I think you meant to prove a point regardless of the crucial issue. I've been talking about non-real solutions
And you've been failing to explain why the Kruskal metric should be dismissed as "non-real". I put both the Kruskal and Schwarzschild metrics in front of you, and you couldn't explain, starting with those actual, raw, predictions of general relativity, why one should be dismissed as "non-real" and the other accepted as "real".
and you're still not understanding that the expressions don't feature c because there's an axiomatic presumption that c=1.
No, I'm not presuming anything. The Schwarzschild metric with the (constant) factor of
c (and
G) left in is
$$
\mathrm{d}s^{2} \,=\, -\, \bigl( 1 - \frac{2Gm}{rc^{2}} \bigr) c^{2} \mathrm{d}t^{2} \,+\, \bigl( 1 - \frac{2Gm}{rc^{2}} \bigr)^{-1} \,+\, r^{2} \mathrm{d} \Omega^{2} \,.
$$
Everything I've been saying to you is an attempt to get you to appreciate that c=1 only because we are "made of light" and thus measure the local speed of light to be the same when it isn't
No, that isn't what either SR or GR is about. I've already corrected you on this several times now. Robert Close, the guy you keep quoting, is basically a century behind the times when it comes to his understanding of relativity. He's trying to solve a problem he doesn't seem to understand Einstein already solved in 1905. So he's trying to reinvent the wheel and doing it poorly at that. Once again: we will always measure an invariant
c as long as we measure the speed of light using
any instruments whose structure is governed by Lorentz-invariant physical laws. This does
not require everything to be "made of light" or even to obey the relativistic wave equation.
Because the reality underlying gravitational time dilation is a reduced speed of light, only "we are made of light" and so can't measure this reduction locally.
If nobody will ever be able to measure it then what merit is there to saying the speed of light reduces at all?
then uses them to measure the speed of light.
No it doesn't. By that point the speed of light is already defined. Since it would be silly to try to measure a quantity with a defined value, using the units in which it has that defined value,
nobody does it. People
did however do experiments and measured an invariant speed of light
before it was made invariant by definition. You seem to keep forgetting that.
No, but we have good evidence from optical clocks etc, and can extrapolate.
Extrapolate how? Observational evidence
alone only suggests that clocks at ever lower gravitational potentials will continue to slow down, but not that they'll ever
stop. Observations of clocks at different altitudes doesn't necessarily imply there even is such a thing as a black hole.
So it's only meaningful to extrapolate on the basis of what general relativity predicts about clocks near black holes. But even there you've got nothing to support your case. For a clock at
constant Schwarzschild radius from the black hole,
both the Schwarzschild and the Kruskal metrics make
identical predictions and both say that a clock sitting on the event horizon is frozen. For the Schwarzschild solution you have to take the limit $$r \rightarrow 2M$$ to work this out. In the Kruskal chart you can work this out
directly: you get the same result as with Schwarzschild without even needing to take a limit.
But for a clock falling
into the black hole the story is completely different: the Kruskal metric predicts that the clock
won't stop, while the Schwarzschild metric blows up on the event horizon and can't be considered to predict
anything. So the only extrapolation you can make, based on GR, about a clock falling
past the event horizon is that it
won't stop.
Come on przyk, remember that pair production. Make it a light clock, so light has frozen, and all electromagnetic phenomena has frozen, including the electrons etc from which the clock is made. They're frozen not just in terms of spin, but also in terms of linear motion. So that clock isn't falling past the event horizon.
That's the whole problem: you are still
assuming, without justifying
anything, that anything at all freezes when crossing the event horizon in the first place.
Because light has stopped. Like everything else, including the macroscopic motion of the clock.
This is something else you just keep repeating without any support. You have defined no meaningful sense in which light "stops" on the event horizon. All the justifications you give are circular: you say clocks stop on the event horizon because light has stopped, and you say light has stopped on the event horizon because clocks stop. But you've never justified
either of these assertions.
You didn't say it directly. But the Kruskal-Szekeres coordinate system is plotting beyond the end of time, and you can't see the problem with it.
I didn't say it at all, directly or indirectly. The only problems are your own unquestioned assumptions. You keep assuming the Schwarzschild coordinates have more physical significance than you've been able to justify. In this case you are assuming that the Schwarzschild coordinates actually cover all of space and time. You have no basis for assuming that, and so you have no basis for assuming that because a clock shoots off the top of the Schwarzschild chart, it's shooting beyond the "end of time".
