And the math will set you free by Cristinel Stoica

Dear Cristi,

You say "at least we know that there is room for free will." You know that and I know that, though many dispute it. But free will, in any meaningful sense, is not deterministic, and, although one may draw an analogy with random numbers, I don't think one can draw it in any detail.

Thus I see no reason to contend that free will is isomorphic to math. Even if one can, post exercise of free will, or even concurrent with the exercise of free will, find some neural correlates. Free will partakes of causal and I don't think mathematics reaches causal. So I don't think "everything is isomorphic to a mathematical structure." You seem to think differently. With reference to time, you say, "there is no conflict between mathematics and causal explanations." But I don't believe there is an 'explanation' for free will. I don't see this as in conflict with your arguments about a theory of everything, to the effect that we cannot be living in a world described by two disconnected sets of laws. That seems to me a self-consistency argument that does not depend upon everything being isomorphic to math.

On another point you note "if it looks like a duck, swims like a duck, and quacks like a duck, then it is a duck, isn't it?"

My essay analyzes why John Bell thought that "it looked like Dirac spin, behaved like Dirac spin, and had an eigenvalue equation like Dirac spin, ['it' being the Pauli eigenvalue equation.] I argue that the Pauli equation of Stern-Gerlach is not the Dirac equation of relativistic QM, and that Bell's oversimplification of this led him to impose what he felt were reasonable constraints that prevent a local model from achieving QM correlations.

I hope you will read my essay and comment.

My best wishes to you,

Edwin Eugene Klingman

"But can we find a property of time that can't possibly be described by mathematics? In fact, time was best understood due to mathematics, in relativity and thermodynamics."

This "understanding" is based on postulates that could be false. For instance, Einstein could have mistakenly "taken from the idea of light waves in the ether the one aspect that he needed" - then not only the "understanding" of time, but theoretical physics as a whole would be wrong:

Relativity and Its Roots, Banesh Hoffmann, p.92: "There are various remarks to be made about this second principle. For instance, if it is so obvious, how could it turn out to be part of a revolution - especially when the first principle is also a natural one? Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether. If it was so obvious, though, why did he need to state it as a principle? Because, having taken from the idea of light waves in the ether the one aspect that he needed, he declared early in his paper, to quote his own words, that "the introduction of a 'luminiferous ether' will prove to be superfluous."

Pentcho Valev

Dear Christi,

You try to go very far in the identification of the object and the words/mathematics that describe it. Your map of all sentences to numbers in the segment [0,1] is very illustrative. But you could as well have selected the formalism of QM where epistemological statements are the rule. I understand from your very good essay that you are a platonist, isn'it? What opinion do you have about the ontology of physics? Do you see a cutting edge betwwen the map/description and the physical object? Myself I am reluctant in accepting that physics is just maths and I am not sure that this reluctance can be formalized.

Michel

Dear Cristinel Stoica,

In your essay you wrote, "... it may be possible that we will be able to find the fundamental physical laws. The reason is that it seems that the universe seems to be very regular. The physical laws appear to be the same at any point and at any time." Does each universe in the multiverse have precisely the same physical laws? What, in your opinion, might be the explanation for the space roar?

Dear Cristi,

I always enjoy reading your essay, full of refreshing information and rational, logical and complete argument. I completely agree with you that there must be one coherent theory with one formula that produces only one Integer number normalized one "1" based on one principle derived from one source. I also completely in agreement with your hypothesis that "our universe has to be Turing complete". This is because the universe wants us to know its secret recipe not only for our own survival but also for the survival of Existence (Creator) itself. If not, it is not possible for mere human like us to find this theory and its formula. In other words, this theory of everything not only knows the mind of our Creator but it is the Creator itself, so that Existence, hence the Creator, would avoid its own extinction by allowing us, the avatar Creator, to save ourselves and our Creator. This is because Existence is precariously in the border of collapse and it does need fine tuning to stay on existing. Existence is living dangerously from extinction at any time, because Existence supposed not to exist. If I may plead that KQID might be such theory that would deliver the good.

Best wishes,

Leo KoGuan

Dear Cristi,

I agree with both of your statements about free will and consciousness.

Your attitude toward Bell's theorem is reasonable. If you read my essay and understand it, but find it in error, there is no need to try to convince me. Yet I would appreciate it if you could give a hint of where you find the error.

