Unigrav applied to problems of time and cosmo constant

[marcus]

The message of the "Why all these prejudices?" paper is an unusual one. So rarely heard in the scientific community that I had better quote the conclusions to make sure that I and others understand what's being said.

==from conclusions of http://arxiv.org/abs/1002.3966 ==

First, the cosmological constant term is a completely natural part of the Einstein equations. Einstein probably considered it well before thinking about cosmology. His “blunder” was not to add such a term to the equations: his blunder was to fail to see that the equations, with or without this term, predict expansion. The term was never seen as unreasonable, or ugly, or a blunder, by the general relativity research community. It received little attention only because the real value of λ is small and its effect was not observed until (as it appears) recently.

Second, there is no coincidence problem if we consider equiprobability properly, and do not postulate an unreasonably strong cosmological principle, already known to fail.

Third, we do not yet fully understand interacting quantum field theory, its renormalization and its interaction with gravity when spacetime is not Minkowski (that is, in our real universe). But these QFT difficulties have little bearing on the existence of a non vanishing cosmological constant in low-energy physics, because it is a mistake to identify the cosmological constant with the vacuum energy density.
==endquote==

These conclusions are not simply stated, they are argued in the paper. Quantitative discussion of why the fact that, for example, it should not be deemed an especially remarkable coincidence that we live in an era when ordinary matter density and putative "dark energy" density are comparable---within a factor of 20 of each other. Or why, for example, it is a mistake to identify cosmo constant with the QFT vacuum energy density. IMHO you get the complete point of view only if you read the supporting arguments.

 

[atyy]

http://math.ucr.edu/home/baez/vacuum.html

 

[marcus]

http://math.ucr.edu/home/baez/vacuum.html

Nice pedagogical accessory to the Bianchi Rovelli article.
Baez always good at explaining.

 

[atyy]

Hmmm, I wonder if we could write a generally covariant Lagrangian and enforce flatness with a lagrange multiplier, and maybe 10 dimensions too ...

And then apply loop quantization ... ;)

Hehe... you're evil ;)
here's a crude attempt at the first part with flatness and 10 dimensions
$$S = \int_\mathcal{M} d^4x \sqrt{-g} \left[ (\frac{1}{2\kappa}R + \mathcal{L}_m) + (R^{abcd}R_{abcd} \phi + g^{ab}g_{ab}\psi - 10 \psi) \right]$$
With the "dynamical" fields $\phi,\psi$

If we were to jokingly take this "seriously", I could puff it up as: By adding the contributions of these psi and phi field terms to GR, we find that the only allowed values of phi and psi fields work to cancel any curvature caused by the matter fields. Futhermore, we find the only allowed spacetime dimension is 10, in agreement with string theory!


The fact that unigrav is essentially just a lagrange multiplier should be more of a warning to people. In other words, unigrav is taking beautiful GR, and limiting it, and claiming the very limits you put in (constant volume element) are instead a wonderful "result" (constant volume element, helping one to folliate spacetime). The other claim involving the stress-energy terms proportional to the metric not gravitating, I of course still dispute.

EDIT:
To counter some of my joking harshness there, it is of course a whole other issue what happens when we try to quantize such theories. Classical equivalence, when extra fields are involved, does not necessarily yield equivalence after quantizing. See Haelfix comments in post #47, for some notes on this regarding unigrav.

Damn - it's been done! (I noticed via marcus's posting of the latest Thiemann paper.)

http://arxiv.org/abs/0805.0208
http://arxiv.org/abs/1001.3505

 

[marcus]

...(I noticed via marcus's posting of the latest Thiemann paper.)
http://arxiv.org/abs/0805.0208
http://arxiv.org/abs/1001.3505

Thiemann calls the papers by Ladha and Varadarajan "seminal" and appears to draw on them in a substantial way. The second L&V paper looks interesting. I will copy the abstract:
http://arxiv.org/abs/1001.3505
Polymer quantization of the free scalar field and its classical limit
Alok Laddha, Madhavan Varadarajan
58 pages
(Submitted on 20 Jan 2010)
"Building on prior work, a generally covariant reformulation of free scalar field theory on the flat Lorentzian cylinder is quantized using Loop Quantum Gravity (LQG) type 'polymer' representations. This quantization of the continuum classical theory yields a quantum theory which lives on a discrete spacetime lattice. We explicitly construct a state in the polymer Hilbert space which reproduces the standard Fock vacuum- two point functions for long wavelength modes of the scalar field. Our construction indicates that the continuum classical theory emerges under coarse graining. All our considerations are free of the 'triangulation' ambiguities which plague attempts to define quantum dynamics in LQG. Our work constitutes the first complete LQG type quantization of a generally covariant field theory together with a semi-classical analysis of the true degrees of freedom and thus provides a perfect infinite dimensional toy model to study open issues in LQG, particularly those pertaining to the definition of quantum dynamics."

As so often happens, L&V do not make clear what version of LQG dynamics they are talking about when they refer to "triangulation ambiguities which plague..." They seem to assume that whatever version they have in mind must be the official version. As far as I know current LQG dynamics (non-embedded spin foam, see for example http://arxiv.org/abs/1010.1939 ) has no triangulation ambs. What the devil would they be triangulating? There's no manifold.

But even if L&V are not fully in touch which the larger LQG picture, and are focused on some definite version of the dynamics (e.g. one of the formulations investigated by Thiemann, a canonical quantization of gr?) that's just context and may be irrelevant. What they are doing sounds quite interesting regardless of how they see it fitting into the program.

 

[atyy]

http://arxiv.org/abs/1010.2535
"On the other hand, diffeomorphism-invariance alone cannot be enough to yield features analogous to AdS/CFT. The point here is that any local theory (e.g., a single free scalar field) can be written in diffeomorphism-invariant form through a process known as parametrization. But it is clear that free (unparametrized) scalar fields are not in themselves holographic since time evolution mixes boundary observables at anyone time t with independent bulk observables (say, those space-like separated from the cut of the boundary defined by the time t). As a result, boundary observables at one time cannot
generally be written in terms of boundary observables at any other time."

"The canonical formalism for parametrized field theories on manifolds without boundary was studied in [5], [6]."

[5] K. Kuchar, “Geometry of hyperspace. I, ” J. Math. Phys. 17, 777 (1976) ; “Kinematics of tensor fields in hyperspace. II, ” J. Math. Phys. 17, 792 (1976) ; “Dynamics of tensor fields in hyperspace. III, ” J. Math. Phys. 17, 801 (1976) ; “Geometrodynamics with tensor sources. IV,” J. Math. Phys. 18, 1589 (1977)

[6] C. J. Isham and K. V. Kuchar, “Representations Of Space-Time Diffeomorphisms. 1. Canonical Parametrized Field Theories,” Annals Phys. 164, 288 (1985).