Computability in the Theory of Theories by Philip Gibbs

Dear Philip,

in my essay I have categorized the kind of work you're proposing 'computational art'.

If you agree, my next question would be: what's your motivation ?

If you disagree, my next question would be: which problem are you trying to solve?

best,

Heinz

"information is actually a continuous quantity with no minimum value."

Not in Shannon's Information Theory. The whole point of that theory, is that information must be encoded into discrete symbols, from a known "alphabet" in order to be successfully (with no errors whatsoever) recovered, in the presence of noise. Unlike any other conception of "information", Shannon's has nothing to do with the states of a physical system - it has to do with the maximum number of independent variables, that can ever be perfectly recovered from any continuous mathematical function, that exhibits a limited duration, bandwidth and signal-to-noise ratio.

"Reductionism, determinism, objective physical reality, simplicity, naturalness and causality: There is a clear message from quantum nature that these concepts do not belong in a fundamental theory."

Absolutely false. There is a trivially simple alternative: Quantum theory is not describing the behavior of physical reality at all. It merely describes the behavior of entities attempting to "detect" the existence of other entities: it is not describing the behavior of any substance, such as a "drug" or photon or electron - it is merely describing the probability that some "drug test" will declare (rightly or wrongly) the drug to have been "detected" - with no consideration whatsoever being given to the fact that all such tests exhibit "false positives".

By exploiting Shannon's conception of information, together with this "detector driven" interpretation of quantum theory, it is easy to demonstrate that Bell's "spooky action" correlations, can be produced by a simple, deterministic, classical system, with detection efficiencies that are supposedly unobtainable, by any classical system. The gross error in all existing interpretations of quantum theory, is that they have never imagined that the problem resides in the fact that entities that manifest only one single bit of Shannon's information, cannot possibly be successfully "measured" in a Bell test - a large number of "false positives" (declaring the polarization to be "up" when it was actually down, and vice versa) are absolutely guaranteed to occur - and systematically bias the correlation statistics - to perfectly reproduce the correlation function predicted by quantum theory.

Rob McEachern

Dear Phil,

It is good to see your contribution. I always enjoy your insight.

You mention that since the 1970s all work on theoretical physics including supersymmetry and string theory has failed to make contact with experiment. I think that you attribute this to a dearth of new experimental results at the energy frontier. An alternative possibility is a theory that predicts what we see and nothing else.

As I understand it, you believe the appropriate starting point for a theory of theories is modeled as a formal sum of the collection of mathematical universes; that is, every mathematical possibility has a corresponding physical possibility (more or less). I think you have explored this approach quite well.

An alternative approach would begin with one physical field, and nothing else, and attempt to derive our current universe from this field. That happens to be my preferred approach. I believe it is compatible with your answer that "up to energies tested so far there was simply "nothing new". I recall particle physicists a decade ago being sort of upset by the suggestion that the only particles that exist are those we know and resonances composed of those that we know. In fact I suggested that the Higgs was not a fundamental particle but just such a resonance. After several years of celebrating the Higgs, the latest Phys Rev Letters papers that I have seen are those analyzing Higgs as 'composite particle'.

You state: "in my opinion they are failing because they still cannot relinquish certain cherished philosophical beliefs." I fully agree with you. Now we just have to agree on the cherished beliefs in question!

My own belief is that the answer is more likely to come from the extreme that you explore, or the opposite extreme that I explore, than it is to come from anywhere in the middle.

My best regards, and good luck.

Edwin Eugene Klingman

Dear Philip,

I am very happy to see you entering a contribution into this year's competition, your essays are always enlightening to read, and provide much food for thought.

The idea of a 'Theory of Theories' is something I have been spending a bit of intellectual energy on, as well, mostly inspired by Russell Standish's 'Theory of Nothing' and Jürgen Schmidhuber's 'Algorithmic Theories of Everything' (see here: https://arxiv.org/abs/quant-ph/0011122). Schmidhuber's approach in particular seems at first blush not too distant from your own---he also appeals to Kolmogorov complexity in the construction of a (formally describable) measure, over possible histories of the universe.

But I have only skimmed your paper as of yet; I'll revisit it when I get some more time, and look forward to engaging with it in detail.

I wish you the best of luck in this contest!

Happy birthday!!

Have a happy birthday!

Edwin,

You nailed it:

"An alternative possibility is a theory that predicts what we see and nothing else."

That is exactly what existing quantum theory does, which is why it has always been misinterpreted - it only (but accurately) predicts the detection statistics of a test, for the presence of "something", rather than describing either the "something" itself, or even how the "something" behaves. It is analogous to accurately predicting that a "drug test" will detect "something", but without ever bothering to consider the likelihood of all the "false positives".

"Now we just have to agree on the cherished beliefs in question!"

Start with the 2,500 year old, ancient, Greek philosophical assumption that "elementary" particles must all be perfectly identical, while taking note of the fact that some [link:vixra.org/abs/1609.0129#comment-4458485189]"fraternal twins" do not behave anything like "identical twins"[/link] in a Bell test. Next, consider the fact that a single Fourier transform (superposition/wavefunction) cannot be used to correctly describe more than one single particle trajectory, at a time, in the presence of any noise; assuming (as quantum theorists did, in the 1920s) that you ought to be able describe multiple particles, via a single superposition, was a huge misconception - that "trick" only works correctly, in an idealistic (AKA unreal) noise-free situation.

Rob McEachern

Happy Birthday Phil!

I have not read the essay yet, but I have been a fan of this line of reasoning for years now. The notion that what makes sense physically would emerge from the spectrum of all possible theories naturally is a compelling idea. When I was struggling to find a proper context for my work - when I first began to see the relevance of the Mandelbrot Set to Physics - the 'theory of theories' notion put things into focus very nicely; thank you.

