Undecidability and indeterminism by Klaas Landsman

Dear Klaas,

I enjoyed very much your essay, from your insightful parallels between Gödel's and Bell's theorems, to your no-go theorem, which I think it's amazing. I still try to grasp its physical implications. I'm also glad to see form your essay that you know Cris Calude. We've met again when he came back to Bucharest a few months ago. He made me realize that randomness is not what we commonly think it is in physics. I realized that we use the word "randomness" pretty much randomly :D Your essay shows that indeed this is an important point, as Cris explained me in our discussions, which is not well understood in physics. Despite his explanations and your eloquent essay, I am still not sure I fully understand the implications. I have a lot to digest, and I also want to find time to go deeper into your ref. [19], a heavy book I have in my library for some time. So I may come back with some questions, but for the moment I am interested into one. Do you think, based on your analysis of the two representative examples of deterministic models and the implication of your theorem on them, that it is possible to distinguish them empirically from nondeterministic versions of quantum mechanics? My interest comes from trying to find falsifiable predictions for a single-world-unitary-without-collapse model, which seems to fit in the same category as 't Hooft's cellular automata, but I interpret it differently than denying free choice of experimental settings, as I explain in the attached pdf. In the last section I mention two possible experiments, and I am interested to see if testing for genuine randomness can be physically done. I expect some loopholes stronger than in the EPR case, due to the fact that measurements are not sharp in general, and that the measurement device and the environment may not be stable enough to allow a comparison of repeated experiments numerous enough to tell if the resulting randomness is genuine or not. But I'm interested if you think this to be possible, at least in principle.

Cheers,

CristiAttachment #1: Cristi_Stoica_The_post-determined_block_universe_draft_2020-04-16.pdf

Dear Professor Klaas Landsman,

Thank you for presenting a wonderful essay written with a very smooth flow....

Your statement about Godel's law as.........Godel proved that any consistent mathematical theory (formalized as an axiomatic deductive system in which proofs could in principle be carried out mechanically by a computer) that contains enough arithmetic is incomplete (in that arithmetic sentences ' exist for which neither ' nor its negation can be proved)...................

I have few questions about it. This law is applicable to Quantum Mechanics, but will this law be applicable to COSMOLOGY.......?????.........

I never encountered any such a problem in Dynamic Universe Model in the Last 40 years, all the the other conditions mentioned in that statement are applicable ok

I hope you will have CRITICAL examination of my essay... "A properly deciding, Computing and Predicting new theory's Philosophy".....

Best Regards

=snp

Dear Klass,

You really wrote a great article. Thank you!

All the best,

Noson

Dear Klaas. While reading your essay I got very excited. I am not a physicist or a mathematician. My major expertise is in creativity and its fit in the world-and- in some respects its relationships with science and mathematics. You provided a very interesting overview of the "battle" between determinism and indeterminism. Several things in your essay as it relates to my essay are "very" exciting. In my essay I describe a process that converts chaos to order - the C*s to SSCU transformation (described in the appendix of my essay) and the scale up of the SSCU to become our (the visible) universe (described in the body of the essay). It appears to me that the C*s to SSCU transformation is the "...internal processing of atoms (in my theory the internal processing of all physicality) that enforce some particular outcome" expressed by Born (1926). In the Successful Self Creation theory that "enforcement" was the self replicating/self organizing progression that eventually became the universe. Also you mention that the "... attempts to undermine the "Copenhagen claim of randomness looked for deterministic theories underneath quantum mechanics" and you concluded that was impossible. I agree with your conclusion. However, those looking to undermine the Copenhagen claim of randomness had it backward. The SSC theory presents a randomness (chaos) underneath and the process that converted that randomness (chaos) to a repeating, self replicating deterministic progression that became the multiverse that contains our universe. There is much more that we should discuss. If you would read my essay and respond it could be the beginning of an exciting discussion of your "musings on (in)determinism" in your easy. I am looking forward to hearing from you. John D. Crowell

Dear Klaas,

Thanks for this brilliant essay. As I also "would personally expect that a valid theory of the Planck scale... would derive quantum mechanics as an emergent theory," have you thought of what seems to be a natural logical extension of the ancient idea of atomism - discreteness not only in space but in time (rather spacetime) as well? (To question a fundamental continuity - continuous existence in time - at the heart of quantum physics.)

