The central claim in particular is not proven because a physical theory P need not be able to express statements like "there exists a number G, which, when interpreted as the text of a theory T, essentially states that the theory T itself is unprovable in the broader physical theory P" as an empirical physical fact.
It's also very hard to verify the sources for some claims: I would expect the snag to be that many model theory results we have (Such as Gödel theorems) require quantifying over an infinite set, but that seems plausibly not possible to model in the physical universe. I quickly found this quote from the paper:
> Arithmetic expressiveness; LQG can internally model the natural numbers with
their basic operations. This is important as quantum gravity should reproduce calculations used for amplitudes, curvature scalars, entropy, etc in appropriate limits. Both string theory [34, 37] and LQG [35, 38] satisfy this by reproducing GR and QM in appropriate limits
Here the citations are four entire books. How am I supposed to very that LQG can model N with that?
The universe is a simulation, question is whether we're running on original hardware or not.
Seems at best they may have proved you can't simulate the universe on hardware that exists within this universe, which is a bit of a no-duh kinda thing.
Imagine running a simulation in our universe and using a hardware random generator. And AI mathematicians inside your simulation proclaiming confidently that it would be impossible for them to be in a simulation because all randomness must be algorithmic and thus impossible to generate such randomness.
Would be fascinating if true, but I'd be very curious what kind of model of "reality" they actually have.
The paper itself [1] seems quite compact and extremely high level, so I'm sure some heavy hitters would try to reformulate it. Would be the most unintuitive thing to happen since Bell's theorem [2].
I think you nailed it. There are true statements which cannot be proven, yes. But those could be true statements also in the simulated universe. The simulation does not need to calculate the correct ANSWER to every question.
Even if they prove our universe can’t be simulated in a computer built the way we build them, how can they prove there aren’t other ways to build computers?
Yea I mean a more generic version of the simulation theory is just that there is an "outside world" within which our universe exists in containment. Seems probably impossible to disprove (or prove) that for the same reason that proofs about the existence of God are hard.
But, making proofs about the capabilities of the exact types of computation we currently use can still be interesting.
The way we build computers can’t simulate quantum fields. Just means our computers are limited.
Doesn’t mean the universe isn’t a simulation.
Everything you perceive is through the brain. Brain could be in a jar receiving the same neuron signals, it wouldn’t be able to know if it is in a simulation or not.
There is no way for a program to know if it’s inside a virtual machine or not.
The central claim in particular is not proven because a physical theory P need not be able to express statements like "there exists a number G, which, when interpreted as the text of a theory T, essentially states that the theory T itself is unprovable in the broader physical theory P" as an empirical physical fact.
> Arithmetic expressiveness; LQG can internally model the natural numbers with their basic operations. This is important as quantum gravity should reproduce calculations used for amplitudes, curvature scalars, entropy, etc in appropriate limits. Both string theory [34, 37] and LQG [35, 38] satisfy this by reproducing GR and QM in appropriate limits
Here the citations are four entire books. How am I supposed to very that LQG can model N with that?
Seems at best they may have proved you can't simulate the universe on hardware that exists within this universe, which is a bit of a no-duh kinda thing.
Imagine running a simulation in our universe and using a hardware random generator. And AI mathematicians inside your simulation proclaiming confidently that it would be impossible for them to be in a simulation because all randomness must be algorithmic and thus impossible to generate such randomness.
The paper itself [1] seems quite compact and extremely high level, so I'm sure some heavy hitters would try to reformulate it. Would be the most unintuitive thing to happen since Bell's theorem [2].
[1] https://jhap.du.ac.ir/article_488.html
[2] https://en.wikipedia.org/wiki/Bell%27s_theorem
It wasn't stated why all truths need to be provable though. Perhaps the paper goes into this detail that I'd like explained.
But, making proofs about the capabilities of the exact types of computation we currently use can still be interesting.
Doesn’t mean the universe isn’t a simulation.
Everything you perceive is through the brain. Brain could be in a jar receiving the same neuron signals, it wouldn’t be able to know if it is in a simulation or not.
There is no way for a program to know if it’s inside a virtual machine or not.