Dear Jochen.

It is only now that I am daring to make comments on your excellent essay because your approach is quite another one as mine. But I think one is learning most with an open mind, so I made the following notes while reading your essay:

"the Newtonian, classical framework, can no longer be upheld". Why not, it is describing our daily macro reality quite good and can be used in many ways. In my opinion, it is the mixing up of the micro and macro, and then especially the quantum "world" that is leading to such remarks. The mainstream of 14 interpretations are created by agents inside an emergent phenomenon (reality) while they are themselves part of it and so are trying to UNIFY the two, while when we are splitting up our emergent reality and its source (in my perception: Total Simultaneity) we can treat them apart. A TOE needs not to be a unified theory of ALL but can be a theory that is dealing with different entities.

Quote

1. Finiteness: There is a finite maximum of information that can be obtained about any given system. 2. Extensibility: It is always possible to acquire new information about any system

Unquote.

I would add the following Finiteness: there is a finite maximum of information that can be obtained by an agent about a given system at a certain moment. Extensibility: no changes it already covers my addition in 1. (you also indicate this with "old" information.

The "Horizons of understanding" are in my perception limited by the borders of our emerging reality, the Planck units and the velocity of light. Heisenberg's uncertainty relation is just describing that at a certain moment there is the only position of a particle, the velocity is a relationship with a new moment in time and space. So velocity can only be measured inside the emergent phenomenon of reality. Superposition: more quantum states can be added together, every quantum state can be represented as a sum of two or more other distinct states. We are reaching out to the borderlines of our reality and nearing Total Simultaneity (unreachable) where each point can be represented as an INFINITY of distinct states. (phase space) Measurements are "events" that are time and space-restricted, so results are always from the past, and only dealing about ONE distinct state.

I think that the first part of your argument " But this means that there exist some state sg and measurement mg such that the value of mg(sg) cannot be predicted by f." should be extended to Any state sg and its measurement mg cannot lead to any "prediction". Because sg and mg are both events from the deterministic past, the future is containing still ALL probabilities, so is always indeterministic.

Entanglement and Bell's Theorem are also explained in my "Total Simultaneity Interpretation", and I hope that after reading these remarks you may be interested to know more about it. Of course, my essay is not so clearly written as yours, but it is quite a new approach to the essence of reality I think so I would be very obliged to hear your opinion.

You can find it HERE .

Best reagards

Wilhelmus de Wilde

    Wow Jochen, this was great!

    You managed to tie together undecidability and epistemic horizons in a way I have never seen before, and which intuitively rang true to me. For what it's worth, I believe that the way quantum mechanics will ultimately escape from the problem of supporting so many radically different ontologies is precisely through the kind of reconstruction you propose, and the fact that you managed to tie this to the kinds of epistemic horizons discovered by Godel and Turing blew me away.

    I have responded to your kind comment on my piece over there.

    Best of luck in the contest!

    Rick

      Dear Wilhelmus,

      thank you for your considered comments. When I say that the Newtonian framework can't be upheld anymore, I mean in an absolute sense---you're right to point out that for almost every practical matter, a Newtonian calculation will yield an adequate answer. But Newtonian mechanics can't be universally valid---necessarily, if my arguments work out. It has to break down at some point, and needs to be amended---or perhaps completed: in the same way as special relativity is a consistent completion of Newtonian mechanics in the realm of velocities approaching that of light, quantum mechanics can be viewed as a consistent completion of Newtonian mechanics in the realm where we're close to extracting the maximum information from a system.

      I agree that a theory of everything may apply different concepts to different domains, but these concepts must be consistent, so as to not 'crack at the seems', so to speak. All domains of physical reality ultimately interact, even if perhaps in a mediated way, and thus, our descriptions of each must match up at these interaction points. Hence, Newtonian mechanics needs modification, even if these modifications are practically unnoticeable in everyday life.

      You make a good point regarding the embeddedness of the observer within the phenomena they observe. That's in fact another way to think about such phenomena, worked out by Thomas Breuer, Maria Luisa Dalla Chiara, and others.

