<p>Since we don't know the ultimate physical laws of the universe, and we would need to know them (or at least know much more about them than we do now) to prove Feynman's conjecture, his conjecture is still a conjecture, and is likely to remain so for some time.</p>
<p>However, almost all the arguments you put forward against the conjecture do not hold water.</p>
<p>Your first argument against Feynman's conjecture is that Xia Zhihong has proved that there are situations in which a physics body can reach infinite velocity at finite period of time. His proof assumes that the Newton's law of gravitation holds, and that point masses exist. The Newtonian laws are incorrect; they are inconsistent with observation, which favors general relativity over Newton's laws of gravitation.</p>
<p>Your second argument against Feynman's conjecture is that analog computers cannot be simulated by digital ones. For analog computers to hold, the laws of physics must involve continuous quantities, and we have no observational evidence that there are continuous quantities (as opposed to quantum quantities) in the laws of physics.</p>
<p>Your third argument against Feynman's conjecture is a paper that shows that it is undecidable to determine if there is a spectral gap between the ground state of a Hamiltonian and the lowest excited state. This doesn't show that there is a physical procedure that is not simulatable by quantum computers. For one thing, any finite-dimensional physical system has a spectral gap. So to show that a physical procedure can decide between these two cases, you have to be able to build an infinite-dimensional quantum system. And another reason is that there is no physical experiment which can decide whether a spectral gap is <span class="math-container">$0$</span> or <span class="math-container">$10^{-50}$</span>.</p>
<p>And the main point of the Spectrum article is that building a quantum computer is really, really hard. I don't think that this fact says much about Feynman's conjecture.</p>

CC BY-SA 4.0
2023-12-25T07:32:29.200Z
Merry Christmas！ So you agree  that what  Feynman says about the topic is not  a proof,   it is just a conjecure. We have  to find evidence to refute  or  prove it.  As I think other question over and over  again,  I think some  other statement   that look like correct   imply Feynman's conjecture  is not correct.
XL _At_Here_There
CC BY-SA 4.0
2024-09-08T11:38:16.653Z
Two articles that try to prove there are physics procedures which can nont simulated by Turing Machine / quantum computer.

https://academic.oup.com/philmat/article-abstract/1/2/97/1482843?redirectedFrom=fulltext&login=false

https://www.sciencedirect.com/science/article/pii/000187088390004X
XL _At_Here_There
CC BY-SA 4.0
2023-12-24T16:40:14.393Z
2023-12-24T16:40:14.393Z
Peter Shor 
<p>Richard Feynman says that all quantum procedures are able to be simulated by  quantum computation，but his argument is not rigid, it seems to be a conjecture.</p>
<p>Is there any physics/math argument supporting the 'conjecture'?</p>
<p>Negatively, I know Xia Zhihong has proved that there is a theoretically physics procedure in which a physics body can reach infinite velocity at finite period of time. And I vaguely remember that analog computer can not be simulated by digital one, which means that analog computer can compute some problems of what Turing Machine can not compute.</p>
<p><strong>Update:</strong> Two articles that try to prove there are physics procedures which can nont simulated by Turing Machine / quantum computer.</p>
<p><a href="https://academic.oup.com/philmat/article-abstract/1/2/97/1482843?redirectedFrom=fulltext&amp;login=false" rel="nofollow noreferrer">https://academic.oup.com/philmat/article-abstract/1/2/97/1482843?redirectedFrom=fulltext&amp;login=false</a></p>
<p><a href="https://www.sciencedirect.com/science/article/pii/000187088390004X" rel="nofollow noreferrer">https://www.sciencedirect.com/science/article/pii/000187088390004X</a></p>

CC BY-SA 4.0
2023-12-23T22:36:37.870Z
The theoretical physics procedure which lets a physics body reach infinite velocity at finite time uses point masses and Newtonian mechanics, neither of which are models of the actual physical world. And because the world is quantum mechanical in nature, it is very doubtful that perfect analog computers also cannot exist in the actual physical world (although very good approximations of them can).
Peter Shor 
CC BY-SA 4.0
2023-12-24T04:33:35.487Z
@PeterShor, nice to meet you, Peter. do you think the article (arxiv.org/abs/1602.05924) is wrong? If it is correct, there must be physical procedure that can not simulated by quantum computation. And quantum physics is theoretical either, what they describe are not exactly consistent with the actual physical world. I think what we say are not argument, and Feynman's argument is just a conjecture.
XL _At_Here_There
CC BY-SA 4.0
2023-12-24T10:46:15.933Z
@PeterShor， https://spectrum.ieee.org/quantum-computing-skeptics
XL _At_Here_There
CC BY-SA 4.0
2023-12-24T11:00:23.767Z
And also I don't know whether $\mathcal{L}$, or $\mathcal{H}$ with the stationary-action principle – also known as the principle of least action together can alway give equation or function of motion, in other word, solvable.
XL _At_Here_There
CC BY-SA 4.0
2024-09-09T03:45:48.603Z
https://wp.optics.arizona.edu/opti646/wp-content/uploads/sites/55/2016/08/Haroche-Raimond.pdf
XL _At_Here_There
<quantum-computing><physics>
Richard Feynman says that all quantum procedures are able to be simulated by quantum computation
XL _At_Here_There
# Richard Feynman says that all quantum procedures are able to be simulated by quantum computation

