Can every process in nature be simulated by a Turing Machine or a quantum computer?

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Given any initial condition or value A, A leads to B after a procedure of physics or nature P. Now is there any turing machine or quantum computer that can simulates P,converting A into B? In other word, is any cause-effect relation in nature computable?

XL _At_Here_There

Posted 2020-04-24T01:23:36.707

Reputation: 117

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Hi @XL_At_Here_There, welcome to QCSE. It seems like you are asking if a quantum Turing machine simulate a Laplace Demon. But right now the wording of the question is a bit confusing. Can you consider revising your question in the formalism of quantum computing, if you can? Are $A$ and $B$ states, and $P$ an operation acting on $A$ to convert it to $B$?

– Mark S – 2020-04-24T17:19:36.220

states? maybe, but it does not matter. – XL _At_Here_There – 2020-04-26T11:55:02.023

I would counsel you to make an effort to clarify your question, or accept @gIS's already informed answer. – Mark S – 2020-04-26T18:02:54.137

Answers

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As far as we know, yes. This is essentially the Church-Turing thesis. Note that this is not a mathematical result, but more of a definition of what it means to be computable. You can find plenty of discussions about this around. A few notable examples are:

  1. What would it mean to disprove Church-Turing thesis? (on cstheory)
  2. Extended Church-Turing Thesis [and QC] (on cstheory)
  3. Why do we believe the Church-Turing Thesis? (on math)
  4. Can a Turing machine simulate a quantum computer? (here)

glS

Posted 2020-04-24T01:23:36.707

Reputation: 12 247

so, we have to believe or prove that any cause-effect relation in nature is computable, or any process P in nature is computable. I think this may be wrong. And it is not about CT-Thesis. CT-Thesis. say that the computability is Turing computability. – XL _At_Here_There – 2020-04-26T08:59:37.990

1you cannot prove that "any cause-effect relation in nature is computable", because that is not a mathematical statement. What is true is that every current physical theory is computable. Also, you would be hard-pressed to even think of what an "uncomputable physical theory" would be. In my mind, accepting such a thing would be the same as saying that no physical theory can describe nature. But again, this is more about phylosophy than physics. Also, it has nothing to do with quantum mechanics. Quantum mechanics only enters the discussion when you care about computational hardness. – glS – 2020-04-26T09:06:11.203

1btw, what (I think) you are asking about is often referred to as the "physical Church-Turing thesis". – glS – 2020-04-26T09:08:38.180

Can we prove that "any cause-effect relation in nature is computable" by physical theory? – XL _At_Here_There – 2020-04-26T11:41:57.950

1@XL_At_Here_There I'd say that physics is concerned, by definition, with physical theories, and thus your question is not about physics – glS – 2020-04-26T11:55:56.623

maybe, but don't you think it is an important question? – XL _At_Here_There – 2020-04-26T12:39:51.023