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(At the suggestion of the user markovchain, I have decided to take a very large edit/addition to the original question, and ask it as a separate question altogether.)

Here it is:

I have since thought about this more, and I have come up with an extension to the original question. The answers already given have convinced me that we can't just leave the metric as it is in GR untouched, but at the same time, I'm not convinced we have to quantize the metric in the way that the other forces have been quantized. In some sense, gravity isn't a force like the other three are, and so to treat them all on the same footing seems a bit strange to me. For example, how do we know something like non-commutative geometry cannot be used to construct a quantum theory of gravity. Quantum field theory on curved non-commutative space-time? Is this also a dead end?

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Jonathan Gleason
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1 Answers1

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Quantum field theory on curved non-communative spacetime is exactly what is used in the "semiclassical gravity" approach, an early example of which is Hawking's original derivation of the Hawking radiation effect. The limitation of this approach should be obvious--when the Hawking radiation ends up having a mass comparable to the original black hole, how can you trust the result? The Hawking radiation has mass and energy, too, and obviously, this should be factored into the result, but the semiclassical problem explicitly ignores it. (and if you try to do an iterative approach, factoring in the Hawking radiation as a source, and calculating the result, you quickly run into a LOT of complexity)

Non-communative geometry is an active area of research and a potential solution, albeit one chosen by a minority of researchers

Zo the Relativist
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