But general relativity and quantum theory contradict each other. They cannot both be correct. Therefore at least half of physics is wrong.

Your first sentence is correct, your second is missing a qualifier, your third is plain wrong. GR and QM are valid each in their own domain. They don't mesh together well, so something has to give in between the two domains. A modification, a wholly different model, something else we have no idea about. It's a consensus in the field that a new revolutionary idea is needed, you are right. And that thousands of smart but "narrowly specialized postdocs" are unlikely to get us there. The five great problems are a good summary of our current views, but I suspect that to make progress in solving, say, #1, the problem itself would have to be restated completely differently. But good luck with learning more about fundamental physics. It's a difficult and thankless task, as close to an efficient market as possible, with no profit to be made unless you have something that the likes of Witten have overlooked. You'll need a lot of sweat and a lot of luck.

Does there anywhere exist a community of folks you might work on this with who aren't derisive of this approach, woefully uninformed on the specifics (I think that's broadly the issue here on LW; we're not selecting for physicists of the sort you'd like to talk to even if there are a lot of them here), or cranks?

My experience has been that it's very helpful to have supportive folks who can at least a little bit appreciate what you are doing and offer feedback, even if you are going super deep in some direction such that you are the expert in ways that means they will often be mistaken even if they can help you avoid making obvious mistakes.

In Smolin's view, the scientific establishment is good at making small iterations to existing theories and bad at creating radically new theories.

I agree with this.

It's therefore not implausible that the solution to quantum gravity could come from a decade of solitary amateur work by someone totally outside the scientific establishment.

For me, this sounds very implausible. Although the scientific establishment isn't geared towars creating radically new theories, I think it is even harder to create such ideas from the outside. I agree that most researchers in acadamia are narrowly specialized and not interested in challenging widely shared assumptions but the people who do are also in acadamia. I think that you focus too much on the question-the-orthodoxy part. In order to come up with something useful you need to develop a deep understanding and to bounce around ideas in a fertile environment. I think that both have become increasingly difficult for people outside of acadamia because of the complexity of the concepts involved.

The evidence you cite doesn't seem to support your assertion: Although Rovelli holds some idiosynratic ideas, his career path led him through typical prestigous institutions. So he certainly cannot be considered to stand "totally outside the scientific establishment".

Smolin's book has inspired me to begin working [LW · GW] on a theory of quantum gravity. I'll need to learn new things like quantum field theory.

If you don't know Quantum Field Theory, I don't see how you can possibly understand why General Relativity and Quantum Theory are difficult to reconcile. If true, how are you able to work on the solution to a problem you don't understand?

Look for a system where the predictions of GR contradict, or at least interact with, the predictions of QM. If there is no such system, then the contradictions are more metaphysical than empirical.

I've wondered for a while if the gravitational anomalies ascribed to dark matter/energy could be the result of linear frame dragging through the quantum fields. The basic idea is:

1) QM says there's a lot of "zero-point energy" surrounding us in every direction related to the quantum fields.

2) This energy has no gravitational consequences because it's pulling equally in every direction.

3) Relativistic linear frame dragging might break that symmetry with gravitational consequences.

I don't have the background to go further with the idea, or even to tell whether it's blatantly stupid. It's a stray thought; if you can make something of it, feel free.

This might be tenable if the foundations of physics (general relativity and quantum theory) were plausibly true. But general relativity and quantum theory contradict each other. They cannot both be correct. Therefore at least half of physics is wrong.

I also don't think the logic of the argument quite holds.

My take is we can interpret the situation better via a clock metaphor. Specifically the old staying about running and stopped watches. The running one is almost always wrong while the stopped (broken/not running) one is correct twice a day (assuming the 12 hour clock).

I don't disagree with the general sentiment here, but think a better way to approach it might be recognizing the essentially all of physics is incomplete. One of the ways this manifests in the science is that disagreement between the quantum and macro theories.

Do you think that the True Fundamental Laws of Physics are definitely not string theory (or anything mathematically related to string theory)? If so, why?