[SciAm] Splitting Time from Space / Horava Gravity

[McC]

Link

Was Newton right and Einstein wrong? It seems that unzipping the fabric of spacetime and harking back to 19th-century notions of time could lead to a theory of quantum gravity.

Physicists have struggled to marry quantum mechanics with gravity for decades. In contrast, the other forces of nature have obediently fallen into line. For instance, the electromagnetic force can be described quantum-mechanically by the motion of photons. Try and work out the gravitational force between two objects in terms of a quantum graviton, however, and you quickly run into trouble—the answer to every calculation is infinity. But now Petr Hořava, a physicist at the University of California, Berkeley, thinks he understands the problem. It’s all, he says, a matter of time.

More specifically, the problem is the way that time is tied up with space in Einstein’s theory of gravity: general relativity. Einstein famously overturned the Newtonian notion that time is absolute—steadily ticking away in the background. Instead he argued that time is another dimension, woven together with space to form a malleable fabric that is distorted by matter. The snag is that in quantum mechanics, time retains its Newtonian aloofness, providing the stage against which matter dances but never being affected by its presence. These two conceptions of time don’t gel.

The solution, Hořava says, is to snip threads that bind time to space at very high energies, such as those found in the early universe where quantum gravity rules. “I’m going back to Newton’s idea that time and space are not equivalent,” Hořava says. At low energies, general relativity emerges from this underlying framework, and the fabric of spacetime restitches, he explains.

Hořava likens this emergence to the way some exotic substances change phase. For instance, at low temperatures liquid helium’s properties change dramatically, becoming a “superfluid” that can overcome friction. In fact, he has co-opted the mathematics of exotic phase transitions to build his theory of gravity. So far it seems to be working: the infinities that plague other theories of quantum gravity have been tamed, and the theory spits out a well-behaved graviton. It also seems to match with computer simulations of quantum gravity.

Hořava’s theory has been generating excitement since he proposed it in January, and physicists met to discuss it at a meeting in November at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario. In particular, physicists have been checking if the model correctly describes the universe we see today. General relativity scored a knockout blow when Einstein predicted the motion of Mercury with greater accuracy than Newton’s theory of gravity could.

Can Hořřava gravity claim the same success? The first tentative answers coming in say “yes.” Francisco Lobo, now at the University of Lisbon, and his colleagues have found a good match with the movement of planets.

Others have made even bolder claims for Hořava gravity, especially when it comes to explaining cosmic conundrums such as the singularity of the big bang, where the laws of physics break down. If Hořava gravity is true, argues cosmologist Robert Brandenberger of McGill University in a paper published in the August Physical Review D, then the universe didn’t bang—it bounced. “A universe filled with matter will contract down to a small—but finite—size and then bounce out again, giving us the expanding cosmos we see today,” he says. Brandenberger’s calculations show that ripples produced by the bounce match those already detected by satellites measuring the cosmic microwave background, and he is now looking for signatures that could distinguish the bounce from the big bang scenario.

Hořava gravity may also create the “illusion of dark matter,” says cosmologist Shinji Mukohyama of Tokyo University. In the September Physical Review D, he explains that in certain circumstances Hořava’s graviton fluctuates as it interacts with normal matter, making gravity pull a bit more strongly than expected in general relativity. The effect could make galaxies appear to contain more matter than can be seen. If that’s not enough, cosmologist Mu-In Park of Chonbuk National University in South Korea believes that Hořava gravity may also be behind the accelerated expansion of the universe, currently attributed to a mysterious dark energy. One of the leading explanations for its origin is that empty space contains some intrinsic energy that pushes the universe outward. This intrinsic energy cannot be accounted for by general relativity but pops naturally out of the equations of Hořava gravity, according to Park.

Hořava’s theory, however, is far from perfect. Diego Blas, a quantum gravity researcher at the Swiss Federal Institute of Technology (EPFL) in Lausanne has found a “hidden sickness” in the theory when double-checking calculations for the solar system. Most physicists examined ideal cases, assuming, for instance, that Earth and the sun are spheres, Blas explains: “We checked the more realistic case, where the sun is almost a sphere, but not quite.” General relativity pretty much gives the same answer in both the scenarios. But in Hořava gravity, the realistic case gives a wildly different result.

Along with Sergei M. Sibiryakov, also at EPFL, and Oriol Pujolas of CERN near Geneva, Blas has reformulated Hořava gravity to bring it back into line with general relativity. Sibiryakov presented the group’s model in September at a meeting in Talloires, France.

Hořava welcomes the modifications. “When I proposed this, I didn’t claim I had the final theory,” he says. “I want other people to examine it and improve it.”

Gia Dvali, a quantum gravity expert at CERN, remains cautious. A few years ago he tried a similar trick, breaking apart space and time in an attempt to explain dark energy. But he abandoned his model because it allowed information to be communicated faster than the speed of light.

“My intuition is that any such models will have unwanted side effects,” Dvali thinks. “But if they find a version that doesn’t, then that theory must be taken very seriously.”

Posting without comment, since there are better-educated folks here who can offer better commentary.

