Epistemic Horizons: This Sentence is 1/√2(|True> + |False>) by Jochen Szangolies

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

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,

Thank you very much for this essay it was a real pleasure to read. Very well written and thought provoking too.

Pardon my slow-mindedness but I would like to grasp the essence of the argument for the non existence of f(n,k) i.e. what are some necessary preconditions for it to hold.

- Is the claim valid even if there are finitely many states?

- If k belongs to a finite interval of integers then I could build a finite set of experiments that would create a f(n,k) table for all possible values of 1 and -1 for each state (like when designing a truth table). In that case the mg operation must bring back an existing row since all rows would have already been exhausted by my truth table.

Many thanks for your help on this.

Best,

Fabien.

Hi Eckard,

Sometimes you know , it is not necessary to extrapolate or discuss about evident truths. It is maybe a lost of time and we are not here to see who is the most rational, deterministic or logic, all rational thinkers respect only the pure determinism and it is not necessary to extrapolate the causality , because the causality in maths can imply confusions sometimes, so I insist only on this pure dterminism if I can say.

We search answers and all assumptions are assumptions if they are not proved simply by experiments or proved mathematical Tools. Is it necessary to discourse about so evident things, I don t Think.

I repeat but we shall can never understand this real infinity beyond this physicality, we cannot define it , and inside the physicality , even if we can rank these infinities, we are limited still and Always , the same for our finite series . We can utilise all the best mathematical Tools that we want and take all the best past mathematicains or actual ones around a table, that will not change our limitations even with the best Tools utilised. We name this the real humility in fact because we are simply Youngs at this universal scale simply. It d be very vanitious to consider the opposite.

We can even take the set theory or others, that will not change our limitations about these finite series, the infinities inside the physicality or this philosophiocal infinity. The zero is not the problems , nor the numbers and their distributions and the correlations with the foundamental objects, we don t know what they are and why they are and how they are distributed really. We just know a small part of this universal partition. You can take all what you want like series and harmonical partitions towards the zero and the infinity or infinities, that will not change this truth of limitations even in considering the speeds and the physicality . Alkl this becomes philosophical.

So if I can Eckard , explain me your general philosophy about this universe and its origin, what do you consider like main cause ? and what do you consider also like main foundamental objects, because it seems necessary to better calculate this physicality and its numbers, particles and fields .

Best Regards

Hi Jochen,

Thank you for your well-written and engaging essay. I agree 100% with your closing thought for the need of a relative realism, except that I would express it as a contextual realism, since context encompasses more than 4D (or 3D+1) inertial reference frames.

You correctly assert that the key attributes of physical reality needed to explain quantum phenomena must include 1) finiteness and 2) extensibility. If physical context includes a non-zero ambient temperature, finiteness and extensibility are immediately accommodated. Absolute zero is an idealization that does not exist in reality, and the universe as a whole has an ambient temperature equal to its 2.7 K cosmic microwave background. For a contextual reality, a finite ambient temperature means that space itself is not infinitely continuous and position-momentum information is finite. A decreasing ambient temperature fine-grains space and creates new information to be discovered. In addition, when perfect measurement is defined with respect to a system's actual and objective context, empirical classicality is restored.

In my essay I analyze the deeply held assumptions that have led to the widely-held conviction that objective physical reality is non-contextual. I develop a conceptual model of physical reality that is objective and contextual, that is fully compatible with empirical models of physics, and that eliminates quantum paradoxes. I would welcome your thoughts on it.

Harrison Crecraft

Dear Jochen,

Thank you for your deep constructive response to my comment.

You write:

"... and on the other, has so far failed to produce any large-scale consensus."

I believe that the FQXi contests are a good "field" for the start of the Big Brainstorming. Look, ideas are already the tenth contests, and physicists and mathematicians have not yet found consensus on the two main fundamental issues for physics, mathematics and cognition in general, which Carlo Rovelli writes about in Physics Needs Philosophy / Philosophy Needs Physics : "What is space?", "What is time?" And today, the time is very worrying for all of Humanity, and we must learn to find consensus on all issues. Especially on the basics of knowledge. Here, just Philosophy, "mother of all sciences" comes to the rescue .. Recall Hegel: "The owl of Minerva begins its flight only at dusk"...