(Asked by: username_0 on 2023-12-23)

Richard Feynman says that all quantum procedures are able to be simulated by quantum computation，but his argument is not rigid, it seems to be a conjecture.

Is there any physics/math argument supporting the 'conjecture'?

Negatively, I know Xia Zhihong has proved that there is a theoretically physics procedure in which a physics body can reach infinite velocity at finite period of time. And I vaguely remember that analog computer can not be simulated by digital one, which means that analog computer can compute some problems of what Turing Machine can not compute.

**Update:** Two articles that try to prove there are physics procedures which can nont simulated by Turing Machine / quantum computer.

<https://academic.oup.com/philmat/article-abstract/1/2/97/1482843?redirectedFrom=fulltext&login=false>

<https://www.sciencedirect.com/science/article/pii/000187088390004X>

**Tags:** quantum-computing, physics

> **Comments:**
> **username_1**: The theoretical physics procedure which lets a physics body reach infinite velocity at finite time uses point masses and Newtonian mechanics, neither of which are models of the actual physical world. And because the world is quantum mechanical in nature, it is very doubtful that perfect analog computers also cannot exist in the actual physical world (although very good approximations of them can).  
> **username_0**: @PeterShor, nice to meet you, Peter. do you think the article (arxiv.org/abs/1602.05924) is wrong? If it is correct, there must be physical procedure that can not simulated by quantum computation. And quantum physics is theoretical either, what they describe are not exactly consistent with the actual physical world. I think what we say are not argument, and Feynman's argument is just a conjecture.  
> **username_0**: @PeterShor， https://spectrum.ieee.org/quantum-computing-skeptics  
> **username_0**: And also I don't know whether $\mathcal{L}$, or $\mathcal{H}$ with the stationary-action principle – also known as the principle of least action together can alway give equation or function of motion, in other word, solvable.  
> **username_0**: https://wp.optics.arizona.edu/opti646/wp-content/uploads/sites/55/2016/08/Haroche-Raimond.pdf  

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## 1 answers

### Answer by username_1 on 2023-12-24. Score: 7

Since we don't know the ultimate physical laws of the universe, and we would need to know them (or at least know much more about them than we do now) to prove Feynman's conjecture, his conjecture is still a conjecture, and is likely to remain so for some time.

However, almost all the arguments you put forward against the conjecture do not hold water.

Your first argument against Feynman's conjecture is that Xia Zhihong has proved that there are situations in which a physics body can reach infinite velocity at finite period of time. His proof assumes that the Newton's law of gravitation holds, and that point masses exist. The Newtonian laws are incorrect; they are inconsistent with observation, which favors general relativity over Newton's laws of gravitation.

Your second argument against Feynman's conjecture is that analog computers cannot be simulated by digital ones. For analog computers to hold, the laws of physics must involve continuous quantities, and we have no observational evidence that there are continuous quantities (as opposed to quantum quantities) in the laws of physics.

Your third argument against Feynman's conjecture is a paper that shows that it is undecidable to determine if there is a spectral gap between the ground state of a Hamiltonian and the lowest excited state. This doesn't show that there is a physical procedure that is not simulatable by quantum computers. For one thing, any finite-dimensional physical system has a spectral gap. So to show that a physical procedure can decide between these two cases, you have to be able to build an infinite-dimensional quantum system. And another reason is that there is no physical experiment which can decide whether a spectral gap is $0$ or $10^{-50}$.

And the main point of the Spectrum article is that building a quantum computer is really, really hard. I don't think that this fact says much about Feynman's conjecture.

> **Comments:**
> **username_0**: Merry Christmas！ So you agree  that what  Feynman says about the topic is not  a proof,   it is just a conjecure. We have  to find evidence to refute  or  prove it.  As I think other question over and over  again,  I think some  other statement   that look like correct   imply Feynman's conjecture  is not correct.  
> **username_0**: Two articles that try to prove there are physics procedures which can nont simulated by Turing Machine / quantum computer.  https://academic.oup.com/philmat/article-abstract/1/2/97/1482843?redirectedFrom=fulltext&login=false  https://www.sciencedirect.com/science/article/pii/000187088390004X  

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