## Wednesday, October 29, 2008

### Non quantum gravity and dark matter

I keep reading Physicsforums, specially the beyond the standard model forum. Recently there was a discussion about a new proposal appeared in arxiv arguing that maybe gravity wouldn’t need to be quantized after all.

The paper in question, authored by Stephen Boughn is this.

It is a very clear paper where the usual assumptions are reviewed. As is commonly known we actually have a quantum theory, the standard model, which describes all known interactions but gravity. The best available description, experimentally supported, of gravity is Einstein theory of gravity, which is a non quantum theory.

In order to approach both theories one can begin by quantizing the standard model in the curved backgrounds of general relativity, instead of doing it in plain Minkowsky space (see my previous post for an easy introduction- in Spanish, sorry for non Spanish people-).

The next step one could try is simply to consider the gravitational field created by the averaged value of the energy momentum tensor and forget the idea of quantizing gravity at all. That is to replace:

1. $G_{\nu\mu}=8\pi G/c^4T{\nu\mu}$

by:

2.$G_{\nu\mu}=8\pi G/c^4 \langle T{\nu\mu}\rangle$

This proposal has many well known problems, both theoretical and practical. The author discuss them in the chapter 6 of his paper. Consider a state of matter, with probability !/2 of being in O1 region of space time and a probability ½ of being in a disjoint region O2. If you use equation 2 you get a gravitational field appropriate for matter being distributed in both regions. If later a measurement is made and the state is resolved to one of the Oi then the gravitational field would change in a discontinuous and acausal manner.

The key point of the paper is to keep eqt. 1 as valid and forget about 2. Of course one can’t do it without further assumptions. The author establish that the energy momentum tensor must satisfy the following prerequisite. In the language of decoherence theory, that the system is in a decoherent, mixed quantum state for it is only then that the probability predictions of quantum theory agree with those of classical physics. (You can read about decoherence in, for example, this paper by Lubos Motl.).

This assumption immediately implies another one, that non-localized, coherent quantum systems are not sources of gravity. That sounds as a very hard assumption, but the author argues that It will turn out that for microsopic systems, in which quantum coherence is most commonly observed, the effects of gravity are, in principle, unobservable. For larger macroscopic systems, decoherence is the norm and classical stress-energy is well defined. This leaves open the question of gravitational interactions of mesoscopic, coherent sytsems.

After that he goes through some chapters reviewing the detectability of possible quantum gravity phenomena. He begins, in chapter two, considering the detectability of gravitons. Remember that a graviton should be the quanta that would mediate gravity interactions if one insist in doing quantum gravity in a particle physicist like way. This chapter is very well written, and it relates the gravitons to gravity waves. Note that one of the authors research activities is precisely in the field of experimental detection of gravity waves so he can be considered an authority in that particular.

In chapter 3 he dwells with gravity and quantum interference, that is, double slit like thought experiments. He concludes the existence of a conditions that must be satisfied for a gravitational measurement to be made that will sufficiently localize the incident particle so as to destroy the quantum interference which are stated in terms of the separation of the two slits, r, the acceleration of the test mass at, the velocity of the incoming particle vi. The actual conditions are:

r >¯h r^2/Gm^3 (here ¯h is h bar, i.e. h/2π)

t >¯h^3 / G2m^5

at < G^3m7 /¯h^4

vi < Gm^2 / ¯h

If the conditions are not satisfied, the gravitational interaction is insufficient to detect the incident particle and quantum interference remains intact..He concludes that for quantum coherent systems with masses less than ∼ 10^7mp (mp=Planck mass), there is not a measurable gravitational effect that would compromise their coherence. He does further analysis and get further restrictions. The conclusion of the arguments is that the question of whether or not coherent quantum systems are sources of gravity is unanswerable for systems with masses < 10^10 mp. That leaves unanswered the question of mesoscopic systems, which he analyzes later.

