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sol invictus · 10th July 2008, 03:34 PM

Originally Posted by Reality Check

To be fair he knows about the asymptotically flat behaviour of the Schwarzschild metric. Instead he looks at the % change in the distance between 2 points in the metric divided by the radial distance. He skips the math in the exact solution and uses an approximation which is the problem.
He may get it published since he reported that the peer reviewer had no problems with the approximation.

OK, just for a laugh I decided to take a look at that "white paper". The quantity defined there is meaningless. Rather than the Schwarzschild metric, I could take flat space and write it in funny coordinates (for example, rescale the radial coordinate by 5). Then I could compare it to flat space in ordinary coordinates and (using Witt's definition) get an even more divergent result than he gets.

Or I could re-define the radial coordinate in the Sch. metric to make it "flat", and get zero - or literally anything else. The radial function means nothing at all by itself, because I can change it to anything by a redefiniion of coordinates.

You could, I suppose, ask about the fractional difference in length between radial geodesics in Scw. and flat space, starting and ending on spheres of fixed radius (that would nail down the radial coordinate). That's actually Witt's eq. (12). Notice that it goes to zero at large R.

Or you could ask that about the absolute difference, and indeed, far away it would get large. So what? There are many random quantities which diverge when you integrate them like that - the electric potential of a point charge, for example. Does that mean Gauss' law is wrong?

The quantity Witt defines is meaningless, because it is not coordinate invariant. It does not measure the deviation of Scw. from flat space in any useful way. If he manages to get it published I will be ashamed of the journal and the reviewer.

10th July 2008, 03:34 PM	#450
sol invictus Philosopher Join Date: Oct 2007 Location: Nova Roma Posts: 5,153	Originally Posted by Reality Check To be fair he knows about the asymptotically flat behaviour of the Schwarzschild metric. Instead he looks at the % change in the distance between 2 points in the metric divided by the radial distance. He skips the math in the exact solution and uses an approximation which is the problem. He may get it published since he reported that the peer reviewer had no problems with the approximation. OK, just for a laugh I decided to take a look at that "white paper". The quantity defined there is meaningless. Rather than the Schwarzschild metric, I could take flat space and write it in funny coordinates (for example, rescale the radial coordinate by 5). Then I could compare it to flat space in ordinary coordinates and (using Witt's definition) get an even more divergent result than he gets. Or I could re-define the radial coordinate in the Sch. metric to make it "flat", and get zero - or literally anything else. The radial function means nothing at all by itself, because I can change it to anything by a redefiniion of coordinates. You could, I suppose, ask about the fractional difference in length between radial geodesics in Scw. and flat space, starting and ending on spheres of fixed radius (that would nail down the radial coordinate). That's actually Witt's eq. (12). Notice that it goes to zero at large R. Or you could ask that about the absolute difference, and indeed, far away it would get large. So what? There are many random quantities which diverge when you integrate them like that - the electric potential of a point charge, for example. Does that mean Gauss' law is wrong? The quantity Witt defines is meaningless, because it is not coordinate invariant. It does not measure the deviation of Scw. from flat space in any useful way. If he manages to get it published I will be ashamed of the journal and the reviewer.