Is a uniform gravitational field a gravitational field?

[JesseM]

The rod I’m talking about is freely falling. By the definition of “freely falling object”, no forces except gravity are acting on the rod. Then if the rod breaks, it must be the tidal force that broke it, because the only force of gravity in GR is the tidal force.

But unless the rod is made up of noninteracting dust particles, every part of it won't really be moving in a locally inertial way (freely-falling), since different sections can push and pull on one another.

Yes, GR says that the tidal force always disappears in the limit locally, but GR also predicts that the tidal force must be what breaks the rod if it breaks, by disallowing any other possibility.

No, I think you're wrong on this. As long as the different parts of the rod interact with each other they won't all be freely-falling, so you don't have to assume it's tidal forces that break the rod. We know that in the case of a rod being dragged along by an accelerating observer, the rod also must break if it extends past the observer's Rindler horizon, and yet this is a flat spacetime situation with no tidal forces.

 

[Zanket]

But unless the rod is made up of noninteracting dust particles, every part of it won't really be moving in a locally inertial way (freely-falling), since different sections can push and pull on one another.

How is this different from saying that there’s no such thing as a freely falling object? Doesn’t this apply to even a dust particle? Even a dust particle is made up of interacting particles.

No, I think you're wrong on this. As long as the different parts of the rod interact with each other they won't all be freely-falling, so you don't have to assume it's tidal forces that break the rod.

You’re suggesting that any object floating in space rips apart due to forces other than tidal forces. (I won’t say “freely falling object” because you’re suggesting that there’s no such thing.) Unless GR predicts that the International Space Station will always break apart for the same reason, it doesn’t show the problem with my argument. For you to be right, GR would have to predict that even a hydrogen atom floating anywhere in space always breaks apart, and even its subatomic particles would have to break apart too. But GR doesn’t predict that.

 

[JesseM]

How is this different from saying that there’s no such thing as a freely falling object? Doesn’t this apply to even a dust particle? Even a dust particle is made up of interacting particles.

I'm talking about the sort of idealized "dust" used in general relativity, like the kind in this paper, not realistic physical dust.

You’re suggesting that any object floating in space rips apart due to forces other than tidal forces.

No I'm not--large objects that occupy regions where there is significant spacetime curvature can of course be ripped apart by tidal forces. My argument is specific to the case you're discussing, since there is nothing in your thought-experiment that requires the rod be particularly large, I don't see why we can't assume an arbitrarily short rod that just happens to be right at the location the event horizon forms when it does. Of course there's a complication in the sense that the event horizon of a star collapsing into a BH is actually supposed to start at the center, then grow until it reaches its final radius, but I don't see why we shouldn't assume the event horizon sweeps past the back end of the rod and then reaches its final radius right at the middle...even if the rod's size is neglible the time for the event horizon to sweep past the back end and reach the middle might not be, I'm not sure, and likewise the time for the stress to increase and the rod to break apart might not be negligible. And since tidal forces only go to zero in short intervals of time as well as small regions of space I could be wrong that the ripping apart has nothing to do with tidal forces. I don't see that we can assume the rod rips apart because of tidal forces though, not without actually doing a mathematical analysis of a specific situation as opposed to handwaving verbal arguments.

Unless GR predicts that the International Space Station will always break apart for the same reason, it doesn’t show the problem with my argument.

What "same reason" would that be? The ISS isn't on the event horizon of a black hole, and the event horizon has other properties that are likely to be relevant besides tidial forces, like the way light cones are tipped over and the fact that the horizon seems to be moving at c as measured by a free-falling observer passing through it.

 

[JesseM]

Actually, thinking about this some more the rod probably does have to break due to tidal forces, since in flat spacetime with no tidal forces it's always possible for an object to remain perfectly rigid with every single point in the object moving inertially, so I can't think of a reason why a small rod couldn't be moving like that for a brief moment if we zoom in on a small region of spacetime around the event horizon. And in this region the event horizon is moving outward at the speed of light in a locally inertial coordinate system, so no part of the rod can move from inside of the event horizon to outside it in this region--the only way any part of the rod could ever avoid being swallowed by the horizon would seem to be if we were considering a non-local region of spacetime which couldn't be treated as identical to flat spacetime with the horizon moving at c. So for the rod to break and part of it to escape the horizon, it seems like we do have to consider a rod of non-negligible length, although I still think some sort of mathematical analysis is needed to be sure.