      Regarding measurements, we must surely admit the fact that in a very large number of cases, we can exactly predict what outcome a measurement will yield, and that outcome will indeed be observed. So, to that end, there are some future possibilities that are excluded by the present state of affairs.

      I'll have a look at your essay.

      Thanks again for your comments, and good luck in the contest!

      Cheers

      Jochen

      Dear Rick,

      thanks for this enthusiastic reply! I'm happy you found something that rang true for you in my essay. The sort of approach to quantum mechanics I pursue has been on the margins for a long time, and still does attract some skepticism (well deserved, in many cases), but I hope that we've gotten to the point that nobody gets thrown out of any offices for making the suggestion (as Wheeler was by Gödel). If my contribution helps with that just a little, I'll be satisfied.

      Cheers

      Jochen

      Hi Jochen,

      great essay that demonstrates that empirical data restrict the freedom to extend quantum theory by some deterministic hidden variables already for one and the same kind of QM-experiment. I think you made a very good job to decrease chances for getting thrown out of an office for making a certain suggestion.

      If you like i would be happy if you could comment on my essay where i also try to link undecidability to quantum events (although not as elegant as you have done).

      Hope you are well an healthy.

        5 days later

        "... since Cantor, we know that there isn't just one infinity, but ranks of them-- ..."

        Sorry, I don't consider a fabrication a scientific finding.

        BTW Scangolies is evidently wrong when he attributes the idea of infinities of different size to Georg Cantor: Already Bernard Bolzano (1781-1848) wrote this, cf. Paradoxien des Unendlichen, Reclam, Leipzig (1851).

        In order to get rid of myths and confusion, we should be careful: It was Leibniz (1646-1716) who introduced what he called the lowest level of infinity: something that is larger than anything, in other words the relative infinity.

        I am suggesting let's learn from Leibniz' sucess story and calculate as if the unbounded plurality of thinkable references was identical with not just Salviati's notion of being infinite, the logical property of simply being endless. But be careful and understand what you are doing. Don't derive nonsense.

        Try and prove McEathern and Kadin wrong. I claim having revealed that Fourier was partially wrong. Maybe, some consequences might be devastating for castles in the air?

        Eckard Blumschein

        Dear Jochen,

        You write: "Instead of trying to infer the underlying ontology ..."

        I believe that in order to overcome the crisis of understanding, the crisis of interpretation and representation in the fundamentals of quantum mechanics and cognition in general, the most profound ontological ideas are needed. Quantum mechanics is a phenomenological (parametric, operationalist) theory without an ontological basis. A. Einstein pronounced the ontological verdict on Quantum Mechanics: "God doesn't play dice with the universe."

        Yes, Planck and Einstein began the Big Ontological revolution in the basics of knowledge, but it remained incomplete. Gödel's theorems - this was the answer to the protracted crisis of the foundations of mathematics, which has been going on for more than a hundred years. And this problem for some reason "swept under the carpet." In overcoming the crisis in the philosophical basis of science, one cannot rely on the "classical ideal", since it is precisely the cognitive attitudes of the "second Archimedean revolution" ("hypotheses non fingo", "physics, fear metaphysics"), the atomistic paradigm (mechanistic, part paradigm) that prevails in science holds back the necessary ontological breakthrough in philosophical basis of knowledge. Now it is appropriate for all physicists to recall the philosophical precepts of A. Einstein: "At the present time, a physicists has to deal with philosophic problems to a much greater extent than physicists of the previous generations. Physicists forced to that the difficulties of their own science" and of J. Wheeler: "Philosophy is too important to be left to the philosophers." Carlo Rovelli calls for such a step towards Philosophy in the article Physics Needs Philosophy / Philosophy Needs Physics .

        With respect, Vladimir

          Dear Jochen Szangelios,

          I apologize for misspelling your name and hesitating to read your essay the title of which was deterring to me. Meanwhile I guess, the successful application of QM doesn't require orthogonal quantum states, and the distrusts of McEachern and of Kadin are not unfounded. Should we still invest more effort into quantum computing?

