Fairly Simple Math Could Bridge Quantum Mechanics and General Relativity

From Scientific American:

AppleCould an analysis based on relatively simple calculations point the way to reconciling the two most successful — and stubbornly distinct — branches of modern theoretical physics? Frank Wilczek and his collaborators hope so. The task of aligning quantum mechanics, which deals with the behaviour of fundamental particles, with Einstein’s general theory of relativity, which describes gravity in terms of curved space-time, has proved an enormous challenge. One of the difficulties is that neither is adequate to describe what happens to particles when the space-time they occupy undergoes drastic changes — such as those thought to occur at the birth of a black hole. But in a paper posted to the arXiv preprint server on 15 October (A. D. Shapere et al. http://arxiv.org/abs/1210.3545; 2012), three theoretical physicists present a straightforward way for quantum particles to move smoothly from one kind of ‘topological space’ to a very different one.

The analysis does not model gravity explicitly, and so is not an attempt to formulate a theory of ‘quantum gravity’ that brings general relativity and quantum mechanics under one umbrella. Instead, the authors, including Nobel laureate Frank Wilczek of the Massachusetts Institute of Technology (MIT) in Cambridge, suggest that their work might provide a simplified framework for understanding the effects of gravity on quantum particles, as well as describing other situations in which the spaces that quantum particles move in can radically alter, such as in condensed-matter-physics experiments. “I’m pretty excited,” says Wilczek, “We have to see how far we can push it.” The idea is attracting attention not only because of the scope of its possible applications, but because it is based on undergraduate-level mathematics. “Their paper starts with the most elementary framework,” says Brian Greene, a string theorist at Columbia University in New York. “It’s inspiring how far they can go with no fancy machinery.” Wilczek and his co-authors set up a hypothetical system with a single quantum particle moving along a wire that abruptly splits into two. The stripped-down scenario is effectively the one-dimensional version of an encounter with ripped space-time, which occurs when the topology of a space changes radically.

More here.