Please understand that I do not claim his mathematical theorem is not correct. Bell's theorem is mathematically correct. I claim that his physics is oversimplified and his model does not represent the actual physics that goes on in the inhomogeneous field. He assumes the physics of a constant field, which will produce null results, and so leads to a contradiction. When one analyzes the physics in a non-constant field, one finds new physics, and no contradiction.

My approach is not to deny entanglement as a starting proposition, but to explore Bell's conclusion that no local model can produce the QM correlation. I have presented a local model that does produce the QM correlations, unless Bell's constraints are imposed.

This would seem to call Bell's constraints into question, and so I have analyzed the reason why he might have imposed such constraints. My essay offers an explanation, based on his confusion of Dirac and Pauli eigenvalue equations, and assumptions of eigenvalue measurements. If this analysis is valid, then the rationale for entanglement is called into question.

I fully realize that questioning The Gospel According to Bell almost automatically puts one in the kook category. But if fear of being labeled prevents all attempts to analyze fundamental physics we will never escape any errors that may be built into our fundamental physics.

My very best regards,

Edwin Eugene Klingman

Dear Cristi,

On the contrary, it is like knowing the rule of the game of Chess, this enabling us to play Chess and the more we play the better we will become. More fun and exciting if we are playing against a grandmaster of Chess, losing and winning is part of the game. Yes, we are in the middle of mathematical game according to FQXI as the creature of Max Tegmark as the creator of this game. Let's continuing on playing as Newton pointed out that the Creator is assumed to help him doing the adjustment to fix the orbits correctly so that our solar system ( our universe at that time) are well behaving and not falling apart. My discovery points me that rather than our Creator is busy in doing so many adjustments in trillions trillions solar systems out there, we as the avatars of our Creator would be the ones doing the adjustments to save ourselves and be the Guardian of Existence.

No bad a job eh, being the guardians of our universe, we will be very busy like in the cartoon,

Leo KoGuan

Dear Cristi,

You claim that Bell doesn't assume anything about dynamics, but on page 141 of 'Speakable...' he states clearly that "the angular momentum, by gyroscopic action, should stabilize the angle between particle axis and magnetic fields." This is most definitely a dynamic assumption and it underlies his overly-simple model.

The first Letter in the Phys Rev Letters I received today, (PRL 114, 040401, 30 January 2015) states that

"To determine if the evolution of the quantum system is governed by one or another Hamiltonian, one must perform measurements on the system and use these outcomes to infer the most likely assumptions."

I don't think Bell should be exempt from that. Nor do I understand why so many physicists are adamantly opposed to investigating a different Hamiltonian than the oversimplified and unrealistic one chosen by Bell to model his local system. I hope that when you read my essay, it might have information that you haven't seen yet. Otherwise there would have been little reason to write it.

My best regards,

Edwin Eugene Klingman

Dear Dr. Stoica:

Your essay focuses on the liberating aspect of mathematics: "And the Math Will Set You Free."

In contrast, my essay asserts that mathematics can enslave us and blind us from the truth. "Remove the Blinders: How Mathematics Distorted the Development of Quantum Theory" questions the orthodox Hilbert-Space Model of QM, and presents a simple realistic picture that makes directly testable experimental predictions, based on little more than Stern-Gerlach measurements. Remarkably, these simple experiments have never been done.

The accepted view of QM is that the physics (and mathematics) of the microworld are fundamentally different from those of the macroworld, which of course creates an inevitable boundary problem. I take the radical (and heretical) view that the fundamental organization is the same on both scales, so that the boundary problem immediately disappears. Quantum indeterminacy, superposition, and entanglement are artifacts of the inappropriate mathematical formalism. QM is not a universal theory of matter; it is rather a mechanism for distributed vector fields to self-organize into spin-quantized coherent domains similar to solitons. This requires nonlinear mathematics that is not present in the standard formalism.

So while mathematics provides essential insights into physics, an incorrect mathematical model that becomes established may be seen as virtually religious dogma which is not to be questioned. That prevents further progress.

Alan Kadin

Dear Cristi Stoica,

Enjoyed your essay. Your comment "there must exist a mathematical structure which satisfies our observations about both the quantum world, and the general relativistic one. Maybe these theories are somehow limits of this theory. But the unified theory must exist, even if we don't have it yet." was well argued and very believable.

I agree with your comment "The idea that the universe is nothing but a mathematical structure leads to many difficult and interesting questions".

My essay revolves around modelling the mathematical structures of the particles of the standard model. I hope you get a chance to have a look at the modelling I use for the particles of the standard model and look forward to any comments you may have.

Good luck on your essay, you deserve a good rating.

Regards,

Ed Unverricht