Undecidability and indeterminism by Klaas Landsman

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

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

Dear Klaas,

major parts of the physical literature, beginning with Newton, can be taken as a reference, if one is prepared to take off one's empirically-tinted glasses. In the scholium of the Principia Newton makes a pretty clear case for an idealistic view of physics:

"Wherefore relative quantities [time, place, space and motion] are not the quantities themselves, whose names they bear.....And the expressions [time, place, space and motion] will be unusual, and purely mathematical, if the measured quantities themselves are meant." So, Newton's space and time, for instance, are not meant to be isomorphic with the everyday use of these notions and he stresses that the notions of physics (=mathematics) must not be confounded with the notions of empirical quantities [vulgaribus mensuris], which I have radicalized to the idea that natural language and physical language can only be Absolutely non-contradictory if they are incommensurable, complementary or orthogonal.

Further, one still finds very empiricism-critical approaches to relativity and quantum mechanics in the early papers of Einstein (1905) and Heisenberg (1925), respectively. Both make very clear that they speak of KINEMATIC representations, not of PHYSICAL theories. The fusion of the 'two languages' and hence the Unanschaulichkeit of modern physics begins with the coup of the Göttingen school of mathematics...

Just in case you are interested in the basics of my thinking (and happen to speak German), google for "Wird die Wissenschaft zum Feind des Wissens?" or "Das Ding an sich", both posted on Philosophie.ch

Heinz

Dear professor, Landsmann,

You write

"...it may be helpful to note that in classical coin tossing the role of the hidden state is also played by the initial conditions (cf.Diaconis & Skyrms, 2018 Chapter 1, Appendix 2). The 50-50 chances (allegedly) making the coin fair are obtained by averaging over the initial conditions, i.e., by sampling. By my arguments, this sampling cannot be deterministic, for otherwise the outcome sequences appropriate to a fair coin would not obtain: it must be done in a genuinely random way. This is impossible classically, so that (unless they have a quantum-mechanical seed) fair classical coins do not exist..."

And, concluding you, state:

"I would personally expect that a valid theory of the Planck scale (including quantum gravity or string theory, though these words are misleading here), far from assuming the Born rule and the rest of quantum mechanics (as these theories normally do), would derive quantum mechanics as an emergent theory (instead, the opposite seems to be the majority goal, i.e. deriving gravity as an emergent phenomenon from quantum theory). Thus quantum mechanics would typically be a limiting case of something else, which would, then, also render the Born rule valid in some limit only, rather than absolutely."

My humble self is interested to see that we can indeed reduce this whole classical/quantum divide to an intuitive picture -- when we think of the self-referencing state (typically every mind/observer) as, by you, own "quantum mechanical seed".

That is, we can approach quantum mechanics from the perspective that it is fundamentally about self-reference such that the observer is by definition the norm/normal e.g. the unit or constant refractive index by which we are at any instance describing our cosmology. Modelled as Gödel's self-referencing state, every mind simply is thus the quantum of own observables (typically the probe energy or beat frequency or quantum vacuum) if the Landauer limit.

This will be just in the exact same way that Planck's quantum (v = E/h) is that norm/normal by which in spectroscopy we are attempting to describe the applicable black-body radiation as a unique arrow of time (the black body spectrum).

In this sense every mind would be as the phase constant own Kolmogorov incompressibility (own energy/time or wave/corpuscular uncertainty threshold); just what the constant refractive index is to all observable dispersion relations of light i.e. to all self-referential splitting of light into constructive versus destructive interference; perhaps your binary string.

Hoping that you can take a look at how I grapple with this vision (being an editor, please don't let poor wordings distract you).

Chidi Idika (forum topic: 3531)

Sorry about the typo in the name. Meant to write Landsman.