does not predict that the behaviour of the rope is dependent on anything other then it's starting radius (from the singularity) and it's starting velocity.

Incidentaly? Pet emay be wrong.
The rope will only break if the acceleration of the rocket is sufficient compared to the mass.

The rope has mass. This mass gives the rope inertia.

The rope under any acceleration will stretch because of the inertia. The force exerted on the rope by it's own inertia exceeds the tensile strength of the rope, the rope breaks. In other words, the rope will stretch until the elastic forces exactly balance the inertia of the rope, and the rope reaches equilibrium. The rope will stretch, but it will only stretch by a finite amount.

I apologize if my logic was too difficult for you to follow, I'll try and simplify it in the future.

 

[zanket]

Regardless, the curvature is perfectly regular at the horizon, and need not even be large for big enough black holes. The equivalence principle is not violated because spacetime is still locally Minkowski.

GR postulates that “spacetime is still locally Minkowski” at a horizon. But GR can contradict itself about that, and the original post (OP) implicitly claims that it does. However, the OP was refuted on page 2 of this thread by Pete (he showed that the rope in Y must break eventually).

 

[Physics Monkey]

GR postulates that “spacetime is still locally Minkowski” at a horizon. But GR can contradict itself, and the original post (OP) implicitly claims that. However, the OP was refuted on page 2 of this thread by Pete.

Hi zanket,

You are incorrect, GR cannot contradict itself. As a particular version of pseudo-Riemannian geometry, GR is a mathematically consistent theory. Nothing anyone can say will change that. Again I emphasize that mathematicians have studied such things for many years (including horizons and black holes, mind you) and have proven them consistent. The theorems are in the text books. Furthermore, the spacetime considered here is a vacuum solution to the field equations and so is pure geometry. Thus spacetime in GR is locally flat because it has to be, it wouldn't be GR if it wasn't. Now maybe GR doesn't describe the world very well, but GR itself is a consistent theory.

 

[zanket]

Within your frame which is crossing the horizon is a stationary observer, and an observer in the rocket. The rocket is moving with respect to a stationary observer. The measurements made by the stationary observer of the rope must be Lorentz transformed to comply with rocket's frame.

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?

I repeat the following questions that you didn’t answer:

If I am moving with respect to the cesium atom (or it is moving with respect to me), I will measure a different value for the experiment, in my frame. In order to make my results consistent with the cesium atom's, I would have to Lorentz transform my observations with a relativistic time dialation.

You agree that this is true whether or not r_1 = r_2, right? So whether or not a Lorentz transform needs to be done is independent of the lab’s r-coordinate, right?

Time dialation.
...
Pion decay, or the example you listed above. I have been quite careful in the past to describe the pion decay experiment and how the Lorentz transformations were to be used.

How would you apply the time dilation formula to make those frames (muon’s and Earth observer’s) comparable so you can compare the outcomes of the cesium-133 experiments? I looked at all your posts and don’t see it. If I apply the time dilation formula to the value of one second that either measures, I just get another value that is the same for either frame. How does that indicate comparability?

By your logic, in the muon experiment the Earth observer’s measurement of the number of muons that reach the ground must be “Lorentz transformed to comply with” the muon’s frame. Let the number of muons that reached the ground be 74. How would you Lorentz transform that number?

There is no sensible answer to those questions. You’re alluding to a problem and avoiding specifics, including direct questions. That is against the Alpha rules.

Either the tidal forces are negligible or they aren't. Negligible means they effect the outcome of experiments. If they effect the physics then they are not negligible.

That boils down to “Negligible means they affect the physics (affect the outcome of experiments), in which case they are not negligible”. That’s a = b <> a, which is illogical.

The tidal force throughout X and Y is negligible. Negligible means they negligibly affect the outcomes of the experiments. Then they do affect the physics (the behavior of the system being observed), but only negligibly.

Using your definition of reference frame, ...

Which, to be clear, agrees with Taylor, Thorne, and Wheeler’s definition.

