Are we living in the matrix? No.

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SUMMARY

The discussion centers on the feasibility of simulating the known laws of physics on a computer, referencing the Nielsen and Ninomiya theorem, which asserts that such a simulation is impossible. David Tong's talk highlights recent attempts to address this theorem, particularly through the paper "Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Mod" by Meng Zeng et al. Participants argue that while elegant simulations may be unattainable, practical simulations can still be achieved by techniques such as adding the Wilson term or using discretization schemes like Frensley’s approach. The conversation also distinguishes between simulating physics and creating a computer simulation of our universe.

PREREQUISITES
  • Understanding of the Nielsen and Ninomiya theorem
  • Familiarity with lattice chiral fermions
  • Knowledge of Wilson term in quantum field theory
  • Basic concepts of discretization schemes in physics simulations
NEXT STEPS
  • Research the implications of the Nielsen and Ninomiya theorem on quantum simulations
  • Study the paper "Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Mod" for advanced simulation techniques
  • Explore the use of Wilson terms in lattice quantum field theory
  • Investigate discretization methods like Frensley’s approach for simulating Dirac/Weyl materials
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Physicists, computer scientists, and researchers interested in quantum simulations, lattice field theory, and the philosophical implications of simulating the universe.

atyy
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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
 
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atyy said:
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.
 
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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.
 
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Morbert said:
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?
 
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Demystifier said:
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.
 
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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.