Sorry to be tardy. It's been a hasslesome weekend.
1911: “If we call the velocity of light at the origin of coordinates c₀, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = c₀(1 + Φ/c²)”.
1912: “On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential”.
1913: “I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis”.
1915: “the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned”.
1916: “In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position”.
The hard scientific evidence is for the speed of light varying with position, like Einstein said.This is silly. You've never sent a clock to or through a black hole event horizon and even if you could you probably couldn't get it back. Nobody has direct evidence about what happens to clocks near or at black hole event horizons. This entire discussion is purely theoretical. General relativity was defined in mathematical detail nearly a century ago, and we are discussing how to understand one of its predictions.
All points noted. But let me reiterate my point: physicists who have been taught relativity don't understand it, and they don't understand gravity or black holes.przyk said:Your assessment of everyone's reaction to you isn't plausible, particularly the reactions of physicists who have responded here and elsewhere:
- A physicist who learned general relativity will be expected to understand the theory, and how to derive predictions and consequences from it, in far more detail than you do. University-level exams will specifically test for this.
- Physics, for better or worse, has a reputation as a hard subject with reasonable (but not fantastic) job and career prospects. It's not the sort of thing you go to study in university if you just want to put a degree on your CV.
- If you think physics is full of book-memorisers, the job market disagrees with you. Physics graduates routinely end up in programming/software architecture, engineering, and finance/banking/insurance jobs for their general technical and model-building abilities. Book-memorising is not a useful skill in these professions.
- The Galileos and Newtons and Einsteins, who completely revolutionised what they worked on, are cultural heroes in physics. That's the lesson everyone interested in physics learns very early: if you can revolutionise the mainstream understanding of physics, you'll be famous for it. Everyone wants to be the next Einstein.
- Many internet forum users are about my age or younger (late teens to mid or late twenties). This isn't a demographic exactly known for being old and set in its ways.
My logical explanations are based on the hard scientific evidence and what Einstein said. They aren't handwavey, and you can't fault them.przyk said:Your "logical" explanations are not based on the mathematical definition of general relativity. You never argue by GR's own inner logic, You instead post handwavy arguments and stories about light clocks and such, and just assume it's the same thing as GR.
Remember the Einstein quote and think about it some more: The measured speed of light isn't the speed of light. The coordinate speed of light is the speed of light.przyk said:That makes no sense whatsoever.
The issue is that general relativity as it is now taught does not agree with Einstein.przyk said:Well you don't agree with general relativity then. It is specifically formulated in such a way as to not depend on the choice of coordinates. This is how Einstein did it pretty much right from the start.
Because they aren't successful. Remember the Einstein quote? "This means the clock kept at this place would go at the rate zero. Further it is easy to show that both light rays and material particles take an infinitely long time (as measured in 'coordinate time') to reach the point r = u /2 ..." If the clock rate is zero it doesn't tick. If it takes an infinite time to get there you never get there. You can't change this by transforming coordinates. It's cloud-cuckoo physics.przyk said:I'd counter that your understanding of my understanding is wrong. Nobody is just putting a "stopped clock in front of a stopped observer". The Kruskal and many other coordinate systems successfully remove the coordinate singularity in the Schwarzschild metric at the event horizon. Why can you never criticise them for what they actually do?
Przyk, go and look up the postulates of SR. Stop kidding yourself in some desperate attempt to claim I'm wrong. I'm not wrong. Nor was Einstein. Now read what he said, and pay attention instead of believing hook line and sinker in some fairy-tale you've been taught:przyk said:You're still not getting this. You quote Einstein saying that the invariance of c postulate has to be abandoned. Fine. But you also admit that the coordinate speed of light is already not an invariant in special relativity. So you tell me: how can Einstein abandon something that was never a postulate in relativity? Do you really not see the contradiction here?
1911: “If we call the velocity of light at the origin of coordinates c₀, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation c = c₀(1 + Φ/c²)”.
1912: “On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential”.
1913: “I arrived at the result that the velocity of light is not to be regarded as independent of the gravitational potential. Thus the principle of the constancy of the velocity of light is incompatible with the equivalence hypothesis”.
1915: “the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned”.
1916: “In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position”.