An Acataleptic Universe by Philip Gibbs

qsa, thanks for reading the essay. I look forward to seeing your essay. Let's take your points one by one

"1.How does the necklace Lie algebra relate to information theory"

The Lie algebras are pure symmetry. They are not embedded in any space or time and are not particles, The symmetry represents redundant information and the invariants are real information. space, time and matter should emerge from these structures and this is demonstrated by the mapping using interated integration which shows they have an equivalence to string states. Alternativeley these could be particle trajectories if you dont like strings, but I prefer strings. Some of the necklace Lie algebras I have defined in the past take the form of strings of qubits making the information element more explicit.

"2.What does this mathematical structure represent (why this math and not others), since you say it is the origin of matter and space. Do you believe in MUH?"

The structures are just infinite dimensional Lie algebras. While finite dimensional algebras can be classified as Lie groups the infinite dimensional versions are largely unexplored territory and have a rich and complex range of possibilities. I can build higher dimensional structures by a iterative process that I identify with quantisation, but I have not described that in detail here. In a more advanced version I expect these to be q-deformed (another part of quantisation) and it may require higher dimensional algebras like n-categories to get the full workings, I am not sure.

I do go along with the MUH (Mathematical Universe Hypothesis) as postulated by Tegmark and have been writing about similar ideas myself for at least 20 years under the title "Theory of Theories". One element that I add myself is that the mathematics that describe our universe could emerge from the MUH through some principle of universality that applies to the grand ensemble of mathematical possibilities. It could be an algebraic principle of universality rather than a purely statistical process (whatever that means) I don't think anyone else has taken up that idea. The details are of course far beyond what we currently understand.

to be continued...

By the way, I prefer not to use the word "believe" which makes it sound like a quasi-religious idea. I would say that in my opinion this could be a useful way to understand how things work.

"3.Does this theory have anything to do with your last year essay?"

It is related to work in my previous three FQXi essays. I have added a more detailed argument in favour of "complete symmetry" from the holographic principle by relating it to the converse of Noether's second theorem, and I have introduced the iterated integration mapping which is a recent development. these are relevant to the "It from Bit" topic.

"4.Will your theory clearly derive QFT or gravity or calculate the SM constants or CC to name a few."

I hope it will derive QFT and gravity. I am not confident that it will calculate SM constants or dark energy. This is a theory about quantum gravity which is relevant to the Planck scale. the standard model is a theory of the TeV scale and below which is many orders of magnitude lower in energy. The theory at the Planck scale should include all of physics in principle but I think that expecting to derive SM physics from QG is like expecting to derive chemistry or even biology from SM physics but even harder. There is probably a lot of physics in between to account for dark matter, inflation and other stuff we have not yet seen.

"5.Speaking of consistency. Are you really content with the three main forces of SM. The carrier of EM force is "virtual photons" then the weak force you get REAL particles W/Z then the strong is carried by "virtual quarks/gluons" where they all unite at GUT ! Can your theory figure out this mess?"

The difference between photons and gluons vs W/Z is that the former are massless and the latter have mass due to Higgs. gluons are also confined so not seen on-shell. All of them manifest as virtual particles and all exist as real particles (in the case of gluons in deconfined phase). That much is well understood. There are many questions including "why so many parameters" "why is there fine-tuning" "what happens at higher energy" etc. I have no idea what happens at the GUT scale, we have along way to go to answer that. In principle a unified theory at the GUT or Planck scale may answer these questions, but it may also be too difficult to calculate what goes on in detail (as in chemistry, nuclear physics etc.) or there may be some arbitrary element (as in biology, geophysics etc.) such as a vacuum selection that can only be determined by experiment. My aims are ambitious enough but they are not so ambitious as to answer all these questions.

"So far you have done a good job engaging, not like last year, where all the top prize winners were silent, a deafening silence. "

This topic is of more interest to me and there have been good essays already so I am keen to engage where I can. It is always hard to get the professionals involved and we should respect any contribution they make. The change of rules may encourage more of them to join in the commenting, or it may put them off entering, we shall see.

Thank you for your excellent questions. I hope I have gone some way towards answering them.

Very good point, thank you

I know, I will get round to reading it again, there is plenty of time.

Is there a link for that or was it a hardcopy?

The formulation that they used for quantization is probably not too important now. The idea comes from decades ago and is probably a bit dated. I just like the multiple quantisation idea in general. I think Weizsäcker ended up with some large number type arguments that don't really make sense anymore.

Leo, Good to see you over here.

I think bits of information are real but they do not have any physical form or shape themselves. However, they have relationships with each other such as entanglement and these relationships have real form. That is just the way I see it.

I like you pictures. I will reread your essay.

By "form" I mean some kind of geometric representation

I would not say myself that light is information. I would say it carries information and it might be emergent from a theory of pure information.

In any case statements like "It From Bit" "Bit From It" "It Is Bit" etc are just philosophical interpretations. These are just things that help guide us to a more concrete mathematical theory that is consistent with observation. If you think of it a different way round from me I can't argue with it. The important thing is where does it lead to in real operational terms.

OK That is quite interesting. Look at it this way.

If I had a bag full of books I might say that the bag is carrying information in the books. That is clearly different from saying that the bag of books is information. The bag has properties of their own aside from the information.

However, you might say that everything we know about the book and the bag is described by information and there is nothing else. OK I like that way of looking at things but I want to come at it from the other direction. I want to start with some pure information that looks like something more fundamental but then when I look at the information more carefully I find that it has the same characteristics as a book of books. In other words, if I use the information to answer questions in a particular way the answers are the same as I would get playing twenty questions when the answer is a bag of books.

Coming back to light and particles I might start with bits of information on a grid. The information might evolve according to some simple rules. In other words it is a cellular automaton. When I study how the system evolves I might find that different types of particles form an travel across the grid. With luck I might replicate something that looks like the physics of photons. Then I would say that the light was emergent from a theory of pure information.

Some people have looked at cellular automata (Fredkin, Wolfram, etc.) The results are interesting but the problem is that quantum field theory includes non-local entanglement and you cant get that with classical cellular automata. 't Hooft has explored quantum cellular automata where he has a hilbert space spaned by the possible states of the system. This is more interesting. He first described the holographic principle using a model of that form and now he claims that string theory can be described that way. Perhaps he can really get it to work.

However, I think this is not enough. Cellular automata already have grid structures that represent space and time is a discrete process put in by hand. I want to see a theory that starts from something more fundamental so that space and time are also emergent/ I think that symmetries are important because they reflect the idea of redundant information. So I want to start from algebras that describe symmetries over Hilbert spaces of information and then reproduce physics as emergent structures from that. It is ambitious but there are mathematical principles that suggest it might just be possible such as the mappings I describe in my essay.

I hope that makes it a little clearer how my thinking works.