Reconciling Einstein and Schroedinger

SciScoop contact Nykolai Bilaniuk brought an intriguing paper to our attention recently, that at first glance looks like a typical cracked conjecture of the kind SciScoop has reported in the past, but, says Bilaniuk, this one has a certain credibility.

The idea is that of UC Berkeley’s Petr Horava, Bilaniuk tells us, and it’s one of those ideas working in the direction of a “theory of everything”, basically, unifying quantum mechanics (QM) and general relativity(GM).

It is well known that in the early part of the twentieth century Einstein was at loggerheads with those developing quantum theory and its probability perspective on reality, not least because he felt that “God” would not play dice. “In situations where QM and GR give conflicting results (such as the value of the gravitational constant on a microscopic scale) at least one of the two theories must be wrong (although it’s possible that both are off!),” Bilaniuk told SciScoop. “My hunch is that if one has to choose between the two, then QM is more likely to be correct, and GR in error.”

He suggests that the reason is that QM has been more thoroughly tested – it has been used to make solid predictions (rather ironically really) and underpins the whole of modern electronics and computing with those predictions. GR, on the other hand, has been tested mostly by astrophysical observations, such as gravitational lensing and time dilation of atomic clocks that have been sent into space and brought back to Earth. While QM may not seem intuitive, there are glaring inconsistencies in our GR observations that have led scientists to invoke dark matter and dark energy, which some observers worry are simply fudge factors. QM is built into billions of modern electronic gadgets and they all work as expected with no fudge factors. “Betting on QM being right is better than betting on GR,” Bilaniuk thinks.

In Horava’s theoretical framework he essentially confirms this viewpoint.

Take the speed of light, it’s the fastest anything can travel and is a constant value in a vacuum. The special relativity (SR) axiom states that the speed of light is constant in all frames of reference, this implies that at relativistic speeds, distance contracts at the same rate at which time slows, a phenomenon known as Lorentz symmetry, which is central to SR.

Horava assumes that to reconcile GR and QM, he should assume GR is broken, and he attempts to fix it by dispensing with two GR assumptions: Lorentz symmetry, and the closely related notion of the uniformity of Minkowski space (i.e. that time is just another arbitrary direction in spacetime).

At this point, it all starts to get a bit beyond my meagre physics training, even though Paul Davies was one of my most inspirational undergraduate lecturers, so here’s the abstract from the paper for you to ponder:

We present a candidate quantum field theory of gravity with dynamical critical exponent equal to z=3 in the UV. (As in condensed matter systems, z measures the degree of anisotropy between space and time.) This theory, which at short distances describes interacting nonrelativistic gravitons, is power-counting renormalizable in 3+1 dimensions. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory flows naturally to the relativistic value z=1, and could therefore serve as a possible candidate for a UV completion of Einstein’s general relativity or an infrared modification thereof. The effective speed of light, the Newton constant and the cosmological constant all emerge from relevant deformations of the deeply nonrelativistic z=3 theory at short distances.

Scientific American puts it quite succinctly in their coverage of the theory a year ago: “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.”

It’s well over a year since Horava published on this and there has been other popular press coverage…is Bilaniuk right in backing QM over GR/SR? Could Einstein be reconciled with Schrodinger by removing Einstein from the equation?

Research Blogging IconHoĊ™ava, P. (2009). Quantum gravity at a Lifshitz point Physical Review D, 79 (8) DOI: 10.1103/PhysRevD.79.084008