Solving Cosmological Constant, Zero-Point Energy & Quantum Gravity Problems

[hakkai]

I was browsing a list of recently published papers on arxiv.org, and I found this paper:

Comprehensive Solution to the Cosmological Constant, Zero-Point Energy, and Quantum Gravity Problems

Authors: Philip D. Mannheim
arXiv:0909.0212

Here's the abstract:

"We present a solution to the cosmological constant, the zero-point energy, and the quantum gravity problems within a single comprehensive framework. We show that in quantum theories of gravity in which the zero-point energy density of the gravitational field is well-defined, the cosmological constant and zero-point energy problems solve each other by mutual cancellation between the cosmological constant and the matter and gravitational field zero-point energy densities. Because of this cancellation, regulation of the matter field zero-point energy density is not needed, and thus does not cause any trace anomaly to arise. We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone. Consequently, there have to be no fundamental classical fields, and all mass scales have to be generated by dynamical condensates. In such a situation the trace of the matter field energy-momentum tensor is zero, a constraint that obliges its cosmological constant and zero-point contributions to cancel each other identically, no matter how large they might be. Quantization of the gravitational field is caused by its coupling to quantized matter fields, with the gravitational field not needing any independent quantization of its own. With there being no a priori classical curvature, one does not have to make it compatible with quantization. "

Now, I haven't gone through the paper in detail, but this struck me "Central to our approach is the requirement that any and all departures of the geometry from Minkowski are to be brought about by quantum mechanics alone." Unfortunately, I can't understand much of the paper, but the author claims that things work out properly. It goes without saying that if what he did is true, it would be phenomenal, and also seem to change our conception of GR.

What are your thoughts? Does this paper seem right to you?

 

[marcus]

"... We exhibit our results in two theories of gravity that are well-defined quantum-mechanically. Both of these theories are locally conformal invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based quantum conformal gravity in four dimensions (a fourth-order derivative quantum theory of the type that Bender and Mannheim have recently shown to be ghost-free and unitary). ... "

Hakkai I don't want to get involved with analyzing the paper and so, I regret to say, cannot respond to your main question. But I can fill in some additional personal detail.
First, posting on arxiv is not usually considered professional-grade "publishing". Arxiv is an open preprint library so you have to look carefully at what you are getting. It is not like a peer-reviewed professional journal. So when browsing arxiv, check the author's other papers, his or her publication track record etc.

In this case, Philip Mannheim has quite a good track record---over 100 papers going back to 1968. Of course that means he is now near retirement age.

In recent years he has been promoting a seemingly eccentric theory which he calls "quantum conformal gravity". In contrast to his earlier work, this has NOT been well received. These recent papers of his, which I think go back to 2006 or so, have not been much cited, when they have been published at all (outside of arxiv and minor conference proceedings). This does not mean that his theory is wrong, it just means he hasn't succeeded in getting the other physicists to pay much attention to it, as yet.

This is merely context---I can offer no opinion as to the merits. Hopefully some others here will be able to comment.

 

[Haelfix]

The merits are fine as a 'what if' scenario, but its very far from being flushed out. The amount of times people have tried to use conformal field theory to solve quantum gravity problems is enormous.

Roughly speaking, its been known for a long time that you could get cancellations from the CC if you uniquely couple the gravitational field with only matter in the context of a conformal field theory. Not unlike supersymmetry (which cuts the CC problem in half logarithmically), you can conspire for a great deal of cancellations when you enlarge the spacetime symmetry group. The problem is the two frameworks he uses to show this off are problematic. They are plagued with unitarity problems and other quantum instabilities, for instance 4 derivative gravity.

He claims these issues have been worked out in 2 other papers, but I don't believe that has been accepted at all.

Other than that, there isn't much freedom to do anything interesting. No scalar fields at all! That rules out a scalar higgs (you would need a condensate for the job, and that comes with phenomenology problems of its own), Inflaton fields and so on and so forth.

Then there are issues with black hole thermodynamics and entropy counting, a host of cosmology issues etc etc.

 

[hakkai]

Ah, I see. Thanks for the perspective, both of you. I guess the title of the paper is a bit of an overstatement...

 

[marcus]

... a bit of an overstatement...

Perhaps so. In any case you spotted a creditable attempt by a respectable guy. I am currently in similar uncertainty myself, having taken an interest in some papers by Kirill Krasnov. He too has proposed a longshot modification of General Relativity. In a sense this is what the more courageous relativists ought to be doing. They ought to be looking for modifications GR which address certain problems. Such as renormalizability, or what Weinberg termed UV "safety"--- such as the cosmological constant problem.