Note from Pete:
I've moved a number off potentially interesting side-tracks from zanket's thread (Alpha) General relativity is self-inconsistent into this thread. The OP has been partly copied for reference.


I will prove that general relativity (GR) is self-inconsistent. First some supporting info (or skip to “Now the proof” near the end):

*snip*

Now the proof:

Let X be an inertial frame falling through the horizon of a black hole. Since the spacetime throughout an inertial frame is flat, it must be possible to set up an inertial frame Y that extends throughout X and in which a free test particle, that is above the horizon and moves away from the black hole indefinitely, stays at rest. But GR predicts that nothing may pass outward through a horizon. Then Y cannot extend below the horizon (if only because otherwise a latticework of synchronized clocks, that stays at rest with respect to Y and is spread throughout Y, would be passing outward through the horizon), and so the spacetime cannot be flat throughout X. Then X cannot be an inertial frame. That is, an inertial frame cannot fall through the horizon of a black hole. GR required this conclusion, yet the theory predicts otherwise, contradicting itself, so it is self-inconsistent.

Note that:
The definitions of flat spacetime and inertial frame in the supporting info account for the tidal force. The tidal force in X need not be nonexistent.
X can be arbitrarily small and its duration can be arbitrarily short. Then the tidal force in X can be nonexistent in the limit.

I agree with you Zanket. Any "inertial frame" that is falling gives me a problem, because without the local gradient there can be no gravity. Note that Einstein didn't agree with the idea of gravity being curved spacetime.

Any "inertial frame" that is falling gives me a problem, because without the local gradient there can be no gravity.
Well, I do think an inertial frame can fall, since that is allowed by its definition. An inertial frame is like a box snugly enclosing the International Space Station, which is in free fall (or "freely falling", to use Einstein's terminology). There is a "gradient" within the box, but it's so slight that gravity is negligible within the box. It's like how a salt flat can seem flat when it's really curved in concordance with the curvature of the Earth.

Note that Einstein didn't agree with the idea of gravity being curved spacetime.
That's interesting; I didn't know that. I'll look further into that.

The point is that it's falling because of that neglible gravity.

Re the curved spacetime, I thought this was in interesting essay by Pete Brown, aka pmb:

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

There was something else I read that said Einstein argued about this for years, but I can't find it, and am real busy at the moment. Please do post up anything relevant you come across.

I have read many posts on the subject of GR Black holes and so on. One thing that strikes me is how people quote, say, Einstein. Eventhough Eintein did not agree with the idea that gravity being curved spacetime, does not mean that Gravity is not curved spacetime. Einstein was not always right, and did not always believe in the predictions comming from his theory (an expanding universe is an example). Without being an expert on GR, as far as I understand it, curved space time is the best explanation on the nature of the force of gravity. And as far as I know, observation fits well with this model.

Without being an expert on GR, as far as I understand it, curved space time is the best explanation on the nature of the force of gravity. And as far as I know, observation fits well with this model.

At the risk of zanket running around and screaming that I'm not obeying the alpha discussion rules, you are absolutely right. The mathmaticians have taught us much since Einstein's discovery, as has the consistent confirmation of Einstein's ideas by experiment. With the precision that GR has been tested to, people who deny its validity stand on the same scientific ground as the people who claim the earth is flat or that God did it all 6000 years ago.

Please can we discuss things rationally instead of trying to discredit the opponent.

For me it's a matter of questioning the postulates and interpretation rather than denying the validity.

Eventhough Eintein did not agree with the idea that gravity being curved spacetime, does not mean that Gravity is not curved spacetime.
Nothing in the OP disagrees with this. It's a side topic.

Re the curved spacetime, I thought this was in interesting essay by Pete Brown, aka pmb:
That's a great article, thanks! To avoid the discussion being sidetracked, I'll reserve comment for a while.

With the precision that GR has been tested to, people who deny its validity stand on the same scientific ground as the people who claim the earth is flat or that God did it all 6000 years ago.
All experimental confirmation of GR is in relatively extremely weak gravity far from a theorized horizon. GR has been barely tested experimentally. And of course no amount or precision of experimental confirmation saves a self-inconsistent theory.

This is a quote by J L Synge from pmb's Einstein's Gravitational Field essay:

"The Principle of Equivalence performed the essential office of midwife at the birth of general relativity, but, as Einstein remarked, the infant would never have gone beyond its long clothes had it not been for Minkowski’s concept [of space-time geometry]. I suggest that the midwife be buried with appropriate honours and the facts of absolute space-time faced".

http://xxx.lanl.gov/ftp/physics/papers/0204/0204044.pdf

From what I've read, it seems to me that the principle that started Einstein thinking about GR doesn't actually hold, but Einstein struggled to persuade people of this. See GRAVITY EXPLAINED for my own mental model of how gravity works:

http://www.sciforums.com/showthread.php?t=63792

Making a sidetracks thread wasn't in the original Alpha rules plan, but it seems like an appropriate thing to do for this thread.
Any objections?