... I showed that both X and Y can be contained in S. My point was that given this definition of "inertial reference frame", and given the physics in the same frame is the same, then the results of experiments at X and Y are trivially the same. Where have I invoked anything but your definitions?

There is no problem with this analysis. You invoked only my definitions. I agreed to this analysis. What I disagreed with is your “clear conclusion” from the analysis that “the rope doesn't break in either case (or it breaks in both cases)”. That’s a non sequitur, a conclusion that doesn’t follow from its premise, because nothing in your analysis shows that GR does not violate the conclusion within your analysis, namely that “the results of experiments at X and Y are trivially the same”. GR must predict that, in order to adhere to the SEP. The OP claims that it predicts otherwise.

Your analysis is valid without GR; one need not know about GR to agree with your analysis. But then you use the analysis, and only that, to claim that GR adheres to the conclusion within the analysis. That’s a leap of logic.

Here’s a rough analogy:

Let a “Bird Equivalence Principle” (BEP) state that:

A bird can be of any color, and a bird’s color is independent of its location.

Let a theory predict that:

Any bird on the ground is yellow.

The theory’s prediction can be used to show that the theory does not adhere to the BEP. But by your logic, the BEP shows that a bird’s color is independent of its location, hence any claim that a theory does not adhere to the BEP is wrong. There’s a leap of logic in your logic. You’d be looking only at the BEP to invalidate a claim that a theory violates it.

If the results of an experiment are affected at all by the difference in tidal forces then there is no way that you may compare experiments preformed in the two reference frames. The word insignificant implies that the tidal forces don't affect the physics.

I repeat the following question that you didn’t answer:

Let the tidal force throughout X be negligible for the purposes of the given experiment. Let the tidal force throughout Y be weaker than the tidal force throughout X. Then you think these frames are incomparable due to their different tidal forces, right?

The word “insignificant” implies that the tidal forces don’t significantly affect the physics; e.g. not enough to break the rope. 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; e.g. not enough to break the rope in either X or Y regardless of the difference in negligible tidal forces between them.

My claim is that you have misunterstood/misused those definitions. But, to get a consesus I will pose this question to the others---it was my impression that one should define the inertial reference frames at a single point in space to ensure that there are no non-trivial curvatures...is this not the case?

You would need more than a consensus to show that I “misunterstood/misused those definitions”. You would also need to refute Taylor, Thorne, and Wheeler, who all agree with me that an inertial frame need not be a single point. “No non-trivial curvatures” is ensured by the dictionary. “No non-trivial” means trivial. Negligible means trivial. Spacetime curvature is synonymous with tidal force. Then trivial tidal forces (“No non-trivial curvatures”) are ensured by the trivial (negligible) tidal forces demanded by my definition of an inertial frame.

A little touchy, are we? Not a personal attack, just a rhetorical question.

Your rhetorical question implies that there is something amiss with those who think GR is wrong, in turn implying that the OP is wrong. That is obviously unscientific reasoning, but all too common, which explains why the Alpha rules specifically prohibit it.

And, as someone else here pointed out, every discussion about GR turns into an indictment of the theory.

The OP is clearly intended to be an indictment of the theory. This forum allows that.

 

[Trippy]

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?

The moths are irrelevant to the OP, and should (by Alpha rules) be moved to a different thread (as hijacking your own thread IS possible).
I will not answer "Why is this neccessary?" when asked in respect to the Lorentz transformations, as the rules of Alpha Threads do not require me to. This is one of the basic things that you (especially as someone claiming to be a research assistant who has worked with black holes for 'many years') can research for yourself, and should already know.

And (ironically enough) to answer your question about the moths.
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.

 

[Farsight]

Basically what you're saying is that you don't think it's valid to assume a strong G-field with negligible tidal forces even though it's possible to define a situation where $$ \frac{dg}{dr} $$ is approximately zero by considering a suitably large mass or a suitably small object?

Yes, approximately zero means you approximate the gravity away.