Still, even if it is tidal forces that break the rod, I'm not convinced about your argument about the tidal forces needing to be infinite. You say that the tensile strength of a material can be infinite, but doesn't tensile strength have to do with resistense to breaking at a single point in that material when Newtonian force is applied to that point, whereas tidal "force" is not localized like Newtonian force, since it always goes to zero in a local region? Also, the page on Rindler horizons I linked to earlier mentions that there is an upper limit to the stiffness of a material in relativity imposed by the speed of light--I can't find definitions of stiffness vs. tensile strength, do you have them, and if so could you explain exactly why you think it would be impossible to break apart an object of finite stiffness with finite tidal forces if it's tensile strength were arbitrarily high?

 

[Zanket]

Actually, thinking about this some more the rod probably does have to break due to tidal forces, since in flat spacetime with no tidal forces it's always possible for an object to remain perfectly rigid with every single point in the object moving inertially, so I can't think of a reason why a small rod couldn't be moving like that for a brief moment if we zoom in on a small region of spacetime around the event horizon.

Agreed.

Still, even if it is tidal forces that break the rod, I'm not convinced about your argument about the tidal forces needing to be infinite. You say that the tensile strength of a material can be infinite, but doesn't tensile strength have to do with resistense to breaking at a single point in that material when Newtonian force is applied to that point, whereas tidal "force" is not localized like Newtonian force, since it always goes to zero in a local region?

I said the tensile strength can be arbitrarily high, not infinite. It seems like you’re suggesting that the ability of the tidal force to break an object is unaffected by its tensile strength. But everything I’ve read says the opposite.

Also, the page on Rindler horizons I linked to earlier mentions that there is an upper limit to the stiffness of a material in relativity imposed by the speed of light--I can't find definitions of stiffness vs. tensile strength, do you have them, and if so could you explain exactly why you think it would be impossible to break apart an object of finite stiffness with finite tidal forces if it's tensile strength were arbitrarily high?

I’m not sure I can prove that. But it doesn’t seem necessary to prove that. To avoid contention on the issue of an infinite tidal force I can modify the argument. The tidal force on the rod must be strong enough to break it. The rod can be arbitrarily small. Any object could substitute for the rod, so the tidal force must be strong enough to break any arbitrarily small object. GR says that SR holds locally; i.e. in an arbitrarily small region. But it cannot hold locally when any arbitrarily small object breaks due to tidal forces on it.

BTW, this isn’t a handwaving argument. Logic can show an inconsistency with a theory. Math is just one form of logic. If logic shows with certainty that GR predicts that the rod must break and also predicts that the tidal force on the rod can be too weak to break it, then GR is self-inconsistent and no math is necessary. We can depend on the math that has been done in spades to show GR’s prediction for a horizon, and we can depend on GR’s postulate that says that SR holds locally. The math would have to support the logic, or else the math that has been done in spades is wrong.

 

[JesseM]

I said the tensile strength can be arbitrarily high, not infinite. It seems like you’re suggesting that the ability of the tidal force to break an object is unaffected by its tensile strength. But everything I’ve read says the opposite.

I didn't say unaffected, because again, I don't really know the relationship between stiffness and tensile strength. But without knowing the precise definitions, it's not at all obvious that making the tensile strength arbitrarily high will always be sufficient to prevent breaking given some large but finite tidal force, given that there is an upper limit to stiffness.

I’m not sure I can prove that. But it doesn’t seem necessary to prove that. To avoid contention on the issue of an infinite tidal force I can modify the argument.

Well, forget infinite. Can you prove that for an arbitary large but finite tidal force, the rod can be prevented from breaking by making the tensile strength high enough, even though we can't make the stiffness any greater than some maximum upper limit?

The tidal force on the rod must be strong enough to break it. The rod can be arbitrarily small.

No it can't, because like I said, "tidal force" is not analogous to a Newtonian force which can be defined in an arbitrarily small region--the tidal force always goes to zero in the limit as the size of the region goes to zero (except in the case that the region contains a singularity).

BTW, this isn’t a handwaving argument. Logic can show an inconsistency with a theory.

But logic is only as good as the assumptions you make. If your assumptions are false, like the assumption that you can always prevent breaking by finite tidal forces if you make the tensile strength high enough, in spite of the upper bound to stiffness, (which is a physical statement that you can't prove by 'logic' alone), then your conclusions will be false too.

 

[pervect]

I think it's about time to lock this thread. We are not here to debate the validity of mainstream science - which is essentially what Zanket is interested in doing with his claims about "GR being inconsistent".

Zanket will have to have this sort of discussion on some other board (if he can find anyone interested in carrying it out).

I've given the thread some latitude because in his misguided attempt to find inconsistencies in GR, Zanket has asked some interesting questions. But I think the questions have basically been answered (even if Zanket isn't listening to the answers).

It's unfortunate that Zanket continues to confuse the ill-behavior of Schwarzschild coordinates at the horizon with deep problems in GR. Schwarzschild coordinates are in fact singular at the horizon - the simple solution to this issue is to use some other coordinate system.