(Alpha) General relativity dissatisfies the equivalence principle

[Trippy]

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

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?"

Ben: I have tried to make the same argument, but to no avail. Zanket's rebuttal was something to the effect of "The experimenter could be observing the spaceship and blackhole through a microscope in a freely falling lab."

Zanket seems to be under the delusion that the concept of locality in relativity has something to do with Proximity.

 

[Trippy]

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

No. Too much work. Besides, quoting you never does any good anyway, you just ignore it.

The Rope in Y, believe it or not, is actually capable of reaching an equilibrium and accelerating as if it were a rigid object. I've tried ad-nauseum to point this out to you as part of the reason why Bell's spaceship paradox is COMPLETELY IRRELEVANT to the OP, however, you have demonstrated a lack of understanding of Bells Spaceship Paradox, and your translation of it makes all sorts of dire predictions for civilization as we know it.

The answer to this 'Paradox' of yours is simple:

"The rope in both experiments must always break. For any spaceship to hover a fixed distance 'above' the event horizon in X will require a fixed acceleration. When this acceleration is applied in Y, then the ships Rindler horizon will be the same distance 'behind' the ship as the event horizon was 'below' the ship, therefore the rope must cross the Rindler Horizon, therefore the rope MUST snap."

For the record. I made absolutely NO claims about Rindler Horizons proving the validity of blackholes. I simply said, or tried to say, that Relativity makes the same predictions of a Rindler horizon that it does of a Schwarzschild event horizon.

Another point I wish to address to Zanket.

Someone with as much experience with relativity as you seem to claim you have would know that it is possible, and acceptable to define a location within any reference frame with respect to the 'Fixed and distant stars'.

Anyone who knows that would understand the point that I was trying to make with my posts about moving the blackhole away from the spaceship.

Let us define the spaceships location in X, and the location of the black hole in X WRT to the fixed and distant stars.
To acheive the situation in Y, you have moved the spaceship away from the blackhole.
You have agreed that an identical situation would be moving the blackhole away from the spaceship.
The spaceship retains the same position relative to the fixed and distant stars.
The (according to your argument) change in results of the experiments is exactly the same as if we had moved the spaceship to another location WRT the fixed and distant stars.

THEREFORE:
1. It is not the change in location of the spaceship that is changing the results of the experiment.

The Corrollaries of this are:
1. It is the change in distance between the spaceship and the blackhole that is affecting the outcome of the experiment. This deduction upholds the SEP perfectly.
2. Relativity makes the same predictions at different locations. This leads us to the conclusion that Relativity in fact upholds the SEP.

What you seem to have struggled with is that defining the locations WRT the fixed and distant stars makes the testing of location absolutely possible, and enables us to test Relativity, and it's adherence to the SEP absolutely.

 

[Trippy]

And if you can't accept that, then we can also perform a similar feat WRT Y at a given moment in time (say T=0) and use that to define an origin point.

The same conclusions apply.

 

[BenTheMan]

Zanket seems to be under the delusion that the concept of locality in relativity has something to do with Proximity.

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

 

[Trippy]

It also occurs to me that a remote observer can not perform a local experiment in a remote location, so in that respect your initial premise is flawed, and your experimental design is flawed.

C’mon you’re grasping at straws now. There is no remote observer. The observer is the experimenter in the lab, conducting a local experiment. The rocket + rope could even be microscopic and viewed in a microscope in the lab.

I goofed that one, I can admit it. I misunderstood my own point, however:

Anothe rpoint that I was trying to work towards is that because (as I understand it) the definition of a 'local' experiment has to do with the lightcones, and because the far end of the rope has crossed a horizon, the far end of the rope can not be considered local to the experimenter, the rocket, or the rope that remains above the event horizon.

But, I decided that I wan't 100% confident in my understanding of what 'Local' means with respect to relativity, or the EP for that matter, and when I went diving through the net, I discovered two very important things

Which is the exact same point that you made (ben). The closest to a reply I ever got from him was this:

Unfortunately “local” is used in multiple ways in relativity texts. It’s used both to indicate “of a range throughout which the tidal force is negligible” and also “in close proximity”. In the SEP in the OP, it means the latter; that is inferable by the fact that the “local” experiment occurs in an inertial frame (throughout which the tidal force is already negligible by definition of an inertial frame).

 

[BenTheMan]

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

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

 

[zanket]

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.

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

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

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

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

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?"

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

 

[zanket]

Zanket seems to be under the delusion that the concept of locality in relativity has something to do with Proximity.

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

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

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

Unfortunately “local” is used in multiple ways in relativity texts. It’s used both to indicate “of a range throughout which the tidal force is negligible” and also “in close proximity”. In the SEP in the OP, it means the latter; that is inferable by the fact that the “local” experiment occurs in an inertial frame (throughout which the tidal force is already negligible by definition of an inertial frame).

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

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

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

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

 

[Trippy]

Zanket.

Your assumption is in error.

You have implicitly agreed that the SEP applies in an inertial frame, so asking us to cite references to that effect counts as obfuscation and misdirection.
You have explicitly agreed that the Rockets behaviour is non-inertial, and anybody in the Rockets frame of reference, and any events occuring in the rocket are in a non inertial frame of reference.
Logically then, the SEP can not be applied to the Rocket in X, and any observations made of teh rocket and rope in X must take into account the existence of an Outside force.

My next point was raised in post #162 of this thread.
You have skipped it, and not addressed it. Are we to therefore assume that the points raised in that post refute your argument?

 

[zanket]

You have implicitly agreed that the SEP applies in an inertial frame, so asking us to cite references to that effect counts as obfuscation and misdirection.

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

You have explicitly agreed that the Rockets behaviour is non-inertial, and anybody in the Rockets frame of reference, and any events occuring in the rocket are in a non inertial frame of reference.
Logically then, the SEP can not be applied to the Rocket in X, and any observations made of teh rocket and rope in X must take into account the existence of an Outside force.

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

My next point was raised in post #162 of this thread.
You have skipped it, and not addressed it. Are we to therefore assume that the points raised in that post refute your argument?

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

 

[Trippy]

Zanket.

I think I've pointed this out before, but you do realize of course that by your logic EVERY theory of gravity must, and will, violate the SEP?

Surely this alone must suggest something to you about your interpretation of the SEP.

By your logic, even the Inverse Square law violates the SEP.

 

[zanket]

I think I've pointed this out before, but you do realize of course that by your logic EVERY theory of gravity must, and will, violate the SEP?

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

By your logic, even the Inverse Square law violates the SEP.

How so?

 

[Physics Monkey]

Physics Monkey: Thankyou for clarifying that. I don't suppose you could post some links to some info? Or send me a PM with some Info in it.

Zanket: I have apologized for any offense caused. I have even gone as far as voluntarily removing the contended post. How about showing a little good faith and addressing the points I raised in my last post? I will attempt to only address one point at a time.

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

 

[temur]

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

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

 

[zanket]

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