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].
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.
This is not really necessary tho; it only requires that the mathematical model has a certain arithmetic complexity. The usual demo is Robinson Arithmetic, which is addition, multiplication on the natural numbers, and a successor operation.
Godel then latches onto that to create an alphabet of the symbols which then are mapped to numbers; thus formulas are even bigger numbers, and derivations are even bigger bigger numbers. So for any statements there should be a derivation that prove the statement is true or a derivation that proves the statement is false. Of course most statements will be false, but even then there will be a derivation showing so.
Then Godel does some clever manipulation to show that there will be some statements for which there can be no such derivation in either way. But that does not need the physics theory to express things about itself. It only requires to be mathematically complex enough (it'd be weird if a theory of everything was simpler than Robinson Arithmetic) and that it has rules of derivation of its statements (ie, that mechanical math can be applied to deduce the truth of the matter from the first principles of the theory).
Of course, the actual undecidable godel number and the associated physical proposition would be immensely complex. But that is only cause nobody has tried to improve on Godel's methodology of assigning numbers to propositions. He used what was simpler, prime factorization, cause it was easy to reason about, but results in astronomical numbers. But there is no reason a better, less explosive way of encoding propositions could be found that made an undecidible Godel number to be translated into something comprehensible.
But this is largely unnecessary; Godel proof forces the mathematical system to speak about itself and then abuses this reflection to create a contradiction. It means the system is not complete, that there are statements in the system that cannot be proven from its first principles and derivation rules; the fact that the one Godel showed to exist is self referential does not mean all the undecidable propositions _are_ self referential. There well could be other, non self referential undecidable propositions, that could very well have a comprehensible physical interpretation.
And, regardless of the universe being a simulation or not, the physical theory will ultimately need to deal with this incompleteness.
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?
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.
There is no disagreement about that. But the simulation hypothesis claims that is is more likely that what we perceive as reality is a simulation, run by someone else, than that we are in "real" world.
I think it is worse hypothesis than even Drake's equation - there, at least we know all factors, we just have no idea what their value is and with sample size of 1, the current uncertainly is like 40+ orders of magnitude. That still brings us closer to "is there inteligent life in universe" answer than we ever got with "is this universe a simulation".
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.
A simulation to what purpose ? What's the difference between a simulation and reality ? What is more "real" about the original hardware than about us ?
It doesn't make obvious sense to waste such vast amount of energy for absolutely no purpose that we can observe: surely you could add a grain of doubt in your absolute statements no ?
The universe is probably nothing very interesting, and reality depressingly obvious once we figure it out. It's like all these astrological sky maps they were doing to predict the mood of the gods above, before we realized we were a rock turning around an hydrogen ball, itself turning around the galactic center, completely non-special, like every other block of rock out there.
Being in a simulation is just a way for you to replace god with a machine equivalent. You want a purpose, a father figure, an observer and a designer. Sadly, I think you and I are as precious as an ant, completely not part of any simulation, having no purpose and barely any effect on the universe. We're here because we could and we'll disappear because we must, with barely a blip, while everything in the universe is turning around senselessly.
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[ 2.8 ms ] story [ 24.7 ms ] threadThe 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.
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.
Godel then latches onto that to create an alphabet of the symbols which then are mapped to numbers; thus formulas are even bigger numbers, and derivations are even bigger bigger numbers. So for any statements there should be a derivation that prove the statement is true or a derivation that proves the statement is false. Of course most statements will be false, but even then there will be a derivation showing so.
Then Godel does some clever manipulation to show that there will be some statements for which there can be no such derivation in either way. But that does not need the physics theory to express things about itself. It only requires to be mathematically complex enough (it'd be weird if a theory of everything was simpler than Robinson Arithmetic) and that it has rules of derivation of its statements (ie, that mechanical math can be applied to deduce the truth of the matter from the first principles of the theory).
Of course, the actual undecidable godel number and the associated physical proposition would be immensely complex. But that is only cause nobody has tried to improve on Godel's methodology of assigning numbers to propositions. He used what was simpler, prime factorization, cause it was easy to reason about, but results in astronomical numbers. But there is no reason a better, less explosive way of encoding propositions could be found that made an undecidible Godel number to be translated into something comprehensible.
But this is largely unnecessary; Godel proof forces the mathematical system to speak about itself and then abuses this reflection to create a contradiction. It means the system is not complete, that there are statements in the system that cannot be proven from its first principles and derivation rules; the fact that the one Godel showed to exist is self referential does not mean all the undecidable propositions _are_ self referential. There well could be other, non self referential undecidable propositions, that could very well have a comprehensible physical interpretation.
And, regardless of the universe being a simulation or not, the physical theory will ultimately need to deal with this incompleteness.
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.
I think it is worse hypothesis than even Drake's equation - there, at least we know all factors, we just have no idea what their value is and with sample size of 1, the current uncertainly is like 40+ orders of magnitude. That still brings us closer to "is there inteligent life in universe" answer than we ever got with "is this universe a simulation".
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.
It doesn't make obvious sense to waste such vast amount of energy for absolutely no purpose that we can observe: surely you could add a grain of doubt in your absolute statements no ?
The universe is probably nothing very interesting, and reality depressingly obvious once we figure it out. It's like all these astrological sky maps they were doing to predict the mood of the gods above, before we realized we were a rock turning around an hydrogen ball, itself turning around the galactic center, completely non-special, like every other block of rock out there.
Being in a simulation is just a way for you to replace god with a machine equivalent. You want a purpose, a father figure, an observer and a designer. Sadly, I think you and I are as precious as an ant, completely not part of any simulation, having no purpose and barely any effect on the universe. We're here because we could and we'll disappear because we must, with barely a blip, while everything in the universe is turning around senselessly.