Then the probabilistic behavior of the quantum object may be represented as a manifestation of a probabilistic distribution of the quantum object itself in the forever given spacetime: an electron, for instance, can be thought of as an ensemble of the points of its disintegrated worldline, which are scattered in the spacetime region where the electron wavefunction is different from zero. Then, in the ordinary three-dimensional language, an electron would be an ensemble of constituents which appear-disappear в€ј10^20 times per second (the Compton frequency); and, obviously, such a "single" quantum object can pass simultaneously through all slits at its disposal in the double-slit experiments with single electrons and photons.

Had Minkowski lived longer he might have described such a probabilistic spacetime structure by the mystical expression "predetermined probabilistic phenomena."

It is true, the above question is more in the spirit of the Einstein-type approach to fundamental physics, whereas now the predominant approach seems to be more Minkowski-type (as we know Minkowski employed such an approach when he discovered the spacetime structure of the world).

Best wishes,

Vesselin

Dear Klass,

Excellent analysis and new exclusion of DeBroglie/Bohm & t'Hooft. Clearly & rigorously argued. My one concern was anticipated in your brilliant last paragraph, but that does then leave a THIRD option not addressed. I alluded to it above, with a proof in my last years essay, with confirmation code & plot in Trails essay. It suggests the elusive 'state after collision'. Your unique understanding, and ability to see QM may be emergent, should allow you to assess it;;

I propose that your conclusion; Randomness "contradicts" determinism needs better definition. My questions on spinning sphere momenta ('OAM') above use a simply 'collision' momentum transfer analogy. A random axis 'pair' state meets Bob's electron, & TWO part vector addition means A,B outcomes are independent!

For collisions on the equator, amplitudes for the question; "clockwise or anticlockwise", will be deterministic, but ALSO uncertain (50:50) so 'random'.

For collisions exactly at a pole; amplitudes for left/right? will be similarly uncertain, but also still deterministic in classical mechanics terms.!What I pointed out in Q5 was that the momentum CHANGE RATE (as Bob turns his dial) across the surface between 0 and 1 is by the cosine of the 'angle of latitude' of the tangent point!. (I then derive Cos2Theta.)

I suggest this is a very important finding, going way beyond just your essay (though meaning your conclusion needs a little tweaking), but ALSO that your last paragraph is correct, as it emerges from a 'Higgs condensate' gravity model-see my essay) and a Gell-Mann 'Quasi' classical derivation of QM should exist, though it may need your help to complete!

If you have a sec do also see my top peer scored 2015 'Red/Green sock trick' essay.

Thought I'm suggesting a minor 'incompleteness' in your analysis, of course agreement on content isn't a valid scoring matter. Well done, and thanks.

Very best

Peter

Hello Klaas,

Thank you for this delightful essay. Theorem 3.5 seems to be dead on. It's an unexpected move, but I think it has to be true intuitively.

That said, let me probe a little bit. I'm a Many-Worlds person (for the purposes of this comment!) For me, I get classical indeterminism from tracing over the wavefunction via decoherence. In this case, I ought *not* to expect algorithmic randomness. Indeed, what happened could be understood as the very deterministic outcome of what I happen to be tracing over. It's a thermodynamic randomness, not a Chaitin one.

In that case, I think, you can only recover the Chaitin randomness if the wavefunction itself is incompressible. (Going back and forth between K(x) and K(f) (f the wavefunction, x the realization) is something that's been on my mind a bit, and is part of the essay I did this year--I'm not sure if I understand it fully yet.) I think your remarks about emergence in the final paragraph suggest you might find this idea sympathetic, if you haven't already done a lot with it already!

I don't quite know how to square the thermodynamic and Chaitin notions of randomness--I think you can get pretty far by talking about K(x | f), but I'm not sure how far! The problem is that if f comes from a deterministic theory that you then trace over with an observer's ignorance, i.e.,

f(x) = sum_y d(x,g(y)) P(y)

g is a deterministic, computable mapping, d(x,y) is a delta function, and P(y) is the observer's ignorance of the rest of the world, I don't know what happens to K(x).