I hope you find renewed vigor and increased confidence with year 60. I was told a story by Joe Lam on my 59th birthday that he thought he'd be washed up at 60 but found the opposite instead, that he had more self confidence and had new horizons opening up - so his life picked up speed. That was the night I had the pleasure to meet and eat with Leo KoGuan, Brian Greene, Paul Joskow, fellow FQXi essayist Brian Ji and also met Ed Witten.

And as with Joe Lam; my life has only picked up speed after 60.

All the Best,

Jonathan

While I hope you're off celebrating your birthday, let me just quickly add a couple of questions:

Why do you restrict your notion of algorithm to those with finite output? It seems to me that a computer enumerating the digits of pi in succession is executing a perfectly sensible algorithm.

What do you think the significance of the Wick rotation is? I can grasp it in the sense of 'Euclideanizing' the path integral, but it's still not fully clear to me what it means, and what one actually does when, like you do, one just Wick rotates an expression to arrive at a quantum version. (Which, by the way, I thought was a little quick; it seems to me that a little more is needed for the emergence of quantum mechanics. In particular, just a complex Hilbert space doesn't suffice, as shown by the Koopmann-von Neumann formulation of classical mechanics. But then, it's a finite-length essay, and I can't really expect you to resolve everything in one fell swoop...)

"Although we think of data as quantised in discrete bits, information is actually a continuous quantity with no minimum value." Should we believe Kolmogorov or Fredkin?

Robert Wright stated, "I talked with Richard Feynman, a Nobel laureate at the California Institute of Technology, before his death, in February. Feynman considered Fredkin a brilliant and consistently original, though sometimes incautious, thinker. If anyone is going to come up with a new and fruitful way of looking at physics, Feynman said, Fredkin will."

"Did the Universe Just Happen?" by Robert Wright, The Atlantic Monthly, April 1988

Consider 3 questions: Does quantum information reduce to Fredkin-Wolfram information? Is Milgrom the Kepler of contemporary cosmology? What is the simplest way of modifying Einstein's field equations? Google "milgrom fredkin wolfram".

Phillip,

Your essay was interesting. I appreciated the description in the supplement of what is meant by the necklace. Also your discussion on Turing's theorem is a nice compact version of that.

I have some points of difference with it. I would say a departure is with the implication of some sort of infinitude. I think that for any observer the number of quantum states available for observation is finite. We may think of the horizon of a black hole with S = kA/4â„"_p^2 = NK for N the number of Planck unit quantum states. The Bekenstein bound and related results imply the number of quantum states available to an observer is finite. So even if the global Hilbert space is infinite dimensional any observer can witness only a finite subset. That might be where the necklace or enveloping algebra can come it, where this could be some general form of separable set of states in tensor products. This may in principle extend infinitely, but any observer has access to a finite quantity. The existence of horizons is a way that Hilbert space available for measurement is finite but unbounded.

Your approach makes the implicit assumption that action = entropy, which is in a Euclideanized time sense t â†' it = ħβ = ħ/kT.the path integral maps into a partition function, where an energy E of a system is computed according to all possible combinations of microstate energies. This is a form of integer partition function. The only extension I can think of is where the measure μ(U) = e^{-S(U)} needs to be extended to μ(U) â†' μ(U)/diff(G), where G is the group of diffeomorphisms of U. However, this action = entropy or an equivalency between

TdS = dW + dU â†" dS = pdq - Hdt,

links quantum information with entropy

My essay concerns how Gödel incompleteness is associated with different entanglement geometry. A heuristic comparison would be with Nagel and Newman's book on Gödel's theorem and Euclid's fifth axiom. The undecidability of the fifth axiom leads to two possible model systems for geometry, Euclidean flat space vs more general geometries of Gauss, Lobachevski and Riemann. This is a case of consistency and incompleteness vs inconsistency vs completeness. Loosely we can think of the Euclidean case as consistent but incomplete, while the more general geometries are more complete, but not consistent with each other. This without details of ω-completeness/consistency is how different entanglements have different topologies.

Szangolies describes this as an epistemic horizon. His paper is worth reading. This has I think connections with my work through the locality of solutions for Diophantine equations, or equivalently p-adic sets.

At any rate the part about the measure μ(U) â†' μ(U)/diff(G) as mod-diffeomorphisms I think is important. This is in gauge theory these diffeomorphisms are what define a moduli. The moduli space describes the topology such as the ADMH construction. In a duality gauge theory â†" entanglement symmetry, here on the right hand side in a SLOCC meaning, there may be a correspondence between topology of entanglement with gauge fields and topological gauge fields.

Anyway, things to think about. I would like to see what you think of my paper.

Cheers LC

You cannot transmit (and thus give to me) the first sentence you stated, in a message only one bit in length. The same is true of your second sentence. Your conception of "information", differs substantially, from that of Shannon. Luck is not necessary, where understanding is sufficient. An essay is not necessary to support my case, since a sufficient demonstration has already been published. Q.E.D.

Rob McEachern

Dear Philip E. Gibbs,

"Information is the basic material of reality, but the processing of information raises paradoxes due to the self-referential nature of computability."

Perhaps I overlooked this statement and something that may substantiate it at the beginning, the end or even any part of your essay on "Undecidability ..."

I was lazy and looked for where you referred to [ 4] Shannon at your p. 2. Maybe you merely corrected Shannon by mentioning that the DNA is a material code. Otherwise, one is tempted to read your theory of theories as new-Hegelian idealism. Anyway, I see you obliged to take McEathern's critical arguments more seriously. He is complaining at my own essay.

Eckard Blumschein