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Representation of the updates in Wolfram Model by linear operators

POSTED BY: Pavlo Bulanchuk
13 Replies

The ZX paper is meant to answer the requirement

it is imperative to make sure that Wolfram model reproduces quantum mechanics to a satisfactory degree

ZX calculus is an important part of quantum mechanics. The adjective categorical is not about the physics, but about the mathematical framework in which quantum mechanics is expressed. Of course, ZX calculus is not the end of the story, it is just the beginning.

Regarding the presence of dimensional constants in the theory, you can find some ideas in the technical introduction: Units and Scales.

Unfortunately, I cannot help you with your other questions, because I am still trying to understand the other papers on general relativity (which I think that pedagogically precede the one you mentioned).

POSTED BY: Ruggero Valli
POSTED BY: Pavlo Bulanchuk

What is "framework"? By "translating into Wolfram's notation", I meant just enriching words and notations of Wolfram Models to include definitions from ZX calculus.

I prefer to use the word framework, rather than notation, because a framework is conceptual (interaction among several concepts), whereas a notation is just a way to write something.

What do you mean by this? (Me: I agree that differential and integral calculus can be realized and embedded in the general formalism of electromagnetism)

Imagine an intelligent extraterrestrial civilization where the formalism of electromagnetism was discovered before than differential and integral calculus because these people are more related to electromagnetism than to mechanics for some historical reason. Then they visit Earth and they find a textbook of differential and integral calculus. In order to understand this textbook, they will express calculus using their formalism of electromagnetism. For example, in order to understand analytic functions of a complex variable they may say: "people from Earth call analytic function what we call static electric fields in a region of the plane containing no electric charge".

In this sense, calculus can be developed from the formalism of electromagnetism, but for historical reasons, it is done the other way around: electromagnetism is developed using calculus. This is the reason why Bob Coecke used the phrase When worlds collide...in a good way! (his world of categorical quantum mechanics and the world of the Wolfram Model). In the example above, the worlds are the formalism of electromagnetism and the world of calculus.

POSTED BY: Pavlo Bulanchuk
POSTED BY: Pavlo Bulanchuk

I am not sure I see how the paper really helps with the questions in the original post. Could you elaborate, please (I am not particularly knowledgeable in ZX calculus or categorical quantum information theory, so would be nice if you could make your point more or less self-contained)?

POSTED BY: Pavlo Bulanchuk
Posted 5 years ago

Thank you for the link. It was quite helpful in the sense that it clarified that Wolfram considers a single link in the multiway system to contribute about $10^{-116}$ to the phase of the path integral. We could assume this is the fundamental constant of "the" Wolfram model, which represents our universe.

POSTED BY: Updating Name
Posted 5 years ago
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