          While I don't overestimate my argument that Fourier was partially wrong, I don't trust in Fraenkel's ZFC since I read how he supported Cantor's (as I see it) naïve idea of Überabzänlbarkeit by taking elements of an infinite set of numbers as fixed. I rather trust in Peirce who spoke of mere potentialities and Weyl who spoke of the sauce of real numbers.

          Pragmatically, Euclidean spaces are thought to be composed like a set of points, which are defined only by the properties that they must have for forming a Euclidean space.

          You Jochen admitted: "it's not easy to see why one should use Hilbert spaces over the complex field".

          Klaas Landsmann wrote: "I would not say that Gödel's theorems imply that mathematics cannot be grounded on logic, except when you mean "grounded" in Hilbert's sense, namely a proof of consistency. Without knowing that e.g. ZFC is consistent, it is still a logical language in which we do our mathematics, most of which is decidable in ZFC."

          I realize minor changes in the language of mathematics. At school I learned "point product" not yet "dot product". Because I am not a mathematician, I had to naively reinvent the distinction between point and dot which I consider decisive from the perspective of logic and physics.

          Let me reiterate: I am suggesting let's learn from Leibniz' success story and calculate as if the unbounded plurality of thinkable references was identical with not just Salviati's notion of being infinite, the logical property of simply being endless. But be careful and understand what you are doing. Don't derive nonsense.

          Eckard Blumschein

            Jochen,

            Great analysis. I appreciate your rare & deep understanding of the issues around QM. I'm reminded of the good advice in your response last year to "focus on observed events", which, yes, I'd done, unfortunately you didn't get to my essay. Yours is flawless (I re-read it to check!) and beautifully written, though QM rarely scores well here, (an exception was my 2015 'Red/Green sock trick' essay).

            I very much agree your linking wider uncertainties to QM, something my essay this year also does, even rather more widely! & highlight your 'Toy Model' project to find; "one or more foundational principles such that the quantum predictions naturally follow". Spot on, and this computer plot by Trail 2018 suggests my essay identifies one(..or more). Viz;

            Bohr made no 'assumptions' about particle morphology, so had to invent 'quantum spin'. But let's hypothesize OAM as already having 2 momenta cases; Polar Rotation (>0 at the equator {90o} then inverting), and Linear, which is exactly the inverse superposed. I also show both change by CosLatitude. But it's the polarizer electrons we need to apply it to! This needs a new way of thinking about OAM, but Ulla kindly identified last yr it's exactly Poincare's spherical vector distribution! Simple vector addition on interaction at any Tan point gives CosLat output. A 2nd Photomultiplier interaction gives Cos2, with amplitude only above trigger point in ONE channel. Spheres can also rotate on x,y,z concurrently. You see where I'm going with this; A,B 'dials' reverse their OWN findings!!

            I hope you might check through it, and also it'll need help from someone with your skills to stand any chance against the "wide agreement..." (your para 1).

            Well done for yours. A breath of fresh air and prize candidate. I do hope you'll read mine this year, but also last years; https://fqxi.org/community/forum/topic/3012 (there are also various papers).

            My 2010-11 essay '2020 Vision' suggested the 'discrete field model' (DFM) that spawned this may take 10yrs to emerge. No sign yet, but you may the one with the vision!

            Very Best

            Peter

              Dear Stefan,

              sorry for taking so long to respond. Thanks for your positive comment! If the essay indeed plays a part in making this line of research a little more mainstream, I would consider it to have fulfilled its purpose---while research on the foundations of quantum mechanics has in the past few years become much more respectable than it was in the years of 'shut up and calculate', I think there's still a ways to go before that message has truly percolated through the community.

              I'll have a look at your essay as soon as I get the time---but with the situation right now, that might unfortunately be a while.

              Take care!

              Cheers

              Jochen

              Dear Vladimir,

              thank you for your comments. I agree (enthusiastically, in fact) that physics needs philosophy, and have often lamented the lack of communication between the two fields. So don't take my remark as suggesting anything else---the comment was a methodological one: the idea of 'backwards-inferring' an ontology to fit the formalism of quantum mechanics---its interpretation, in other words---is on the one hand well-trodden ground, by now, and on the other, has so far failed to produce any large-scale consensus.

