Splitting Time and Space

November 26, 2009

The twentieth century saw the development of two new frameworks in theoretical physics: Einstein’s theory of General Relativity, which updated our understanding of gravity, and quantum mechanics, which gave us a window into processes that happen on a subatomic scale.  Predictions from both theories have been verified by experiments, but there is just one problem: the theories don’t seem to be consistent with each other.  Reconciling the two is the central problem in theoretical physics today.  Much of the work on various forms of string theory, for example, is directed towards this goal.

The December issue of Scientific American has an article describing another attempt to bridge this theoretical divide.  Gravity really is the anomaly, because the other fundamental forces can be reconciled within the existing framework:

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.

Now a  new theoretical approach has been developed by Petr Hořava, a physicist at the University of California at Berkeley.  In essence, his approach reverses one of the core concepts of General Relativity, namely that time is, in essence, just another dimension of the universe, like the more familiar spatial dimensions. Prior to Einstein’s work, time had been conceived of as a sort of giant clock ticking away in the background, unaffected by the presence or absence of matter.  What Hořava’s approach does is to restore the special character of time, “decoupling” it from space.  The effect of this, in the theory, is only apparent at very high energies; at lower energies, the solutions of General Relativity emerge as a special case:

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.

This is an intriguing idea: perhaps, just as Newtonian mechanics is a special case that applies under “normal” conditions, General Relativity is a special case that applies at the energy levels we see in the universe today.  There is some early evidence that Hořava is onto something:

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.

There is also some evidence that the new theory might account for the mysterious “dark matter” that seems to be required in order to explain the magnitude of observed gravitational forces.

The theory is still being developed, and is far from perfect.  But it’s another interesting attempt to reconcile two very successful ideas in theoretical physics; everyone’s intuition, including Einstein’s, was that the reconciliation was possible, but that there is a piece of the puzzle we have not yet found.

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