Dear Simon, Thank your for these comments and questions (meanwhile I have also read you own essay with interest, it will take me some time to digest the main point you make but so far I agree with it). Since your question is posed in the context of the MWI, let me confess that in my early twenties I decided not to smoke, drink alcoholic beverages, eat meat, own a car, curse or shout in public, betray any lover, or waste my time on string theory and the many worlds interpretation (the latter two for the same two reasons: first, the religious zeal and sense of certainty of adherents of said ideas, and second, once more against the spirit of science as I see it, both assume QM as absolutely true and given, which already then I felt would need to be replaced at a more fundamental level - now that I have become familiar with the notion of emergence, I feel this even more strongly). However, your question can be detached from the MWI and one may validly ask what it means for a wave-function to be uncomputable: this may already happen for a two-level quantum system, if the (pure) state, seen as a point on the Bloch sphere, has non-computable coordinates. Inspired in part by the recent work of Gisin (and his collaborator Del Santo), but also by the much earlier work of the Dutch intuitionistic mathematician L.E.J. Brouwer, with my student Tein van der Lugt and others I am currently pursuing such questions, which come down to analyzing the role of real numbers in physics, including questioning even the definition of the real numbers in mathematics (which in intuitionism is very different from classical mathematics). Ultimately, I hope for a theory in which random sequences (in the sense of Kolmogorov, Chaitin, etc.), lawless choice sequences (in the sense of Brouwer), the output of repeated measurements on quantum systems, the role of (non)computability, finite precision even in classical physics, hidden variables, etc. all fall into place. You would also be well qualified to contribute to this program.

Stay in touch! Best wishes, Klaas

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

      Dear Heinz,

      Thank you for adding this extremely interesting perspective. Is there any relevant literature I could read to understand this issue in more detail? Surely, almost every physicist including even Newton himself has failed to distinguish between these two notions of time, if they are indeed distinct (for the physicists may have been right in identifying them after all). What, for example was the original Classical Greek notion of determinism, other than "order" in the Platonic sense, which seems timeless to me?

      Best wishes, Klaas

      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.

        Dear Heinz, Thanks, I found your essays and will read them as soon as I have time (we are in the middle of a teaching period here, which takes far more time than normal). As to the "Unanschaulichkeit of modern physics begins with the coup of the Göttingen school of mathematics..." I wrote a historical essay about that which might interest you, seehttps://arxiv.org/abs/1911.06630. You surely know that Einstein reprimanded both Heisenberg and his earlier (1905) self for insisting on too much empiricism, see e.g. Heisenberg's autobiography "Der Teil und das Ganze". I would say this "Unanschaulichkeit of modern physics" already started with Newton's law of gravity, which he saw as a purely mathematical description and warned against any physical interpretation. Best wishes, Klaas

        Dear Chidi, This is hard to reply to, especially since we are in the middle of a teaching period here, which takes far more time than normal. Some comments one my paper ask direct questions about it which I try to answer quickly, others forward their own theories which are typically only peripherally related to my paper. These take far more time to answer, however good they may be. I hope you understand this. Best wishes, Klaas

        You are right. Bear with me, sir.

        And when you find the time please do take a peak I'm sure will find the connection interesting.

        Dear Klaas,

        Please do not bother to react to my question above; I also know what is like to have to try to reply to all comments while teaching. Moreover, I posted the question rather for your consideration and did not expect an answer, but should have made that explicit. The reason for posting the question was that, personally, I think it is interesting to see what bringing the idea of atomism to its logical completion looks like.

        Best wishes,

        Vesselin

        Hi well , like I said your essay is a good essay with a good ranking of all the different thinkers and a mix of their ideas about the computabilities, the randomness, the mathematics, we see a very good knowledge of all their works, Solomonoff, Kolmogorov, Chaitin, Svozil ,Downey, Hirschfeldt, Born, Bell, Godel, Hilbert,Durr, Goldstein, Zanghi, Hooft,and others that I forget to name.

        So indeed you have well learnt their works and you play with all this, but I see in all humility maybe a big problem , you consider these strings and correlted bits and a kind of wave pilot, so it is correlated with these 1D main strings at this planck scale and the 1D main field form this cosmology if I can say, you search the good road to correlate the universe, the quantum mechanics and the quantum computing in trying to consider the good randomness, series finite and infinites in a kind of universal converging partition, but for me if the main essence is made of particles instead of fields like in the strings, branes, Mtheory , so you are not going to converge with this universal foundamental mechanics if I can say.

        We cannot affirm that all is made of fields and philosophically the same, the strings consider a 1D main field at this planck scale and extradimensions but we cannot affirm that it is the truth to explain our geometries, topologies, matters and properties.

        My model considers 3D spheres coded but I am not here to speak about this, we are not here to prove philosophically who is right about these foundamental mathematical and physical objects and the correlated philosophy of this universe, we cannot affirm simply. Like I told your essay shows that you have well studied all these works and that you perceive the generality, it is important. But if I can , if your strings generally are not correct , so never you shall explain the quantum computing , I recognise good mathematical Tools with these strings to rank the fields, but witten has created a prison and I beleive that many confound his field medal wich is a very good mathematical work with his theory of strings. I doubt that this universe is only made of photons and that they oscillate due to strings to imply the physicality. Witten and Einstein even if the GR and SR are correct have created a prison for the thinkers. So the landscape is complex and we cannot affirm the main cause and the philosophy.

