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

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  • 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

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        • 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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