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It is often written that the simulation hypothesis cannot be proven or disproved. There is also a lot of talk about the fact that the simulation hypothesis is not science.

But the people also write that future experiments on the Planck scale will be able to prove the simulation hypothesis. Quantum space and time or quantum information is often discussed as proof of the simulation hypothesis.

Tell me please:

Has science proven that the simulation hypothesis is true?

Has science proven that we all live in a simulation?

Does science have evidence that the simulation hypothesis is true.

Does science have evidence that the simulation hypothesis will be true in the future?

Does science have reason to believe that the simulation hypothesis is true?

Does science have reason to believe that the simulation hypothesis will be true in the future?

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    $\begingroup$ this is about the closest one can get to it "In the beginning was the Word, and the Word was..." (It is more scientific in the original: Ἐν ἀρχῇ ἦν ὁ λόγος, καὶ ὁ λόγος ἦν πρὸς τὸν θεόν, καὶ θεὸς ἦν ὁ λόγος.) $\endgroup$
    – hyportnex
    Commented Feb 16 at 13:43
  • $\begingroup$ Logos is the big key to what reality is (waxing philosophical here, but with real and genuine conviction). $\endgroup$
    – Albertus Magnus
    Commented Feb 16 at 14:01
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    $\begingroup$ If some hypothetical being were clever and powerful enough to create a detailed simulation of our universe and they did not want us to know that it was a simulation then they would presumably be clever and powerful enough to create a simulation that did not include evidence that it was a simulation. $\endgroup$
    – gandalf61
    Commented Feb 16 at 15:06
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    $\begingroup$ @gandalf61 - but what if that being was, itself, in a simulation where the creator of that one programmed it so the simulation would never allow things in it to preclude evidence of their creation being a simulation. It’s turtles all the way down… $\endgroup$
    – Jon Custer
    Commented Feb 16 at 15:49

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There is no such evidence, and it seems insane to me. Simulation is hard. It takes a massive amount of supercomputer time to accurately simulate even very simple physical systems, while even complicated physical systems behave naturally, on their own, just fine. Simulate a whole universe? With what? A computer orders of magnitude of orders of magnitude more complicated than a universe?

This, incidentally, also speaks to the ideology that mathematics is an unreasonably effective description of physics. It isn't. It may be the best tool we have to abstract general features of physical systems, but generally, real physical systems naturally behave in ways that mathematics struggles to capture in detail.

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    $\begingroup$ It might be that math is flexible enough to model more or less any laws. Simple math (E.G. linear math) is unreasonably effective for a lot of physics. We struggle to come up with more complex math to capture all of physics. $\endgroup$
    – mmesser314
    Commented Feb 16 at 14:27
  • $\begingroup$ @mmesser314 But it's not. In real life, you very quickly hit the limitations of linear math. Looks good on the whiteboard, though... $\endgroup$
    – John Doty
    Commented Feb 16 at 14:39
  • $\begingroup$ An important concept here is complexity theory, which allows you to understand how much computing resources are required for a given problem. You may have heard of things called NP-hard, or NP-complete. There are many classical problems that cannot be solved with a modern computer. Factoring large numbers is an example. $\endgroup$
    – JQK
    Commented Feb 16 at 16:20
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    $\begingroup$ Although I appreciate this earnest answer, it illustrates the problem with even considering the simulation hypothesis. If one’s every observation is illusory, if consensus logic doesn’t exist, then it’s nonsensical to reason one’s way through logic. In other words, you might have been programmed to think that simulation is hard. The concept of computation, and all other concepts you mention, might be illusory, this exchange nonexistent in any sense we would consider real, if we were real. (See the problem?) Ultimately, the original question is simply not a physics question. $\endgroup$
    – Chemomechanics
    Commented Feb 16 at 17:21
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    $\begingroup$ I have to go down the lane of agreeing that the whole thing is outside the realm of science. $\endgroup$
    – Albertus Magnus
    Commented Feb 16 at 17:43
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The first question to ask is, Is Physical Church-Turing Thesis true? That is: can any physical process be simulated on a Turing machine to any desired accuracy (at least probabilistically), given enough information about its initial state? --> This is an open question.

However, there is an interesting example of the problem of simulation called the "fermion doubling problem," whereby if you try to simulate the Standard Model on a computer (ie. using a discrete grid) you end up with a huge problem with a new symmetry emerging that violates all sorts of physics. This exists regardless of how "fine" you make the grid. Is this fundamental? ie. Can someone figure out a way around this? It remains to be seen.

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  • $\begingroup$ +1 This answer speaks to the question as a physicist not a philosopher. What are the observable consequences? $\endgroup$
    – mmesser314
    Commented Feb 16 at 14:30
  • $\begingroup$ A violation of Lorentz invariance, and symmetry properties of the standard model $\endgroup$
    – JQK
    Commented Feb 16 at 15:25
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A universal computer can simulate any physical system with arbitrary accuracy and all that is required for such a system is the ability to implement a small set of computational gates and there are multiple sets of universal gates:

https://www.daviddeutsch.org.uk/wp-content/ItFromQubit.pdf

As a result, if we are living in a simulation, it is impossible for us to know anything about the underlying hardware. By the same token, it is impossible for us to know if the simulator exists and so impossible for us to have any evidence relevant to its existence. As such, the simulation hypothesis has roughly the same scientific status as the idea that the world is just a dream or that god created it five minutes ago, complete with records of billions of years of evolution since the big bang. The simulation hypothesis is pseudoscience.

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    $\begingroup$ You don't need a "small number of gates". You need a transcomputable number of gates selected from a small set of gate designs. $\endgroup$
    – John Doty
    Commented Feb 16 at 13:40
  • $\begingroup$ In principle the complexity of any simulator must be at least as complex as that which it simulates, and in reality, it must be many orders of magnitude more complex. Honestly, this is quite tantamount to saying God. $\endgroup$
    – Albertus Magnus
    Commented Feb 16 at 17:49

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