              Hence, I advocate going the way in the other direction: start with some reasonable assumptions and inferences about ontological matters, and see whether the quantum formalism can be reconstructed from there---the project of finding a foundational principle for quantum mechanics. I'm not saying that this should be pursued to the exclusion of the interpretational project, but merely that it's received comparatively little attention so far, so an investigation might have a chance to dig up something worthwhile. And who knows, maybe the two ways eventually meet up in the middle?

              I think that physics still suffers from the hangover of what Feyerabend memorably called the generation of 'savages' in physics, who lack the philosophical depths of Bohr, Einstein, and others. In a sense, this is just a historical pattern that plays out after every major paradigm shift in physics, as you seem to be aware---it seems that after each conceptual revolution, physics retreats to an essentially instrumentalist stance, licking its wounds, only to slowly come back around to the investigation of its conceptual foundations. That's the sort of project I see myself engaged in.

              Cheers

              Jochen

              Dear Eckard,

              thank you for your comment. Regarding quantum computing, to me, this is a 'the proof is in the pudding'-kind of case. Either it will work, which will then legitimize at least some of the foundational principles at the heart of quantum mechanics; or it won't, in which case, we'll likely have learned something excitingly new about the world. Since that appears to be a win-win situation, I don't see why one should not continue to put in the effort.

              The reasoning in my article has important similarities to that of Cantor, so if you reject the latter, I can see you having some trepidation regarding the former; however, it does not seem that you have the same reservations against the Gödelian argument, which is in the end yet another example of the same technique (diagonalization, or more generally, the application of Lawvere's theorem). Or do you see an essential difference?

              Cheers

              Jochen

              Dear Peter,

              thank you for the kind comments! 'Flawless' is high praise indeed, though I myself keep going back and thinking of ways I could've done better, or be more clear about. But if it all hangs together in the end, I'm willing to be content.

              Your project seems engaged in questioning the foundations of logic---revoking the law of the excluded middle invokes comparison with dialetheism, and of course, quantum mechanics has itself been argued to lead to similar revisions, see Reichenbach's three-valued logic, and the more familiar von Neumann/Birkhoff logic. Although of course, in a sense, trying to make logic empirical, or at least, renege on it due to experiment, is sort of putting the cart before the horse.

              I will try to get to your essay, in the hope of understanding the rest of your comment better. However, due to recent circumstances, my time for this has rather been slashed, so it might be a while, I'm afraid.

              Cheers

              Jochen

              Hi Eckard, I can understand what you say, but let s go deeper in philosphy and about our physicality. What is the main cause of our physicality and how we must consider this infity and these infinities and our finite series. Can we really understand this universal distribution at this moment, we can take all the past thinkers having worked about this, that will not change our limitations due to a lack of knowledges generally speaking.

              We don t know the main philosophical cause of this universe, I consider an infinite eternal consciousness beyond this physicality and this thing that we cannot define is so Deep and so far of our understanding. This infinity , the real infinity has created a physicality with a system in evolution with informations, particles and Waves and we see that this physicality is under a kind of universal partition where the numbers, the particles and Waves create this physicality and its topologies, geometries, paproperties of matters. We see these infinities appearing everywhere like mathematical Tools and physical ones but they don t explain this infinity really, they are just like Tools simply inside this physicality.

              The philosphy and ontology appear indeed but we are limited simply, we cannot affirm because it is far of our understanding. It d be odd to pretend the opposite, nobody can prove what is this non physical infinity. We can analyse all what we want inside this physicality with the maths, numbers, and physics , that will not change our limitations, nobody can prove philosophically the orogin of this universe, the same for the main codes at this planck scales or the foundamental objects , all what we can is to study and improve our limited knowledges inside this physicality. The aim is to accept these limitations I beleive and respect simply the pure determinism inside this physicality.

              Regards

              Dear Jochen,

              I see it as horse first, as the problems in logic ('paradox') and Philosophy were worse than physics, needing resolving by checking starting assumptions. How do we imagine Aristotle dreampt those up anyway! We now have far better information than he did, but the foundational issues took a long time to dig down to. The sound consequences of the proposed revisions alone seem to confirm veracity.

