Are we living in the matrix? No.

[atyy]

David Tong gives an interesting talk about the lattice chiral fermion problem here.
https://weblectures.leidenuniv.nl/M...uium/watch/5de33fbc14cd4595a6614ca7683bf71e1d

Abstract: Are we living in the matrix? No. Obviously not. It's a daft question. But, buried underneath this daft question is an extremely interesting one: is it possible to simulate the known laws of physics on a computer? Remarkably, there is a mathematical theorem, due to Nielsen and Ninomiya, that says the answer is no. I'll explain this theorem, the underlying reasons for it, and some recent work attempting to circumvent it.

At the end of the talk, he mentions there might be a breakthrough with the simulations in this paper, although it's unclear if the techniques will extend beyond 1+1D.

Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Mod
Meng Zeng, Zheng Zhu, Juven Wang, Yi-Zhuang You
https://arxiv.org/abs/2202.12355

 

[Demystifier]

is it possible to simulate the known laws of physics on a computer? Remarkably, there is a mathematical theorem, due to Nielsen and Ninomiya, that says the answer is no.

I disagree. There are many ways to fix the fermion doubling problem on the lattice, e.g. by adding the Wilson term to the action. This breaks the chiral symmetry (in agreement with the Nielsen-Ninomiya theorem), but the breaking can be made arbitrarily small. An ugly feature is that this requires a fine tuning of a certain free parameter, but ugly simulation is still a simulation. It is one thing to claim that a simple elegant simulation on a computer is impossible (which is true), but completely another thing to claim that any kind of simulation on a computer is impossible (which is wrong).

So, are we living in the matrix? Maybe, but the code must be complicated.

 

[Morbert]

You can also just use a discretisation scheme a la Frensley to get rid of Fermion doubling. Lots of device physicists use that approach to simulate Dirac/Weyl materials.

 

[atyy]

You can also just use a discretisation scheme a la Frensley to get rid of Fermion doubling. Lots of device physicists use that approach to simulate Dirac/Weyl materials.

Could you give a pointer to papers on this?

 

[PeroK]

So, are we living in the matrix? Maybe, but the code must be complicated.

Or, you simply hard code a specific output. That's then just a lot of preset data.

 

[Morbert]

Could you give a pointer to papers on this?

E.g. https://arxiv.org/abs/1510.08424

 

[.Scott]

David Tong seems to be mixing two separate problems.
The first is to simulate the laws of Physics on a discrete computer.
The second is to create a computer simulation of our universe that could host us.

The difference is that first project gives us a view from the outside - where we can look at the methods that are attempting to fool us, disprove it, and describe the experiment that would make it fail.
The second project places us in the simulation where our experiments to disprove the simulation are, themselves, simulations.

I would claim that the universe cannot be simulated on a discrete computer for an entirely different reason: I believe that consciousness is a part of quantum superpositions and human consciousness is that kind of QM information processing applied to human survival problems. Since we are conscious, perhaps within this matrix, either our brains or the Matrix uses more than discrete components.