# User talk:Tsumetai/TJ

This page is for discussion of Russell Humphreys' white hole cosmology, as presented in the Journal of Creation, formerly the Creation Ex Nihilo Technical Journal. Articles for and against WHC published in TJ can be found here. I submit that Humphreys' physics is hopelessly wrong, and that no credible science journal would have published his work.

Since there's a fair bit in those articles, and I'm short on time, I'm going to pull out two specific points for now. If anyone wants me to cover some other point, or to go into more detail on these two, just ask.

## Initial Arguments

### Humphreys doesn't understand the concept of spherical symmetry

Spherical symmetry violates the Copernican principle...to be spherically symmetric, their mass distribution would have to extend radially an equal distance in all directions from the centre of their sphere. They say that their Newtonian cosmos extends without limit, that is, the distance is infinite. But if it is infinite, there is no way to claim the distance is equal in all directions.

This is, to be blunt, nonsense. A spherically symmetric solution to Einstein's field equations is one which is independent of direction around some point; that is, you can spin your coordinate system about the origin in any direction and leave the solution unchanged. This is trivially true of the FRW metric, which depends only on time and radial distance from an (arbitrary) central point. Indeed, isotropy is not only consistent with the Copernican principle, it is required by the Copernican principle.

### Humphreys confuses the map with the territory

GR is the study of curved spacetime manifolds. Just as one can describe a flat, 2D space in a variety of ways - for example, with Cartesian or polar coordinates - one can choose from an infinite set of coordinate systems to describe any given manifold. However, the geometry remains the same regardless of our choice of coordinate system.

In describing the territory of the Big Bang Universe, Humphreys abandons the usual map - the FRW metric - claiming that it is 'incomplete.' Instead, he chooses to work with the Klein metric, which he claims reveals 'new physics.' But the Klein and FRW metrics are related by a simple coordinate transformation; they are different maps of the same territory. If the timeless region he claims to have found in the Klein metric is real, it must also exist in the FRW metric. But Humphreys states that it does not. His claim is simply incoherent.

To forestall such objections, Humphreys cites an example of a new coordinate system revealing new physics; that of black holes, which can be described using either Schwarzschild or Kruskal-Szekeres coordinates. Problem is, these two maps are not describing the same territory. The Kruskal-Szekeres coordinate system is an analytic continuation of the Schwarzschild map to cover a larger manifold, and is equivalent to two Schwarzschild patches.

If you don't have the time to read all of the TJ articles, you can find the relevant parts of Humphreys' position in this article, section 8.2, and the beginning of sections 9 and 7.

## Response

Tsumetai,

When I asked for you to substantiate your claim about faulty physics, I thought that you might come up with something like I had thrown at me on Wikipedia that God must have altered the laws of physics after the flood in order for a rainbow to appear (that's what he was claiming creationists believe). But what you've posted above is clearly not something as simple as that for me to answer, so I asked a friend about it.

It turns out that he doesn't agree with Russell Humphreys on these particular points (which I wasn't surprised at, because I knew he didn't agree with Humphreys on everything), but neither did he agree that publishing it impugns TJ's credibility. His comments follow.

In reference to your quote of Humphreys (beginning with "Spherical symmetry violates the Copernican principle..."):

I see what RH is trying to say but I don't agree with him. Spherical symmetry does not necessarily violate the CP. We need to understand isotropy and homogeneity. A homogeneous distribution is automatically also isotropic. So FRW theory assumes homogeneity which also means isotropy. But if the matter distribution is not random and has circular , ie concentric structure then it cannot be homogeneous but it can be isotropic. In this case CP is violated. I disagree about the last part to do with infinite distances-it is hardly relevant.

Responding to most of your reply to that ("This is, to be blunt, nonsense...central point."):

It is only trivially true if the universe is homogeneous--but that is assumed. Then the rest of what he says is correct.

Responding to your next line ("Indeed...principle"):

True, because the CP requires homogeneity.

Responding to the body of your second section ("GR is...Schwarzschild patches."):

I agree with everything he says above. But there are two points worth stating in defence. One, a different coordinate system can illuminate some physics that was not apparent in the other system, like transforming away a singularity by appropriate choice of coordinates. Secondly it is the new boundary conditions that causes the physics to be different. Because one assumes different boundary conditions often one is forced to choose a different solution of Einstein's field eqns. This is like the solution of a problem either inside or outside the matter distribution, different boundary conditions require different solutions.
and
It seems like always, people are blinded by their own biases. The person addressing the points above is largely correct, but in error by omission himself. To a spherically symmetric metric is valid in a smooth universally distributed matter filled universe. But the FRW metric requires that this is true at all points, hence also the universe must be homogeneous, and could equally well be described by a non-spherically symmetric metric, ie arbitrary coordinates. If spherically symmetric metric is not valid at all points, ie but at only one point, then it means the universe must be finite and that point is the unique center. Then there is the issue of the concentric structure to the matter distribution. If that were true, the universe could still be infinite and validly described by a spherically symmetric metric but it could not be also described by a metric that is not spherically symmetric. In this case a finite or infinite universe may be correct depending on the extent of the sphere of symmetry.

"Reputable" scientific journals do (reasonably often I would think, but at least occasionally) include papers that turn out to be wrong in some way, but that's part of the process of science. Having a paper published is not a guarantee of truth. I think the same applies here. TJ has published something from Humphreys that it seems is not correct. But does that mean that TJ's credibility is shot? According to you, clearly it does, but then you are hardly impartial in all this (i.e. you have your own bias in the matter). According to my friend, it doesn't (although I'm not claiming that he is any less biased).