"... 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 believe that the search for the "fundamental principle" is necessary not only for quantum mechanics, but for knowledge in general.

In an interview with mathematician and mathematical physicist Ludwig Faddeev ( in the journal "EXPERT" (2007), entitled "The equation of the evil spirit" it is written: «Academician Ludwig Faddeev believes that today mathematical rigor is more important than physical intuition and it is thanks to mathematics that a "unified theory of everything" will be built.

The long-standing debate of scientists about what is more important - mathematical rigor or physical meaning, a correctly solved equation or an intuitive understanding of a natural phenomenon, continued throughout the 20th century, but at some time physicists seemed to win in it: Einstein as the creator of a special and general theory of relativity is better known to the average man than Poincare or Hilbert, Schrödinger is more popular than Weil, and Landau is more popular than Bogolyubov. But in recent decades, the situation began to change: it turned out that successful mathematical techniques have not just technical significance, but deep physical meaning. Mathematical intuition in solving increasingly complex physical problems may be more important than physical. And this caused a noticeable irritation of many great physicists. In the second half of the 20th century, a new generation of scientists appeared who could no longer be called pure physicists or mathematicians. Ludwig Faddeev is one of them. After graduating from the Physics Department of Leningrad University, he gained worldwide fame as a man who, together with his student Viktor Popov, solved the most complicated mathematical problems of the Yang - Mills theory, which later formed the basis of the theory of superstrings. The effects that were discovered were called "Faddeev-Popov spirits" and under this name entered all modern textbooks of theoretical physics. Faddeev is convinced that just as physics solved all the theoretical problems of chemistry, thereby "closing" chemistry, so mathematics will create a "unified theory of everything" and "close" physics. Faddeev is convinced that just as physics solved all the theoretical problems of chemistry, thereby "closing" chemistry, so mathematics will create a "unified theory of everything" and "close" physics. "

But can mathematics, the "language of Nature" "close biology? ... Big doubts ... Big questions .. Everywhere is the problem of the ontological basis of knowledge. I believe that there will be Pavel Florensky: "We repeat: worldunderstanding is spaceunderstanding."

I am very concerned that the crisis of understanding in the fundamentals of knowledge has spread to global society ... Let's begin this brainstorming session ... I score the highest rating for your constructiveness and the ideas of the "epistemic horizons". Please look at my ontological ideas and give critical comments .. .

With kind regards, Vladimir

Dear Jochen,

I loved your essay, very interesting approach to reconstruct quantum mechanics from first principles. I like the epistemic horizons idea, and the diagonal argument making connection with undecidability. Very nice interpretation of Wheeler's suggestion that you mention in the conclusion. I also liked that you try to get close to the classical ideal of local realism by using what you define as relative realism. In this respect, you may find interesting, I hope, a result that QM can be formulated on the 3d space or 4d spacetime, rather than on the configuration space, and especially that this gives a local dynamics as long as there is no collapse (possibility that I think is still on the table, as explained in the attached pdf).

Cheers,

CristiAttachment #1: post-determined-block-universe.pdf

Dear Jochen,

Thank you for your reply. That there are hierarchies of halting problems was insightful.

With regards to my initial question, I suppose I was mostly confused by the leap from the two states of coin tossing to infinitely many states at the core of any diagonalisation argument.

As I said, I am just trying to restate what is actually being stated in your proof and in particular what are the necessary assumptions for the proof to hold. That the system can be in infinitely many states appears as such an assumption.

That the system can be in infinitely many states does appear actually reasonable a priori, for we never know what "the" state of a system is before we measure it in some way.

I actually think that the coin example could be used to go beyond the two state system. In fact m1 would still be "Head is showing once the coin has landed" but the state could be something much more complicated linked to the initial setting of the experiment...or to the mechanical state of the coin.

Then I believe what your proof is saying is that:

"Given that a system can be in infinitely many states, there necessarily exist states such that the outcome of some measurements on those states is undetermined"

If that is the case, different physical theories can choose to work only with subsets of the states the system can be in (in the same way that one can decide to work with integers instead of the reals...in some sense, as long as this subclass of states forms a closed set under some dynamical rules and chosen operations, then it seems fine). Classical physics restricts the states to those that are determinable while QM embraces both kinds of states.

Is that a fair restatement of what you are saying?

Many thanks.

Best,

Fabien