Thus spacetime in GR is locally flat because it has to be, it wouldn't be GR if it wasn't.

Apologies if I've misunderstood, but Einstein spent years arguing against the interpretation of gravity as spacetime curvature. Read this essay from a guy called Pete Brown then have a dig to check what he says.

http://xxx.lanl.gov/abs/physics/0204044

"There exists some confusion, as evidenced in the literature, regarding the nature of the gravitational field in Einstein's General Theory of Relativity. It is argued here the this confusion is a result of a change in interpretation of the gravitational field. Einstein identified the existence of gravity with the inertial motion of accelerating bodies (i.e. bodies in free-fall) whereas contemporary physicists identify the existence of gravity with space-time curvature (i.e. tidal forces). The interpretation of gravity as a curvature in space-time is an interpretation Einstein did not agree with...

 

[Physics Monkey]

Hi Farsight,

If Einstein had written down GR and then spent every remaining moment of his life opposing it, it would change nothing about the theory. GR would still be self consistent and it would still describe reality. What Pete Brown claims Einstein thought is doubly irrelevant. This is not a battle of personalities. My argument rests of the properties of GR, and it is a logical fallacy to suggest that GR depends for its validity on the opinions of certain "luminaries."

As an aside, after reading some of the article I can tell you that Pete Brown has very little idea what he's talking about, but that is a topic for another time in accord with the alpha rules.

 

[Farsight]

Physics Monkey: Einstein didn't oppose GR, just an interpretation that was drifting away from what he originally said. If you can point out where Pete Brown's essay is factually/historically wrong I'd be grateful.

 

[Trippy]

I just realized, I screwed up.

I should have said $$\frac{dg^2}{d^2r}$$
I think.
My logic being this:
The (instantaneous) slope of space time is proportional to the strength of the gravitational field - I believe this is consistent with GR and Einstein.

Tidal forces are the rate of change of that slope, or the curvature.

So it then becomes possible to define a region of time space that has a non-zero slope, with zero curvature, and the absence of a gravitational feild leads to 'horizontality', then we're comparing a flat, but not horizontal piece of space time, to a flat and horizontal piece of space time.

Note: It would seem from reading the Abstract that Pete Brown is saying the same thing: Slope governs field strength. curvature (rate of change of the slope) governs tidal forces.

 

[BenTheMan]

You agree that this is true whether or not r_1 = r_2, right? So whether or not a Lorentz transform needs to be done is independent of the lab’s r-coordinate, right?

It seems that the answer wasn't as aparent as I thought it should be. If r_1 watches what is happening at r_2, and then calls him on the phone and reports what he found, r_2 will probably disagree. Then r_1 remembers that he was moiving in relation to r_2, and must Lorentz transform his data to fit r_2's, so that r_1's data is now in the same frame as r_2.

By your logic, in the muon experiment the Earth observer’s measurement of the number of muons that reach the ground must be “Lorentz transformed to comply with” the muon’s frame. Let the number of muons that reached the ground be 74. How would you Lorentz transform that number?

Well, "number" is a dimensionless quantity, so "number" is a Lorentz invariant. Perhaps you should pick another example. And when I said "should be Lorentz transformed to comply with", I was misunderstood---a point which you won't let me acknowledge... I was unclear when I first advanced the Lorentz transformation arguments.

Let's start again.

Explain to me everything you know about Lorentz Transformations. Aparently I am assuming that you know something of them when it is aparent that you don't. If we are just misunderstanding ourselves, then apologies all around.

Then you think these frames are incomparable due to their different tidal forces, right?

Zanket we are arguing on different levels. "Insignificant", as per the definition provided in your initial post, means that it has no bearing on the outcome of the experiment. So, in this sense, insignificant and nonexistant are the same. If the tidal forces affect measurements in any way, then they are not "insignificant".

Forgive me if I am getting tired of arguing about semantics, it is the physics that is actually important.

Another thing:

That boils down to “Negligible means they affect the physics (affect the outcome of experiments), in which case they are not negligible”. That’s a = b <> a, which is illogical.

