Dear Dr. Flavio Del Santo,

As a layperson (I am a lowly undergrad and majoring in CS), I found your work to be simultaneously profound and accessible!

Prior to reading your work, I presumed determinism was built into the foundations of classical physics, and it was a joy to discover otherwise.I kept a copy your essay on my computer for repeated reading and future references ( some of the formalism eluded me).

Indeed, showing how determinism contradicts physicality provided me with a lot of food for thought ( determinism implies infinite information content, which violates the physical nature of information was a very interesting thing for me to know)

I dare to say the common view of classical physics as inherently deterministic is usually told and taught to everyone ( I was never told otherwise until now) is because:

a) Many find determinism to be powerful;knowing a sufficiently advanced intellect can predict with absolute certainty gives us hope that human civilization may become that intellect, so this tacit assumption is mistaken to be a part of the orthodox position.

b) Mathematics is deterministic in most cases ( we can prove with certitude certain statements from a set of axioms; thought Godel's Theorem gets in the way of perfect determinism, some statements cannot be proven) and we like physics to confirm as closely possible to mathematics ( something my and my co-author's essay (link: https://fqxi.org/community/forum/topic/3563) addresses).

Kind Regards,

Raiyan Reza

    Dear Flavio,

    Perhaps we are just talking past each other, but I must ask you to reread your Principle of Infinite Precision and ask yourself why you include the important qualifier THROUGH MEASUREMENTS. Then think about generating an uncomputable Real as follows:

    1. Write down the first million digits of the square root of 2.

    2. Bring a radioactive atom into the room

    3. Continue writing down digits of the square root of 2 until the atom decays as you write the Nth digit

    4. Then change and start writing down digits of pi, starting with the Nth digit of pi

    From an information point of view this an uncomputable Real

    From a measurement point of view it is completely equal to (utterly indistinguishable from) the square root of 2.

    Now perhaps if you review my comments, my insufficient clarity will nevertheless become intelligible.

    Thank you

    John

    Dear Flavio,

    Very nice.

    It sounds almost like you want to say that an indeterministic classical mechanics amounts to something like an ontological/physical interpretation of chaos. While usually the sensitivity to initial conditions is just a result of our ignorance of the initial state so that our models diverge from physical reality (which is itself deterministic), here you are saying such a state cannot even exist (since real numbers are not physically meaningful, and yet seem to be demanded by determinism). Would this be one way of interpreting the basic idea in this paper?

    Secondly. Does your position depend on a discrete view of space (i.e. to rule out the infinite capacity)? What if space is dense so that it can contain infinite information? I don't see how the spatial limitation of Gisin's follows from Landauer's Principle - it itself should follow whatever the best physics says about spacetime, not the other way around.

    This is just a nitpicking point - I thought it was a great paper.

    Best

    Dean

      Flavio,

      Your essay is very thoughtful and well written. But I don't see that you've made determinism at-all plausible, so I don't understand your conclusion that the question of determinism-or-indeterminism is undeterminable.

      In my essay I've suggested a third alternative: From the quantum level to the mental, the universe is essentially spontaneous - neither determined nor undetermined/random. As highly organized systems of spontaneity, each of us is self-determined, capable of arbitrarily responding to our surroundings.

      Jim

        Dear Falvio

        This is quite an interesting essay.

        I was particularly intrigued by the alternative classical theory possessing some features analogous to quantum theory. The implementation of the ontological indeterminacy aspect is noteworthy.

        However as I understand the scheme there seems to be some problematic aspect with the minimal requirements for measurement.

        Let's recall that the framework is meant to deal with the in-principle infinite number of digits that determines a real number, (associated with a physical quentity) and pass to a modified scheme in which only a portion of those digits have well defined values.

        So let me start with the second requirement :

        2 Intersubjectivity: Different agents can access the same measurement outcomes.

        This seems to make a lot of sense at first sight however, it must be emphasized that i is only so if it the different agents are truly referring to the SAME quantity. That means among other things the quentity at the same time ( or spactime event). Consider now for instance a particle moving in one dimension. We would like to focus on the value of its velocity ( ina given frame), but of course if we want to assign it, a value we should specify at which time or at what positio . Once those data are specified, it makes all the sense to look at the corresponding value of the velocity... but if time and position are subject to the same indefiniteness as everything else how can we make sure that two agents refer to the same quantity ( i.e. the velocity at time t or at position x).