              BUT the most important thing for you to study is the apparent physical solution to QM you suggest your'e looking for on page 1. It's verified by computer, but I trust a good well informed brain more! You didn't get to it last year so I suggest I'm owed a priority look!

              Ridiculous Simplicity fqXi 2018.

              I do hope your problems aren't family

              Very best. Stay safe.

              Peter

              "respect simply the pure determinism"

              I agree if determinism is not meant as the wrong belief that anything can be reduced to laws. I rather trust in causality rather than such demon even in cases of chaos.

              Is there any reason to question truly fundamental logic?

              Wasn't Leibniz correct and wrong at a time when he introduced the useful in mathematics quantity of being relative "infinite"?Just the name infinity for it was inappropriate. We may often calculate as if it was identical with the property

              oo 1 = oo.

              In general, I dislike attempts to question basic logic. Euclid's point corresponds to the irrefutable idea of endless divisibility. Equality of numbers implies the TND up to infinite acuity. That's why assumption of real numbers contradicts to Hausdorff's dots at zero.

              Eckard

              Dear Jochen,

              Thank you kindly for your comment on mine. My reply is here;

              Jochen, Thanks, My mentor Freeman Dyson agreed, ANY advancement means all OTHERS will "feel sort of lost", also Lorentz, Feynman etc. And yes I also studied logic & philosophy, both in crisis! Yes I pack a lot in, testing conventional thinkers, but all refs are given.

              You wrongly infer I suggest loosing "the absolute identity of quantum particles.", I just suggest they can have different polar axis angles, except when 'paired', but I DO challenge that only a "statistical approach to QM", can work, & show how we can "do better" as Bell suggested! Shocking? Tes. But seems also true (I cited the verification plot). That's what I'd like you to test.

              I hope you get a mo as it may be rather important to advancement.

              Very Best

              Peter

              I've learned that when seeking to explain "existence" using "diagonals" it's more practical (than "uncountable sets") to consider one zero-origin number line from opposite side of a professor's closed window; so I disagree with the foundational math in the title as suggests classical arithmetic like "squaring negatives" and "prioritizing zero". Other than that, I believe one square root of three disproves zero-evidence-cubed, as suggested in my essay, and in your essay here:

              "The above has the form of a diagonal argument. Diagonalization was first introduced by Cantor in his famous proof of the existence of uncountable sets, and lies at the heart of Godel's (first) incompleteness theorem, the undecidability of the halting problem, and many others. "

              It looks like I'll be graded as a 1/10 hack but there is at least one good Cantor quote in mine. Help yourself to naming rights on "definition" vs "infinition". I liked another essay I read better for the simple reason it wasn't about being right it was about including our own pretending of "general authority"; otherwise this essay would be perfect so I'll give it a fair 9/10.

                Dear Jochen,

                What I see is not a difference between Cantor who died in a madhouse, perhaps because his trust in his own point set theory was shuttered by König, and Lawvere who is hopefully still very healthy. I am rather concerned with differences between reality and mathematical models. Many years ago I got health problems because mathematicians rejected "for mathematical reason" my argument that future data are not yet directly available by means of measurement in reality.

                Meanwhile, mandatory mathematics seems to require sophisticated efforts to fabricate new definitions of good old ideal notions like point and line. Why?

                As I tried to exemplify in my current essay, mathematical pragmatism (calculate as if ...) must not be one to one translated into a universal tool for description of reality. Are orthogonal quantum states still required if I am correct concerning Fourier?

                My hint to Kadin's extraordinary courage was meant as a challenge: How to apply your theory?

                Eckard

                Dear Daniel,

                thanks for your comment. I'm glad you found something to like about my essay, and thanks for the generous score. I'm not sure I'd say my essay is about 'being right'; I think about it as an 'essay' in the original sense of the word---it's an attempt, something that may well fail. So it's less 'this is how it is', and more 'wouldn't it be neat if this were how it is'.

                Anyway, thanks for reading; I'll have a look at your essay soon.

                Cheers

                Jochen