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I recently learned that the physical world is also undecidable. For example, the spectral gap problem in quantum mechanics is one such problem. Scientists have

I recently learned that the physical world is also undecidable. For example, the spectral gap problem in quantum mechanics is one such problem. Scientists have proven that no matter how perfectly and completely we can mathematically describe a material on the microscopic level, we're never going to be able to predict its macroscopic behavior. This has profound implications, such as for the possibility of a theory of everything. This does not necessarily mean that a theory of everything is impossible, but it does indicate that such a theory might not be able to provide a complete description or prediction of all physical phenomena, which is contrary to the belief of some physicists.

VirusNewbie 3y ago
>Scientists have proven that no matter how perfectly and completely we can mathematically describe a material on the microscopic level, we're never going to be able to predict its macroscopic behavior Surely this has more nuance, as it is some ways we can falsify the statement as is
- Kranar 3y ago
  Yes there absolutely is nuance. The mathematics used to determine whether a quantum system has a gap or not is indeed undecidable, but that undecidability only kicks in as the size of your system approaches infinity. For any finitely sized system, basically any actual system in the universe, the solution is computable/decidable.
snarkconjecture 3y ago
There is of course a catch, since physics can be simulated (with an exponential slowdown) by a Turing machine. The catch is that "macroscopic behavior" in this context includes things that are not really macroscopically observable, or require conditions that cannot easily be specified. For the spectral gap, I think the way this manifests is that you can't ever be certain that you're in the ground state, but I'm not sure this is correct.
- klyrs 3y ago
  > since physics can be simulated I must object. Our current models of physics can be simulated. But we cannot model what we do not understand, such as quantum gravity. And even then, we don't even have that many decimal places for certain bits of our models.
  - zeroonetwothree 3y ago
    By definition the universe can “simulate” itself. Although it’s true we have no proof that this doesn’t go beyond Turing machine in power (yet it’s a reasonable assumption). Of course the goal of physics is to compress the universe into simpler laws. But there’s no inherent reason that it should be possible.
    - User23 3y ago
      > By definition the universe can “simulate” itself. A 1:1 scale map is still just a map. Simulation isn't an identity operation. > yet it’s a reasonable assumption What are the reasons for this claim?

VirusNewbie 3y ago

>Scientists have proven that no matter how perfectly and completely we can mathematically describe a material on the microscopic level, we're never going to be able to predict its macroscopic behavior Surely this has more nuance, as it is some ways we can falsify the statement as is

Kranar 3y ago
Yes there absolutely is nuance. The mathematics used to determine whether a quantum system has a gap or not is indeed undecidable, but that undecidability only kicks in as the size of your system approaches infinity. For any finitely sized system, basically any actual system in the universe, the solution is computable/decidable.

snarkconjecture 3y ago

There is of course a catch, since physics can be simulated (with an exponential slowdown) by a Turing machine. The catch is that "macroscopic behavior" in this context includes things that are not really macroscopically observable, or require conditions that cannot easily be specified. For the spectral gap, I think the way this manifests is that you can't ever be certain that you're in the ground state, but I'm not sure this is correct.

klyrs 3y ago
> since physics can be simulated I must object. Our current models of physics can be simulated. But we cannot model what we do not understand, such as quantum gravity. And even then, we don't even have that many decimal places for certain bits of our models.
- zeroonetwothree 3y ago
  By definition the universe can “simulate” itself. Although it’s true we have no proof that this doesn’t go beyond Turing machine in power (yet it’s a reasonable assumption). Of course the goal of physics is to compress the universe into simpler laws. But there’s no inherent reason that it should be possible.
  - User23 3y ago
    > By definition the universe can “simulate” itself. A 1:1 scale map is still just a map. Simulation isn't an identity operation. > yet it’s a reasonable assumption What are the reasons for this claim?