Yours,

Simon

Congratulation Klaas Landsman,

I see your essay a if not the most mature proficient one. However, is Bell's theorem really the key to something new in science? What consequences does your set theoretical based reasoning have in physics?

Perhaps you are excellently improving the map. Schlafly and I are distinguishing the map from the territory. Obviously, you didn't convince for instance McEachern and Kadin that they are wrong. Well, I too am unable to swallow Peter Jackson's alternative explanation. From Petkov's comment I learned the somewhat intentional sounding expression "predetermined probabilistic phenomena". De Wilde seems to be still waiting for your reply. I am not in position to judge some possibly relevant raised question questions for instance by Crecraft, Klingman, and Gupta and don't ask you to deal with them.

How many decades will Kadin have to wait until his prediction comes wrong? I feel helpless against accepted mathematics that I consider questionable. When I showed in my recent essay that Fourier was partially wrong, this was an attack on the fundamental adaptation of mathematics on very basic physics.

Unfortunately your training made you blind for my hints to what I consider unjustified related maneuvers in mathematics. Isn't R reasonable even if not Hausdorff at zero?

Incidentally, appreciating your logical reasoning, I hope you will understand me if admit that I am arguing, so far in vain, against the use of "present state" between the alternatives past and future. I also tend to restrict "initial values" to ideal models, not to the physical reality.

Best further success,

Eckard Blumschein

I am sorry, I wrote the comment above quickly and omitted half of the information in the last sentence of the second paragraph:

"and, obviously, such a "single" quantum object can pass simultaneously through all slits at its disposal in the double-slit experiments with single electrons and photons."

It should have been:

"and, obviously, such a "single" quantum object (i) can pass simultaneously through all slits at its disposal in the double-slit experiments with single electrons and photons and (ii) can still be detected as a point-like particle - when the first of the appearing-disappearing constituents of the electron falls in a detector, due to a jump of the boundary conditions, all other constituents continue to appear-disappear only in the detector."

Dear Professor Landsman,

While I am trying to understand your wonderful essay, your last paragraph caught my attention. In my recently proposed theory of Spontaneous Quantum Gravity, I indeed derive quantum theory as an emergent theory, from an underlying *deterministic* matrix dynamics at the Planck scale. This new theory actually forms the content of my essay here: The pollen and the electron. This theory builds on the earlier work of Stephen Adler on `Quantum theory as an emergent phenomenon'

My purpose in submitting this post on your page is not so much as to ask you to read my essay, but rather to request you to kindly have a look at the technical references given at the end of my essay. I am curious to know what you think of this new theory, and will be so grateful for your critical comments. Also useful could be arXiv:1912.03266

I will try to understand the proofs in your very interesting essay.

Thanks so much,

Tejinder

Hello Ed,

sorry not to have yet read your essay, I've been concentrating on practical matters and have only looked in on the contest pages. You and I have discussed the idealized Spin co-ordinate system in the past and the Bell dependence on it. So the issue of incompatibility of QM statistical models with a rational realism is perhaps inevitable. You make an excellent point in paragraph 4 about 'one free particle' ( the classic hypothetical 'free rest mass' ) being capable of local deterministic theoretical construct, while globally interactions would have to be treated statistically. So the Bell arguments come down to a simple; 'Why Not?'. QM was designed on purpose to idealize for the sake of granular simplicity. It was not intended to be realistic and its precision derives from intentional extensive reiteration. It is expedient, and Bell is yet another iteration. And so, 'why not?', there is surely room enough in physics for both realism and expediency. Best wishes, jrc

Hi well, see well on other essays how I have explained, reached, quantified, renormalised this quantum gravitation, see the universal balance necessary between entropy and negentroy, cold and heat in considering the 3 main finite series of 3D coded spheres, one for the space and two fuels, photons and cold dark matter, I have respected this newtonian mechanic, we search this quantum gravitation, it is the holy graal, but the thinkers could be less in their works and recognise the works of others, I repeat it is quantified in changing simply the distances anad mass, the standard model is just emergent, I will published this year several papers, the thinkers have forgotten to Think beyound the box and consider new parameters superimposed, they are in an electromagnetic and relativistic prison.