        You can utilise all what you want for a general universal landscape, if the foundamental objects and the philosophy general are not correct, so just a part is correct but not the generality. And the non commutativity is not the problem but the foundamental Tools , objects and the general philosophy yes. I consider like I told you these 3D spheres in a kind of superfluid gravitational aether, space. And 3 main primordial coded series, one for the space and two fuels, the photons and the cold dark matter and when they merge they create these topologies, geometries, matters and properties with fields.

        he wave particles duality is respected also because all is in contact when we consider specific finite primordial coded series of 3D spheres. I formalise all this with these mathematical Tools, an intrinsic ricc flow, the Hamilton Ricci flow, an assymetri Ricci flow that I have invented to explain the unique things, the lie derivatives, the lie algebras, the lie groups, the topological and euclidian spaces, the Clifford algebras, the poincare conjecture, the deformations of spheres also. Who is right ? me or the strings theorists ? we don t know and nobody can affirm but when I see the nature, it seems evident that these spheres, spheroids, ellipsoids,....are the choice of this universe, why I don t know but this geometry is different, it is the perfect equilibrium of forces and has no angle and can create all geometries.

        The big problem is philosophical in fact. It is not easy I know to change a road of thoughts for the thinkers but the doubt is the real torch of generalists, if they are persuaded about unknowns , so it is a problem of Vanity for me, in all case these strings and these 3D spheres can converge because they oscillate also and are in motions, and in contact due to this universal superfluidity of the space.

        All this to tell you that for a quantum computer , we must absolutelly utilise the good foundamental objects , if not we cannot reach it, the aim is not to play with all the mathematical Tools invented by all our best thinkers in maths about this randomness, the infinities, the real infinity, the finite series, the Waves, fields... the aim is to find the good universal partition with the foundamental mathematical and physical objects and their universal philosophy.

        Regards

          My comments are based on the text presented in the essay, without a consideration to any work cited, and my limited knowledge of the subject.

          1. "For a fair coin flip the probability of each string Пѓ within 2^|Пѓ| is 2в€'|Пѓ|, so that an apparently "random" string like Пѓ = 0011010101110100 is as probable as a "deterministic" string like Пѓ = 111111111111111. Therefore, whatever its definition, the "randomness" of a string cannot be defined via its probability."

          I am not sure why the string 111111111111111 is referred to as deterministic? If we consider the fair coin flip generated strings then this is as probable as 0011010101110100 as you stated, but if we consider 111111111111111 to be deterministic for its given generator mechanism produces only 1s, then all sequences are to be deterministic to be the outcome of their respective generator mechanisms, not a result of fair coin flips. I presume the difference in string length is typographical (16 vs. 15 bits), but that is intended, then I missed the point. Indeed the Kolmogorov complexity of a given string 111111111111111 may be very low, but the Kolmogorov complexity of the process of generation (coin flip) has to have infinite detail to generate truly random sequence of any length. Moreover, complexity of even 0011010101110100 can be as low as one bit if we compare against the pre-set base sequence of 0011010101110100. That is the complexity depends on the basis of generation or comparison.

          Furthermore, if we leave the definition of randomness of a process on interpretation, then by ignoring the generator mechanism any physical process can be interpreted to have a degree of randomness.

          But, if we consider the underlying reality of quantum system to be analog or continuous with infinite possible configuration and require transitions to be always in quanta depending on the gate with discrete allowances presented by the observing system, then the process will have genuine randomness as discussed in my essay -- Mother of All Existence.

          2. "Theorem 3.2 With respect to P^в€ћ almost every outcome sequence x в€€ 2^N is 1-random."

          Quite a few places, 2^N notation has used the space of integers in the power rather than a number N, which I could not follow if that was intended.

          Rajiv

            Hi, why Always strings like foundamental objects`? like it was sure that they are the foundamental objects at this planck scale with a 1D main field ? if the universe is not like that, so we cannot reach with the strings the quantum computing , so the binaries 1 and 0 even with Pi digits cannot converge,

            regards

            The problem is complex and mainly philosophical. Why the majority of thinkers now consider that all comes from the fields ? it is due to the strings theory in fact and Witten, they consider that we have only photons due to an infinite heat and that this thing oscillates these photons with strings at this planck scale in 1D connected with a 1D main Cosmic field. And after with the geometrical algebras they create extradimensions towards 11D. and they explain the emergent topologies, geometries and matters, I can respect these strings and recognise good mathematical plays to rank these fields but the generality for me is totally false, because we have probably coded particles and 3 main finite series of particles coded merging in a superfluid to create these emergent topologies, geometries, matters and properties of Waves, fields and particles. I consider a pure 3D at all scales. In fact it is logic that these particles are the main essence , we cannot have fields without particles because without motions, we have particles but no field, not the opposite, this strings theory and general relativity have really created a prison, and it is difficult now to discuss with these strings theorists, they cannot change their line of reasonings, they are persuaded. But these strings have a big problem philosophical ,they don t explain the evolution...

            Dr Landesman -

            A brilliant, erudite essay. Unfortunately I do not have the expertise to follow the mathematical reasoning and I am puzzled about the epistemological significance of the findings. I was left "in the weeds" so to speak. But I do agree that physical determinism has been shown to be false - although that result is not provable.

            I have made a more ambitious effort to bridge the gap between the quantum and mathematical challenges using a three-worlds framework. I'd appreciate your review if you have the time.

            Cheers - George Gantz: The Door That Has No Key: https://fqxi.org/community/forum/topic/3494