This is why I very much dislike Popperism. Popperites are convinced "science = falsifiability." If I argue that the universe is made of cheese and the mechanism is a wizard that you can only see through a telescope with a special handcrafted ruby lens that I sell at my shop for $4000, should research institutions be expected to take my claim seriously and buy my ruby lens to test it? I mean, it's technically falsifiable, either they will look through the lens and see the wizard and universe of cheese or they will not. If you are a Popperite you have no choice but to admit that it is a legitimate scientific theory.
There should be more to a scientific proposal than it technically being "falsifiable." Penrose's "theory" is quantum mysticism, it is not a scientific theory just because it is in principle testable.
- He bases it on a claim that Godel's theorem shows certain things are non-computable but we can choose to believe those non-computable things anyways, therefore that proves "consciousness" is non-computable. This is just a comically ridiculous argument. You can program an AI to believe in things it cannot prove as well. It doesn't prove anything.
- He claims that there is a physical collapse of the wave function, with zero evidence to back it, and it is caused by gravity. His theory is incredibly speculative and not compatible with the predictions of quantum mechanics and not even with special relativity, and all attempts to test it have turned out negative.
- He claims that since this "collapse" isn't computable and his comically bad argument #1 shows "consciousness" isn't computable, therefore quantum mechanics causes consciousness, and so we should search desperately for anything in the brain that looks vaguely quantum mechanical as "evidence."
It's even more ridiculous when you realize that microtubles are structural, they don't play a role in information processing in the brain, and you have microtubules all throughout your body. Them having quantum effects in them is meaningless. Even if you could empirically demonstrate without a shadow of doubt that microtubules do somehow create coherent quantum states that the brain makes use of, that would just be an interesting fact on its own. It would not prove #1 or #2. Microtubules are not a "mechanism" for #1 and #2, even if they played a role in decision making as if the brain is a quantum computer (they don't), then you cannot derive from this that somehow quantum mechanics explains why people can believe things without proof (why do I even have to say this, it's so stupid!) or that the reduction of the wave function is a physical process caused by gravity.
There is no good argument to believe even #1 or #2 are tied together. Even if you proved there is indeed a non-local physical collapse and overturned all our modern scientific theories, that wouldn't demonstrate #1 or #3 either. None of the claims in the theory have any obvious connections to one another other than spurious, largely incoherent arguments. This is not his domain of expertise. You could argue #2 is within his domain, but #1 and #3 are nowhere near his domain.
Physicists have proposed speculative physical collapse theories before, like GRW, and we forget about them because they were interesting but went nowhere because there is zero evidence "collapse" is a physical process, and treating it as such requires overturning all of modern physics, as it could not be made compatible with special or general relativity nor could it reproduce the predictions of quantum mechanics, requiring you to rewrite all of physics from the ground-up. The reduction of the wave function is a measurement update, it is epistemic, there is no evidence that it is a physical process.
Even then, theoretical physicists speculate about a lot of things that turn out to go nowhere, that itself is par for the course. But Penrose goes above and beyond this and branches into philosophy, biology, and neuroscience and starts using comically bad arguments to try and tie them all together. Those are not his areas of expertise at all. It reminds me of the old essay Natural Science and the Spirit World from the 19th century that documented a lot of renowned scientists who also had completely crazy side projects, like Alfred Wallace, the guy who co-discovered evolution by natural selection, who believed he could also raise spirits from the dead and converse with them.