Regards

I d like to have relevant mathematician here on FQXi like Connes, Wittem Susskind, Witten, John Baez, with them we can make a revolution, they are better than me in maths I beleive even If I have utilised these Tools, like the Ricci flow, the Hamilton Ricci flow, the lie derivatives, the lie groups, the lie algebras, the poincare conjecture, the topological and euclidian spaces and the Clifford algebras and matrix of Dirac and matrix of Clifford, I need help, there are maybe several errors in my mathematical extrapolations, I have also invented with a person the assymetric Ricci flow to explain the unique things probably in the smaller volumes of my finite series of 3d coded spheres where this space disappears and having the same finite number than our finite cosmological finte series of spheres.The universe shows us the generality and how it acts with the universal balance between heat and cold, gravitation and electromagnetis, order and disorder, entropy and negentropy, sometimes the complexity returnms to simplicity, the universe is simple generally, the human psychology and its Vanity that said is complex and not really rational lol

"Both experts and amateurs seem to agree that Gödel's theorem and Bell's theorem penetrate the very core of the respective disciplines of mathematics and physics." If nature is finite and digital then are Gödel's theorem and Bell's theorem fundamentally irrelevant to the reality of nature? I have suggested that my basic theory is wrong if and only if dark-matter-compensation-constant = 0.

If my basic theory is wrong, then the Koide formula and Lestone's theory of virtual cross sections might be valid (although not in the way hypothesized by my basic theory).

Assume dark-matter-compensation-constant = 0 and string theory with the infinite nature hypothesis is empirically valid.

Lestone's theory of virtual cross sections might explain the numerical value of the fine structure constant.

Lestone, John Paul. Possible reason for the numerical value of the fine-structure constant. No. LA-UR-18-21550. Los Alamos National Lab.(LANL), Los Alamos, NM (United States), 2018.

Lestone, J. P. "QED: A different perspective." (2018). Los Alamos report LA-UR-18-29048

If Lestone's theory of virtual cross sections is empirically valid, then does it require a new uncertainty principle?

According to some of the string theorists, spacetime is doomed. If spacetime is doomed then is a new uncertainty principle required? What are the criticisms of the following?

There exists a (finite) Lestone-maximum-mass > 0, such that for any massive elementary particle in the Standard Model of particle physics,

(standard deviation of position) * (standard deviation of velocity) ≥

(reduced-Planck's-constant/2) / (Lestone-maximum-mass) .

If, near the Planck scale, the concepts of time and space fail, then could uncertainty in the speed of light allow Lestone's theory to be empirically valid?

Dear Klaas Landsman,

Gödel's and Bell's works were on processes (or algorithms) in 'time', which make the question of (in)determinism the driving notion of your essay. Determinism, as we understand it today, deviates substantially from the Classical Greek interpretation and originates from the heyday of historiography in enlightenment. Hume, the historian, was exponent of the temporalization of affairs and belonged to the firsts who misinterpreted the symbol t in Newton's equations as historical time, thus initiating a ghost-debate on (in)determinism.

What happened in enlightenment is the change of view from a priori (law) to a posteriori (model), with the latter arousing 'time'. It is not such that a posteriori empiricism observes and models real processes in 'time', rather it provokes the psychological idea of time by its inherently probabilistic and hence undecidable models. So, empiricism itself is the cause of 'time', with the consequence that whatever it 'observes' MUST be indeterministic for the reason that the 'historical future' exists only as deviation from expectation. And since the a priori natural law is devoid of deviation from expectation, it is not in 'time'.

In short, a priori laws are deterministic by being literally time-less knowledge, while a posteriori models, and be they axiomatic, animate a timeless Parmenidean world and end up in complexity, undecidability and indeterminism. So, from my point of view your essay appears to administer pseudo-problems.

Heinz