The chapter 4 is a continuation, in a certain sense, of the previous. The most interesting is the chapter 5 where he fully analyzes the central issue of the paper. The key point, if I rightly understand is the following statement:

“Because macroscopic systems
invariably undergo decoherence on very short time scales, they behave as they would
in a classical world, i.e., no quantum interference effects.”

Or stated, together with another claims of the chapter, in a more generic way it could be said: “the experimental data available to date only takes account of interactions between matter systems in a decoherent state.”
That raise the question of what would be the behaviour of macroscopic, or at least, mesoscopic, systems which are in coherent states. He talks about the copper pairs in superconductivity, Bose-Einstein condensates and systems like that. Here I would add a few things. A few years ago an condensate-matter physicist, Podkeltnov, made a claim, in a press conference, about some kind of gravity shielding that appeared unexpectectly in experiments which implied some kind of high temperature superconducting devices. He didn’t provide all the details of the experimental device and ulterior attempts to reply the experiment, based on the available data, are until now unsuccessful. Later Podkelnov he improved the experiment and even tried to conjecture an explanation. His argument was related to the suppression of Fourier modes of gravity because of coupling of the Landau-Ginzburg lagrangian which could be used to describe the superconductor to the energy of the cosmological constant. Certainly the “non quantum gravity” proposal could be considered as an alternative explanation if one would try to insist in explaining an effect non firmly established experimentally, of course.

To conclude my review of this proposal I’ll mention a few problems that the own Stephen Boughn recognizes. The main one, in my opinion, is that if a coherent system exchange momentum with a coherent one, and later becomes non coherent his proposal could lead to a violation of momentum conservation. Another one is a legitimate criticism of the conjecture put forward in this paper is its lack of predictive power. Except possibly in the case of the coherent to decoherent transitions in mesoscopic systems, and even in these cases the conjecture makes no specific prediction, the nonquantum conjecture makes no additional predictions that can not already be made by quantum theory and general relativity. There are some more concerns, that the author acknowledge in the final chapter and I´ll not talk here about them.

Let’s go now with the next topic of this post, dark matter. A few weeks after this paper appeared Sean Carrol in his blog, cosmic variance, made this post. Soon there was a reply by Lubos Motl here.

They are very interesting posts in their own. But I bring them here because it is stated there that dark matter, if it interact only by means of gravity with itself, and the rest of the universe, would decohere very solowly. In fact, if the non quantum gravity proposal would be taken to it’s full consequences it could be expected that it wouldn’t decohere at all. But if so, it wouldn’t interact gravitatorilly at all. That is a very bad thing because dark matter is postulated to explain unobserved mass in the universe which accounts the observed rate of cosmological expansion.

In fact, in a very recent paper it is discussed the possibility that dark matter could not exist, or, at least, not be the main responsible of some experimental data. The paper is this. It is discussed in a blog entry by Lubos Motl here. Quickly, the idea is that a field associated to string theory, could take a nonvacuum expected value and that if particles are actually strings, would couple to it resulting in a Lorentz type force which would explain the problem with the way galaxies rotate in an alternative way to the usual explanations of dark matter of MOND (modified newtoninan dynamics). If this non quantum gravity proposal would be taken seriously the stringy paper would gain additional value because dark matter, even if it exists, could not interact gravitationally, or at least not too much.. Of course if we accept the nonquantum gravity proposal string theory would loose one of it’s more important reason to exist, it’s status as a quantum theory of gravity and it would have to be questioned if it’s explanation of galaxies rotations could be still accepted.

In fact I admit that I actually didn’t do the actual calculations of exactly how much dark matter would interactuate gravitationally if the non quantum gravity proposal would be truth. I find surprising that the author, Stephen Boughn, wouldn’t consider it in his paper when he claims that he is actually working on cosmology, but, of course, he could easily not have realized this lack of coherence in dark matter, which is only obvious once one is told about it, but not before.

Anyway, the paper is interesting in it’s own, even if it’s wrong, because of the review of many aspects related to gravity and it has served me to take quote of some issues that have happened in the quantum gravity world in the recent times. Hope the reader would find them interesting.