        Related concerns arise when considering the first requirement:

        1. Stability: Consecutive measurements of the same quantity leave the already determined digits unchanged.

        To start with it seems to me that this can only be sensibly demanded if the quantity in question is one not expected, classically, to depend on time ( i.e. say a quantity which in the normal version would vanishing Poison brackets with the Hamiltonian) , otherwise a change can be expected even in standard situations. So perhaps one should at least place a bound of the time elapsed between consecutive measurements, but how to do so precisely if such precision is discarded ab initio.

        Finally, similar concerns apply to the last postulate:

        3. Precision improvability: With more accurate measurement apparatuses, more digits become available (with the former two properties)

        It seems we might properly talk about improvement of the measurement only as long as it is a measurement of the same quantity at the same time, etc. and as we have seen those notions seem to be made problematic by the basic ideas underlying the proposal.

        So perhaps Flavio could clarify these issues for us.

        In any event, as I said, the general idea is quite interesting.

          Dear Dean,

          thanks so much for your feedback and the interesting comments.

          Indeed, what you point out, that my proposal of "indeterministic classical mechanics amounts to something like an ontological/physical interpretation of chaos" is a way of regarding this matter.

          As for your second question, this is a natural assumption. We don't assume a discrete space(-time). But we just try to remove the infinities (and the infinitesimals) from the physical domain by positing that a finite region of space can only contain a finete amount of information. Landauer's principle and Beckenstein bound back up this idea.

          Thanks again and all the best,

          Flavio

          Dear Raiyan,

          glad to hear that you find some food for thought in my essay. And thanks for your comments.

          All the best,

          Flavio

          Dear Jim,

          thank you for your comment. I made determinism less plausible than before, but clearly its tenability stands as usual. For more insightful discussion of why the question of determinism vs indeterminism is undecidable on an empirical basis have a look at, for example, Suppes' "The Transcendental Character of Determinism" (referenced at the end of my essay).

          Best wishes,

          Flavio

          • [deleted]

          • Post #154

          I wanted to note that some earlier work reached the same conclusions regarding classical physics being indeterministic and real numbers being non-physical. Also that these things were very likely pointing towards the measurement problem. This was in the context of rejecting points of time, space, and instantaneous magnitudes due to their being non-physical (which, although different, is at least partly related to the infinite precision argument given by Flavio and Nicholas Gisin). This was the first of the papers. Time and classical and quantum mechanics: Indeterminacy vs. discontinuity (2003).聽

          I only recently learned聽of Nichola's and Flavio's work, and contacted them a few weeks ago. They were unaware of my work. Although聽we take different approaches, and my writing was terrible, there are enough similarities in the main conclusions that I must admit reading some of the comments here irks a聽little. There was little support for my conclusions at the time! For possible context, see this personal essay

          Flavio, if you are not aware of a paper, you obviously can't reference it, but I can't be expected to sit back and say nothing (if a part of me would really prefer to). Although a cough probably wasn't the best choice (particularly now), I also gave you a chance to perhaps say something in connection to acknowledging my work with my "Ahem" comment above.聽

          Regardless, yours is a brilliant essay and I hope it does really well.

          Best wishes

          Peter

          Dear Flavio,

          What a wonderful essay!聽 It took me on a very insightful journey and I have given it a top vote!聽聽

          I enjoyed the historical background, the articulation of the principle of infinite precision, and relating this to ideas on Kolmogorov complexity, information theory and measurement.聽 Your central thesis along with bringing these various topics together was very聽crafted.聽 I very much enjoyed your "surgical" approach to breaking topics and finding their underlying essence.

          Good luck for the contest!聽

          聽

          Cheers,

          Del

            Thank you for your reply! I think the question of understanding 'what the differences between classical and quantum physics boil down to' is fascinating and is certainly a very important research program, and I have enjoyed your other work on this topic.

            I do still have a question though. In order to approach this question, it's important to first resolve the question of what we mean by 'classical physics.' I myself see two ways to answer this:

            First, classical physics is what the physicists of the time understood it to be. In that case, the way to understand the difference between classical physics and quantum physics is to study the writings of the classical physicists. Here my understanding is that most classical physicists believed in an ontology which admitted variables that could take any real number value. On its own terms, then, it was deterministic. (Of course, I'm sure that there were some dissenting voices, but I suppose that in this approach to understanding classical physics one should try to identify the 'consensus view' and then run with it).