[Surlethe]

I really wasn't sure what to make of it when I heard it, and I couldn't find a paper in the brief time I looked. At a GR singularity, is he dealing with it by splitting the 4-manifold into a 1-manifold and a 3-manifold that are sort of glued together there? (That's a topological no-no, but it sounded like that's what he was doing.)

[Kuroneko]

Einstein famously overturned the Newtonian notion that time is absolute—steadily ticking away in the background. Instead he argued that time is another dimension, woven together with space to form a malleable fabric that is distorted by matter. The snag is that in quantum mechanics, time retains its Newtonian aloofness, providing the stage against which matter dances but never being affected by its presence. These two conceptions of time don’t gel.

This is very misleading. Relativistic quantum mechanics is quite possible, and gels with relativistic time well enough to produce the single most successful theory in existence: quantum electrodynamics.

Perhaps a better way to characterize the incongruity is that of background dependence: relativistic quantum field theories (QED, ...), string theory, etc., assume that the physics happens in a fixed arena of spacetime. This is somewhat indirect in string theory, as the higher-dimensional 'bulk' is fixed by some physically necessary properties, rather than brane of our universe proper. Nevertheless, in all of those theories, there is some fixed background geometry. In GTR, that's not true, and the canonical quantization of GTR, while being fairly simple to write down, fails to work properly precisely because it requires the universe to be some kind of superposition of different geometries.

Hořava's proposal introduces anisotropy between space and time, which might resolve some of the difficulties in quantum gravity, but it is inaccurate to attribute the usual isotropy to the primary cause of said difficulties. If anything, the key difference is background dependence.

Hořava gravity may also create the “illusion of dark matter,” says cosmologist Shinji Mukohyama of Tokyo University. ... If that’s not enough, cosmologist Mu-In Park of Chonbuk National University in South Korea believes that Hořava gravity may also be behind the accelerated expansion of the universe, currently attributed to a mysterious dark energy. One of the leading explanations for its origin is that empty space contains some intrinsic energy that pushes the universe outward. This intrinsic energy cannot be accounted for by general relativity but pops naturally out of the equations of Hořava gravity, according to Park.

This is also misleading. The paper in question is
-- Mukohyama, Shinji. Dark matter as integration constant in Hořava-Lifshitz gravity. Phys. Rev. D 80, 064005.
I don't have anything against the paper itself, but in GTR, the cosmological constant ('intrinsic energy' of vacuum) is accounted for very naturally, and is in fact itself an integration constant in some derivations of the Einstein field equation. Therefore, GTR's handling of dark energy is approximately equiexplanatory with Hořava-Lifshitz's handling of dark matter.

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I really wasn't sure what to make of it when I heard it, and I couldn't find a paper in the brief time I looked.

Hořava, Petr. Quantum gravity at a Lifshitz point. Phys. Rev. D 79, 084008. arXiv:0901.3775.
Brandenberger's paper can be found at arXiv:0904.2835.

At a GR singularity, is he dealing with it by splitting the 4-manifold into a 1-manifold and a 3-manifold that are sort of glued together there?

I only briefly glanced at it, but appeared that the idea is that the special scaling (a-)symmetry between space and time to introduces a negative energy density that redshifts faster than the usual matter or radiation, thus avoiding the singularity altogether.

I suspect that Brandenberger's equation (16) has a wrong sign on the p/4α term, although I don't really know, not having done the variation myself. My suspicion is based solely on the fact that if that term is taken to be negative, then taking α = 1/4 and dropping the ~k/a4 term that represents Brandenberger's "dark radiation" (i.e., for large scale factor a≫1) reproduces the standard Friedmann equations of general relativity in units of c = 4πG = 1. In any case, the ~k/a4 dominates when the scale factor is small, so the rest of terms are irrelevant in that regime, as long as the universe is not spatially flat (i.e., k = ±1). That's what's supposed to make the universe 'bounce'.

[Gil Hamilton]

This is very misleading. Relativistic quantum mechanics is quite possible, and gels with relativistic time well enough to produce the single most successful theory in existence: quantum electrodynamics.

I would think that relativity in quantum mechanics wasn't just possible, but necessary. For example, fine structure in spectral lines fall out of relativity, where the reference frame is shifted to be centered on electrons with their nuclei processing around them, causing a magnetic field that causes spin-orbit coupling. That splits the degeneracy of some energy levels and is something we can measure with a reasonably sensitive instrument.

[Kuroneko]

True. Even before that, spin itself is an ad hoc mechanism in nonrelativistic QM, but falls out fairly naturally from the structure of the Lorentz group. Thus, in some sense it's necessary even before the relativistic correction.

[Kuroneko]

Looking a bit more into this, it turns out that Hořava's gravity does not reproduce GTR in the low energy limit, but rather has the structure of a special kind of quintessence with an infinite speed of sound coupled to gravity [2]--a 'cuscuton' field, so named because it follows introduced no dynamics of its own, merely following whatever it is coupled to. What's interesting about it is that (surprisingly enough) the theory is causal due to its lack of dynamics, conveying no superluminal information.

Or rather, it would be if not for the the existence of an absolute frame of reference with uniform time lapse. As it is, Hořava's gravity is effectively slain, months before the news article was printed.

[1] D. Blas et al JHEP10(2009)029.
[2] N. Afshordi. Phys. Rev. D 80, 081502 (2009). arXiv:0907.5201.