Are we living in the matrix? No.

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Discussion Overview

The discussion revolves around the feasibility of simulating the known laws of physics on a computer, particularly in the context of lattice chiral fermions and the implications of the Nielsen-Ninomiya theorem. Participants explore various approaches to overcoming challenges in simulation, while also engaging with the philosophical question of whether we might be living in a simulated reality.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • David Tong's talk suggests that simulating the known laws of physics on a computer is fundamentally problematic due to the Nielsen-Ninomiya theorem.
  • Some participants argue that the fermion doubling problem can be addressed through methods like adding the Wilson term, which breaks chiral symmetry but allows for simulation.
  • Another approach mentioned is the use of discretization schemes, such as those proposed by Frensley, to avoid fermion doubling in simulations of Dirac/Weyl materials.
  • One participant distinguishes between simulating the laws of physics and creating a computer simulation of the universe, suggesting that the latter involves more complex considerations, particularly regarding consciousness and quantum mechanics.
  • There is a suggestion that hard coding specific outputs could be a method of simulation, though this raises questions about the nature of such simulations.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the Nielsen-Ninomiya theorem and the feasibility of simulating physical laws. While some propose methods to overcome the challenges, others question the fundamental nature of simulation in relation to consciousness and reality. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants highlight limitations related to the assumptions underlying the Nielsen-Ninomiya theorem and the implications of discrete versus continuous simulations. The relationship between consciousness and quantum mechanics is also presented as a complex factor that may influence the discussion.

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.