Quite inconvenient---there was a typo. The quoted section should read (emphasis added):

"Either the tidal forces are negligible or they aren't. Negligible means they don't effect the outcome of experiments. If they effect the physics then they are not negligible."

Which, to be clear, agrees with Taylor, Thorne, and Wheeler’s definition.

Which, to be clear, relies on your interpretaion of this definition.

There is no problem with this analysis. You invoked only my definitions. I agreed to this analysis. What I disagreed with is your “clear conclusion” from the analysis that “the rope doesn't break in either case (or it breaks in both cases)”. That’s a non sequitur, a conclusion that doesn’t follow from its premise, because nothing in your analysis shows that GR does not violate the conclusion within your analysis, namely that “the results of experiments at X and Y are trivially the same”. GR must predict that, in order to adhere to the SEP. The OP claims that it predicts otherwise.

I disagree---if we agree that physics in the same frame is the same, and I can define the frame S, then the physics at every point in S should be the same (i.e. the outcomes of experiements preformed at every point in S).

Ill repeat the argument, and you show which step doesn't follow:

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.

Please show which line doesn't follow from the previous line.

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;

My office mate and I had quite a laugh at this. Look---either the tidal forces matter or they don't. I am almost 100% sure that Taylor and Wheeler and anyone who has done any calculation "to first order" would agree with me. If the tidal forces aren't enough to break the rope, then you can completely disregard them.

Your rhetorical question implies that there is something amiss with those who think GR is wrong,

Yes, just like those who want intelligent design taught in schools.

in turn implying that the OP is wrong.

I have been implying that your original post is wrong for three weeks.

 

[Trippy]

Zanket:

Here's something for you to consider:
gregegan.customer.netspace.net.au/SCIENCE/Rindler/RindlerHorizon.html

You'll have to C&P it and slip an http in front of it.

Basicaly, it boils down to this.

An accelerating spaceship (In this case Y) has an event horizon - a straight, linear worldline that the world line of the spaceship can approach asymptoticaly, but never reach or cross.

It is possible for the ship to tow a rope or string that can cross it's own event horizon.

Relativity predicts that should an experimenter manage to do this, the ROPE WILL ALWAYS BREAK

Yes, that's right. If you put a big screen up so that the experimenter or the pilot of the Rocketship can not see the event horizon for the Schwarzschild Singularity, there is NO WAY that either person can tell whether the rope has crossed the event horizon for a singularity, or the ships rindler horizon

This was something that I had wondered when I was looking for information on event horizons, and came across something similar to what I have posted.

And so, once again we see that Relativity upholds the SEP as defined by Wikipedia, within the context of your original post, and beyond, because it predicts all of the behaviour (as near as I can tell) associated with the event horizon , including time dialation, red shifting, length contraction, and even an analog to Hawking Radiation (Unruh radiation).

Note: I imagine it's trivially demonstrable that a rope long enough to cross the event horizon of a Schwarzschild Black hole, will in the case of Y (by definition of the OP, having the same acceleration, and the same rope length) always be long enough to cross Y's Rindler horizon.

 

[Trippy]

Hi zanket,
We know that it must stretch and continuing stretching for as long as the rocket accelerates, just as in X. In both cases, we know that it must eventually break because no rope can stretch indefinitely (if it could, then the rope in X need not break either.)

So why must it stretch and continue stretching?
Because the rope at any given point doesn't "know" what the rocket is doing until some time later. This means that the speed of the rocket in Y is always greater than the speed of any part of the rope in Y. The speed of the rope in Y will be greatest at the rocket, and least at the other end.

In a sense Pete was right, however the rope provides an elastic restoring force, this is proportional to the amount that the rope has stretched, and goverened by Hooks Law. The rope in Y will only break if the force caused by the acceleration acting against the inertia of the rope exceeds the elastic restoring force acting on the rope.

There is, however, a Horizon present (see post 99).