So what you have done is demonstrate that Humphreys got some particular details wrong. What you have not done is demonstrate that TJ's credibility is destroyed as a consequence.

Philip J. Rayment 10:02, 8 April 2007 (EDT)

## Response II

First of all, thanks for getting back to this. Please thank your friend on my behalf, too.

I see what RH is trying to say but I don't agree with him. Spherical symmetry does not necessarily violate the CP. We need to understand isotropy and homogeneity. A homogeneous distribution is automatically also isotropic. So FRW theory assumes homogeneity which also means isotropy. But if the matter distribution is not random and has circular , ie concentric structure then it cannot be homogeneous but it can be isotropic. In this case CP is violated. I disagree about the last part to do with infinite distances-it is hardly relevant.

Minor point, but homogeneity doesn't actually imply isotropy; there are various Bianchi metrics which are spatially homogeneous but anisotropic, for example.

I agree with everything he says above. But there are two points worth stating in defence. One, a different coordinate system can illuminate some physics that was not apparent in the other system, like transforming away a singularity by appropriate choice of coordinates.

True, coordinate singularities are often much easier to spot under a change of frame. But it's never necessary to change; a coordinate singularity can be identified as such in any coordinate system, precisely because some physical quantities are invariant under coordinate transformations.

The signature of the metric is one such invariant. But Humphreys isn't simply claiming that both the FRW and Klein metrics contain a region of Euclidean signature, and that it's easier to spot in the Klein metric. He's claiming that the Klein metric contains a Euclidean region which is absent in the FRW metric.

It's worth pointing out that the invariance of the signature isn't exactly obscure; it's a fundamental part of the maths employed in GR, and probably the first thing most students will actually learn about the signature, beyond definitions.

Secondly it is the new boundary conditions that causes the physics to be different. Because one assumes different boundary conditions often one is forced to choose a different solution of Einstein's field eqns. This is like the solution of a problem either inside or outside the matter distribution, different boundary conditions require different solutions.

I should make it clear that Humphreys seems to have at least three distinct claims going:

1. The interior of a homogeneous, isotropic matter distribution with spherical boundary experiences time dilation which the equivalent region of an infinite homogeneous, isotropic matter distribution does not.
2. The Klein metric contains a region of Euclidean signature which the FRW metric does not.
3. One can construct a self-consistent cosmological model by joining an FRW region to a region of Euclidean signature, such that the Earth is young while most of the Universe is old.

My comments on coordinate transformation refer to claim 2), whereas your friend is discussing claim 1) here, which I didn't get into last time around. Nevertheless, while it's true that in general different boundary conditions lead to different solutions, it's false in this case. The interior of Humphreys' sphere is described by the FRW metric; it's exactly identical to a spherical subsection of a Big Bang Universe. Introducing the boundary alters gravitational dynamics only in the exterior region, which by Birkhoff's theorem is simply the Schwarzschild solution.

Slight digression, but this is actually where the Klein metric comes from. While both FRW and Schwarzschild metrics are defined over a set of coordinates t, r ,  and , they're not the same coordinates. The Klein metric is what you get when you transform the FRW interior to match the Schwarzschild exterior. Humphreys ought to know this, since if memory serves, the derivation he follows does precisely that. So where he gets the notion of modified dynamics within his bounded region, I have no idea. Seems to be a case of trying to apply intuition and ignoring the maths.

For completeness, I'll quickly address claim 3) here also. Humphreys correctly points out that it's possible to construct a model with regions of different signature. What he hasn't done is actually produced such a model. He needs more than just signature change. He needs a model which allows:

• a young Earth
• an old Universe
• no significant departure from observational record
• sufficiently well-behaved metric such that the Earth is not, say, destroyed by gravitational tidal forces

He's actually provided:

• nothing whatsoever

Enough said on that score, I think.

It seems like always, people are blinded by their own biases. The person addressing the points above is largely correct, but in error by omission himself. To a spherically symmetric metric is valid in a smooth universally distributed matter filled universe. But the FRW metric requires that this is true at all points, hence also the universe must be homogeneous, and could equally well be described by a non-spherically symmetric metric, ie arbitrary coordinates.

Not so; symmetry is a property of the underlying geometry, not of any coordinate system. It can't be transformed away.

If spherically symmetric metric is not valid at all points, ie but at only one point, then it means the universe must be finite and that point is the unique center. Then there is the issue of the concentric structure to the matter distribution. If that were true, the universe could still be infinite and validly described by a spherically symmetric metric but it could not be also described by a metric that is not spherically symmetric. In this case a finite or infinite universe may be correct depending on the extent of the sphere of symmetry.

Well, yes, were the Universe not homogeneous, we'd be dealing with a different situation. But since Humphreys' interior region is homogeneous, it doesn't matter.

Although having said that, I strongly suspect that as long as the matter distribution is isotropic, the boundary will prove to be irrelevant to the interior metric.

"Reputable" scientific journals do (reasonably often I would think, but at least occasionally) include papers that turn out to be wrong in some way, but that's part of the process of science.

Absolutely! But we're not talking about material which initially seemed reasonable and later turned out to be wrong. We're talking about basic errors which any reviewer competent in GR should have picked up. Were something this bad to make it into a mainstream journal, I'd expect a retraction at the very least, and you can bet there would be some interesting letters to the editor.

And it's not like it's an isolated case. Does this really strike you as quality material?

Tsumetai 07:01, 11 April 2007 (EDT)