            Second, classical physics is a theory which applies in some specific limit - i.e. the limit of large sizes and low speeds. And it seems that in this limit, classical physics is deterministic, since the problem of infinite precision that you refer to will presumably only appear once one gets down to very small sizes. (At least, this is how I understand what you suggest - please correct me if I'm wrong).

            Since you argue that 'classical physics' can be indeterministic, I take it that what you mean by 'classical physics' is neither of those two things. Sp my question is simply - what do you mean when you refer to classical physics? How do you demarcate its domain of applicability?

            Dear Falvio,

            Your essay was perfect! Not only did you manage to flip current assumptions regarding determinism/indeterminism on their head, you provided grounds on which science in an ultimately non-determined world still makes sense.

            Best of luck in the contest!

            Rick Searle

              Dear Flavio,

              You can certainly write an interesting essay. It will take me quite some time to absorb all the ideas you have covered. I particularly liked: " We can only have the certainty that the future of the battle between determinism and indeterminism is open, too." in your conclusion, as it paves the way for centuries of intellectual sparring.

              For my first entry in this competition I have produced a light weight essay that I hope is enjoyable, even though I push the line of indeterminism through free will. I, like Tejinder, think it is the coarse graining of emergence that brings out aspects of indeterminism.

              Best wishes

              Lockie Cresswell

                Dear Prof. Sudarsky,

                thank you for your feedback and your very interesting comments on the minimal requirements for a (empirically adequate) measurement process.

                Let me instead start my reply in inverse order with respect to your question:

                1. Stabilty. Your concerns are torally right, and I should have been more precise. What I had here in mind is an axiom similar to that of quantum mechanics. Namely, the state of a system remains unchanged when it is not measured, modulo a unitary evolution. I was here assuming the trivial evolution and focusing only on the chenges of the states due to measurements.

                3. Precision improvability. Here it does not need to be at the same time. I am again thinking of repeated measurements on the same system. If even time is smeared and not sharply defined, there is an operational procedure that we call measurements that returns a certain number of digits. If one improves the precision of the measurement (dividing into ten a ruler, for instance) we should be able to find a new digits. However, all the previous determined digits are required to remain stable.

                1. Intersubjectivity. I think what you say about this is a good point. Indeed, admittedly time remains the most difficult issue of our FIQs framework. At least, if one wants to determine a quantiti which does not depend on time (a natural constant of physics, for example) this must apply. Then, to compare two dynamical quantities at the same instant, is indeed not fully spelled our in our model.

                I inted to wrote ore about general processes of measurement in non-deterministic theories. I will treasure your latter criticism to clarify this matters.

                Thank you again and best wishes,

                Flavio

                Thank you, Del, for your very kind words! Glad that you found my essay enjoyable.

                All the best,

                Flavio

                Dear Rick,

                thanks very very much for your kind appreciation. I am glad that you find something interesting in my work.

                All good wishes,

                Flavio

                Dear Tejinder,

                thanks for pointing it out. In fact, I had already read your essay and found some interesting ideas there.

                I wish you success, too!

                Best regards,

                Flavio

                Dear Lachlan,

                thanks for your feedbac and glad that you find my conclusive remarks inspiring.

                I did read your nice essay already some time ago (and positively rated it).

                I wish you good luck for the contest.

                All the best,

                Flavio

                • [deleted]

                • Post #165

                Hi Flavio,

                Regarding my earlier message, I'll try a different tack. In your essay you write:

                "As we will show in the next section, one can indeed envision an alternative classical physics that maintains the same general laws (equations of motion) of the standard formalism, but dismisses the physical relevance of real numbers, thereby assigning a fundamental indeterminacy to the values of physical quantities, as wished by Born. In fact, "as soon as one realizes that the mathematical real numbers are not really real, i.e. have no physical significance, then one concludes that classical physics is not deterministic." [13].

                In relation to the above anyway, can you explain whether or not you think there is anything different between our two works? Also, and although they're in a somewhat different context, do you or not think my work is closely related to the idea of infinite precision? Finally, had you known about my paper, do you think that you and Nicolas Gisin would have referenced it?

                I'm sorry to push Flavio, but considering a few things, I don't think I have much choice.

                Once again, I wish your essay and your work all the very best.

                Peter

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