## Stephen Wolfram’s Theory of Everything

On April 14, 2020 Stephen Wolfram published a long article summarizing the results of his research towards a fundamental theory of physics. He does not use the terminology “ToE” (Theory of Everything) but many science journalists and scientists refer to this as Wolfram’s Theory of Everything.

Early response by physicists are rather critical of Wolfram’s approach to physics. Adam Becker’s article in the Scientific American reflect these negative views.

I have spent a weekend to read Wolfram’s long and difficult text representing distilled knowledge from almost 50 years of intense work. After reading it, all I could say was “Wow!” Being a lazy person, I admire people like Wolfram who have the capacity and drive to work tirelessly.

It is difficult to write a comprehensive commentary. Here’s my random comments.

Philosophically, I believe in multiple perspectives. My initial assessment is that Wolfram approach to physics will be one of many possible perspectives. There are other perspectives already: geometric approach to physics, algebraic approach to physics, Twistor Theory, qubit networks, etc. He claims that other approaches such as String theory and Loop-Quantum-Gravity (and possibly others) will all emerge from his system.

I was a little taken aback to read about finding “the rule of the universe”. Why does he look for a fixed rule? But then, towards the end of the article, he allows that maybe the universe is running all possible rules. In my opinion, “rules” can change, we should allow for this possibility. But then, the entire project becomes hopelessly intractable.

I have read somewhere that self-organizing schemes based on fixed rules generate limited complexity. His schemes seem to be generating enough complexity, but I am not sure.

The main obstacle in his approach to physics is what he calls “computational irreducibility”. We have to apply the rule zillions of times. This is computationally costly. But, he says that “there’s a lot one can understand before one hits computational irreducibility”. He also says that there are “tunnels of computational reducibility”.

Speaking of “rules”, any mathematical mapping is a  “rule”, I suppose. Graph theory is part of mathematics so Wolfram approach is still mathematical even though he would not accept that description. He says his approach is “computational” as opposed to “mathematical” per se.

I am in agreement with his views on “space”. He says “Underneath, it’s a bunch of discrete, abstract relations between abstract points”. In my post titled On the emergence of space and time I described various views and at the end mentioned my prejudice on the order of emergence (space -> time -> matter). On this Wolfram has a rich and detailed answer. It will be worthwhile to revisit his answer and try to understand better.

His comments on “energy” are very interesting. “…energy corresponds to the flux of causal edges through timelike hypersurfaces….energy is associated with activity in the hypergraph that propagates information”.

Each “step” in applying the rule involves multiple “updating events”. This reminded me what happens with virtual particles. Indeed, he sees this connection as well. He ties the “updating events” to “many histories”, Feynman approach, etc.

Repeated application of the “rule” and the evolving graph represents a type of confinement. I am trying to develop ideas based on confinement/liberation duality. As a generalization, I say that any type of “confinement” action will be countered by “liberation” reaction. We may be able to discover the modalities of the confinement/liberation interplay but there will always be some intrinsic uncertainty because modalities evolve, in my opinion. In Wolfram language this would correspond to changing “rules”.

His “oligons” reminded me the “microvita”.

Planck scale: $10^{-35}$ meter , Wolfram scale: $10^{-93}$ meter. Wow!

I believe in the motto “simple, explanatory, predictive”. I am not sure Wolfram project can fulfill this ideal.

In terms of categories, he mentions “physical space”, “branchial space”, “rule space”. I like these categories.

He answers the question “Could there be other universes?” as follows: “The answer in our setup is basically no….because in a sense our universe already contains all possible rules, so there can only be one of it”.

He thinks that the fundamental theory of physics will have similarities to language design. My intuition tells me that this is worth pursuing.

I just don’t see physics PhD students jumping on the Wolfram bandwagon. It will be long time before the academic world joins in this great project. But, it does not matter. He is well prepared to continue and grow this project using the resources of his company.

Stephen Wolfram is making great contributions to science. I congratulate him and wish him success.

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