The other day I was amused to find
a quote from Einstein, in 1936, about how hard it would be to quantize gravity: “like an attempt to breathe in empty space.” Eight decades later, I think we can still agree that it’s hard.
So here is a possibility worth considering:
rather than quantizing gravity, maybe we should try to gravitize quantum mechanics. Or, more accurately but less evocatively, “find gravity inside quantum mechanics.” Rather than starting with some essentially classical view of gravity and “quantizing” it, we might imagine starting with a quantum view of reality from the start, and find the ordinary three-dimensional space in which we live somehow emerging from quantum information. That’s the project that ChunJun (Charles) Cao, Spyridon (Spiros) Michalakis, and I take a few tentative steps toward in
a new paper.
We human beings, even those who have been studying quantum mechanics for a long time, still think in terms of a classical concepts. Positions, momenta, particles, fields, space itself. Quantum mechanics tells a different story. The quantum state of the universe is not a collection of things distributed through space, but something called a
wave function. The wave function gives us a way of calculating the outcomes of measurements: whenever we measure an observable quantity like the position or momentum or spin of a particle, the wave function has a value for every possible outcome, and the probability of obtaining that outcome is given by the wave function squared. Indeed, that’s typically how we construct wave functions in practice. Start with some classical-sounding notion like “the position of a particle” or “the amplitude of a field,” and to each possible value we attach a complex number. That complex number, squared, gives us the probability of observing the system with that observed value.
Mathematically, wave functions are elements of a mathematical structure called
Hilbert space. That means they are vectors — we can add quantum states together (the origin of
superpositions in quantum mechanics) and calculate the angle (“dot product”) between them. (We’re skipping over some technicalities here, especially regarding complex numbers — see e.g.
The Theoretical Minimum for more.) The word “space” in “Hilbert space” doesn’t mean the good old three-dimensional space we walk through every day, or even the four-dimensional spacetime of relativity. It’s just math-speak for “a collection of things,” in this case “possible quantum states of the universe.”
Hilbert space is quite an abstract thing, which can seem at times pretty removed from the tangible phenomena of our everyday lives. This leads
some people to wonder whether we need to supplement ordinary quantum mechanics by additional new variables, or alternatively to imagine that wave functions reflect our knowledge of the world, rather than being representations of reality. For purposes of this post I’ll take the
straightforward view that quantum mechanics says that the real world is best described by a wave function, an element of Hilbert space, evolving through time. (Of course time could be emergent too … something for another day.)
The rest here:
http://www.preposterousuniverse.com/...tum-mechanics/