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The two big mistakes of the twentieth-century physics

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I would like to share an excerpt from the lecture Science beyond the Horizon: Stephen Wolfram on a Fundamental Theory of Physics given at the Institute for Advanced Studies of the UvA, where it is mentioned that in twentieth-century physics there were two big mistakes:

Mistake in Special Relativity: The assumption that space and time are the same kinds of thing (spacetime). The scientist responsible for this mistake is Hermann Minkowski and there is evidence that Einstein disliked this approach. For a correction of this mistake in the Wolfram Model, read Time and Spacetime.

Mistake in Quantum Mechanics: The assumption that magnitude and phase of a quantum amplitude come from the same place. The responsibility for this mistake could be shared among the fathers of quantum mechanics. For a correction of this mistake in the Wolfram Model, read Quantum Formalism.

Understanding the correction of these errors is an important advance in the initiation of the Wolfram Physics Project.

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It is a bit of an overstatement to call them "mistakes". Both principles work great and are satisfied to the highest precision we could achieve.

I believe, what Wolfram meant, is that the assumption that the fundamental "theory of everything" must reside on the aforementioned principles may not be true, and the principles can emerge from simpler structures. Actually, there have been many successful attempts to "emerge" gravity and special relativity from non-Lorentz invariant structures.

I am not sure about Wolfram's point about phase and amplitude of the wave function, since there is no underlying symmetry between the phase and the amplitude in Shoroedinger's equation. As far as I know, writing Shroedinger's equation for the general wave function (as opposed to amplitude and phase separately) requires only linearity and unitarity of the evolution. Does Wolfram model violate any of those?

Concerning

It is a bit of an overstatement to call them "mistakes". Both principles work great and are satisfied to the highest precision we could achieve.

we can say the same for Flat Earth theory: it works great in everyday life, but it was a scientific mistake. A Flat Earth worldview would avoid the use of satellites among other engineering advances. A worldview where the above-mentioned mistakes are taken for granted may prevent new scientific revolutions, e.g., S. Wolfram was able to propose a way to travel faster-than-light by overcoming the mistake of considering spacetime in the same way as H. Minkowski did. There is a way to experimentally test that spacetime is not as H. Minkowski proposed, but as S. Wolfram proposed: measure whether the interior of a black hole causally influences its environement (if this happens, then faster-than-light travel was realized in nature). In other words, in the Wolfram Model, black holes are just an approximation, they are not absolutely black, since there may be microscopic space tunnels between the interior of the black hole and the exterior.

Concerning

As far as I know, writing Shroedinger's equation for the general wave function (as opposed to amplitude and phase separately) requires only linearity and unitarity of the evolution. Does Wolfram model violate any of those?

at the end of the paper

J. Gorard, “Some Quantum Mechanical Properties of the Wolfram Model,” Complex Systems, 29(2), 2020 pp. 537–598. https://doi.org/10.25088/ComplexSystems.29.2.537

the time-dependent Schrödinger equation (equation (152)) is derived as a variation of the diffusion equation in graphs. Notice the role of the branchial space, related to phase (page 589):

Our diffusion equation assumes the form of a Schrödinger equation rather than a regular heat equation because of the presence of imaginary branchlike distances in the discrete multiway metric.

This graph-theoretic approach is a proposal to overcome the restrictions (no-go theorems) of traditional physics, based on the mathematics of the continuum.

we can say the same for Flat Earth theory: it works great in everyday life, but it was a scientific mistake.

I think you are misusing the words. We don't call theories a "mistake". Theories can be "wrong", if their predictions contradict experimental results within the area they claim to be applicable. It doesn't make them a "mistake". A "mistake" is an action that leads you away from your goals. For instance, you can say "Building a theory of everything based on Lorentz invariance is a mistake". Building a theory of everything here is the goal, and building it based on Lorentz invariance is the action, which, according to the author, does not serve the goal well. Calling a scientific theory or parts of the theory a mistake does not make an intelligible sentence and just sounds crackpottish.

If you imply somehow that the assumptions of Lorentz invariance or postulates of quantum mechanics are wrong, it is important to specify the context, that you really mean that they are wrong in the context of the theory of everything. I am not sure that even putting it within the context would make it true, though. It may turn out that the principles of QM or GR are correct (see string theory). There is simply no evidence at this point.

Theories can be "wrong", if their predictions contradict experimental results within the area they claim to be applicable.

Using your terminology, in the case of Flat Earth theory, it does not contradict everyday life experience (taken as experiments). So, it is not "wrong" in this sense, considering everyday life as the area where it is applicable. Of course, in a more precise area, e.g., satellite engineering, it clearly contradicts experiments. So, it is "wrong".

A "mistake" is an action that leads you away from your goals.

According to this definition, if the goal of someone is to put a satellite in orbit, then the Flat Earth assumption is a "mistake" since it prevents the goal.

If you imply somehow that the assumptions of Lorentz invariance or postulates of quantum mechanics are wrong

Using this terminology, the claim of "two mistakes in physics" is not intended to mean that Lorentz invariance and the postulates of quantum mechanics are "wrong", using your definition of "wrong". Indeed, they agree with experiments. The "mistakes" are conceptual, in the sense that the mathematical realization of spacetime and quantum amplitude as a continuum manifold and a complex number, respectively, are rather restrictive. The mathematical realization of spacetime and quantum amplitude as a causal graph and a combination of multiway graph and branchial space, respectively, is more general. Hence, in these formalisms (Wolfram Model), there are fewer restrictions in order to search for a theory of fundamental physics.

It may turn out that the principles of QM or GR are correct (see string theory)

I agree, in string theory, there is a proof that quantum mechanics and general relativity are not mutually exclusive, since they can be developed in the same framework. Indeed, S. Wolfram wrote:

I suspect that the continuum limit of the operations I discuss on character strings is actually related to string theory in the modern physics sense

In the framework of the Wolfram Physics Project, string theory is a triumph of theoretical physics, despite keeping the "two mistakes" mentioned above, not because of it. One of the promises of the Wolfram Model is to reconstruct the results of string theory as a limit case of a discrete framework. If someday the mainstream approach to physics is able to solve all the problems of fundamental physics, which according to Ed Witten are finite in number (see Physics and Geometry), then there will be no reason to consider that the conceptual structure of mainstream physics contains mistakes. Nevertheless, it may happen that the only way to solve these problems is by overcoming the "two mistakes" mentioned above. Therefore, the status of "mistakes" of the two claims is relative to the Wolfram Model, i.e., if the Wolfram Model can be used as an accurate description of nature, then the "two mistakes" mentioned above are actually mistakes.

I must side with Pavlo. Saying that Minkowski and Einstein and others did a mistake really sounds crackpottish. It sounds like we should throw away general relativity and quantum mechanics because they were mistakes. Of course it is not the case, because both theories are perfectly capable of explaining a plethora of new phenomena: "success" is better suited than "mistake" to describe them.

But I am sure that Wolfram didn't mean to discredit Minkowsky and the others for their great work. I just dislike the wording, that makes the statement sound presumptuous and crackpottish

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