## A Typology of Quantum Gravities – Followup on Quantum Gravity Panel

Catherine Asaro, Jay Wile, & I had a good crowd for our quantum gravity panel at Philcon: I was impressed that that many people (perhaps 40 or 50) wanted to hear about a relatively esoteric subject. Esoteric but hot: there are (right now) 663 papers on the physics archive with quantum gravity in the title, in just the last five years!

It was hard to know where to begin with this. The panel started by pointing out that there is a problem. For one thing, gravity is much weaker than the other forces. A refrigerator magnet can hold up a paperclip, in spite of the gravity of the entire rest of the planet trying to pull it down.

Then there is the problem of time.

Time in quantum mechanics functions like a butler, leading wave functions to and from the party, but not part of the action. We can think of time in quantum mechanics working like the frames in a movie: at each step the wave functions are a bit different, but the time parameter, the frame count, just clocks forward tick by tick. Dull, dull, dull.

But in relativity, time goes all twisty. If you go slower, your time goes faster. But if you, like Alice, fall down a gravity well, your time goes slower. If you are careless enough to trip and fall into a black hole, your time can slow down to the point where it comes to a complete halt & then seems to turn, so the maths tell us, into something like a space dimension. And if you go thru a wormhole (not recommended if you are less stretchable than Wile E. Coyote) you could wind up in your own past. Awkward at best, significant potential for paradox at worst. In relativity, time is part of the action; the butler gets to join the party.

But when it comes to space, now, quantum mechanics gets a bit of its own back: now everything is fuzzy, nothing has a well-defined position. We don’t know where an electron is, only its probability to be at any particular location.

Given that both relativity and quantum mechanics are true, what is going on here? For one thing, because gravity is weak, you can only see its effects for large objects. But because the fuzziness of quantum mechanics tends to average out over lots of particles, you typically only see its effects for a few atoms at a time. So normally the situation is like the cold war: the two opposing powers do not meet directly. But at the Big Bang, near a black hole, and in a few other cases, both sets of effects will matter. And in any case, it is all one universe: there must be some resolution. The wall between quantum mechanics and general relativity must come down!

So, how can we combine general relativity and quantum mechanics?

One thing the audience seemed to find useful was a typology from Christopher Isham. He divides approaches to quantum gravity into four categories:

**Quantize general relativity.**The leading example of this is loop quantum gravity. Here you replace space with a network of spins, called a spinfoam, and quantize the spins.**General-relativize quantum theory.**The leading example is string theory.**Start with a quantum theory that has general relativity as the low energy limit.**An example of this might be Sakharov’s induced gravity, where gravity is a result of interactions of the quantum fluctuations of the vacuum with foreground particles.**Do something completely out of the box that turns into general relativity and quantum mechanics in the appropriate limits.**An example of this might be Barbour’s Machian Quantum Gravity, where he takes as his starting point Mach’s principle, that local physical laws are determined by the large-scale structure of the universe.

All in all we had a pretty energetic panel discussion about gravity; the quantum; time; time and gravity; time and the quantum; quantum gravity; and time, the quantum, and gravity. Lots of questions from the audience and occasional answers from the panelists (along with more questions).