Essay Abstract

We propose that science should proceed under the assumption that Nature is discrete unless discrete models are proved untenable. We outline an argument that explains the reasoning for this position. We also describe examples of simple quantized mechanisms which give reason to believe that the discrete approach can capture all the observed symmetries of nature.

Author Bio

Alexander Lamb is a freelance researcher in computational physics, network science, machine learning, and population modeling. When not conducting research, he works in both business simulation technology and communication skills training for scientists. He teaches improv theater, writes science fiction novels, and speaks internationally on the use of behavioral science and improv for organizational change, innovation, and maximizing creativity in scientific collaboration. Alex obtained his Masters in Artificial Intelligence from Edinburgh, UK, and has ongoing research collaborations with UC Santa Cruz, UC Berkeley, and CNR-ISTI in Pisa, Italy.

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7 days later

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  • Post #2

Dear Alex,

Your essay gives me a lot to think about, especially the quantum mechanics (section 3.3) part. Simplicity is beauty -- I fully agree with your point about aiming for the simpliest model. Nevertheless, personally, I wish you had predicted a higher chance for continuous models, especially after my essay proposing such a hyper-continuity model. :-)

Honda

    Dear Alex

    I read your extraordinary essay. The coincidences with what I am trying to propose are so shocking that my legs are trembling. I try to explained why, I think you have the information I am missing. The discrete models that you are proposing are just a partial description of the order I am trying to find, that it explains why we see the properties of the classical world we see. Particularly, the fact of no locality in my approach is expressed by the fact that when we collapse to a classical world we are taking a generic ultrafilter on the order topology which is a global fact. The way you relate the nodes of the graph is just the structure of the order, for example, the Continuum Hypothesis example shows that if the order is not choosen right, we don't get the result in the classical world, this is what it is happening in your models. When you say how we should iterate your models what are you doing is describing how the order topology should behave locally, i.e. you are choosing the ultrafilter.

    Finally your concern about the logic we should use it is missing something. We already use classical logic to describe and model quantum reality, it is what the classical approach does, but we can't understand very well quantum reality. What you do is construct your model by try and error and you try to explain why some iterating model gives the result you are looking for and others not. Why I am trying to say is that, if we introduce non classical logics, in my case a intuitionist one, we can explain these phenomena perfectly.

    I would like to hear your opinions again.

    J.Benavides

      Hi Honda,

      Delighted to hear your comment. I actually think that your hyper-continuity approach may be an excellent continuum approximation to the kind of structures I'm proposing. I don't know how far you've gone with creating a mathematical formalism for the sort of structures you discuss, but I'd be very interested to see what such a formalism would look like.

      Here's an example of the sort of question your approach made me think of, and which I'd love to be able to answer:

      If we associate with each point in an infinite set some other points from that same set, what are the requirements that have to be satisfied for some consensus notion of manifoldness to emerge from that set, even if that notion is not shared by every point?

      Hi John,

      Thank you very much for following up on my ideas and writing back. I'm very glad that you find merit in them. Certainly you're right that the kind of models I propose don't make ideal predictions. Each experimental particle only produces a single outcome. I'm also delighted that you're thinking about these topics from the continuum direction, as what my work lacks is a continuum approximation and I'm still struggling to generate one. (Regardless of whether we expect the universe to be continuous or discrete, it still appears continuous at familiar scales and a working physics theory needs to be able to reconcile with that fact in order to be useful!)

      One researcher whose work you may be interested in is Andrei Khrennikov. I saw him talk at DICE 2010 and he was very persuasive. He has a working model of QM that is continuous but not dependent on complex numbers. It seems tantalizingly close to the wave expansion model that I employ. I'd be keen to hear your opinion of his approach and wonder if it may be of use to you.

      Alex

      16 days later

      Dear Alex,

      I very much enjoyed your essay, and your analysis of discrete models and symmetry groups. Your "Principle of Minimal Complexity" seems useful. A fascinating and thorough approach!

      Best wishes,

      Paul

      Dear Alex,

      I'm glad to see you participating in the contest. Interesting essay.

      Best.

      Dear Alex,

      Your essay may be a strong demonstration that Lorentz invariance is possible in a discrete approach. On some posts, some people just says that lack of Lorentz invariance simply falsify all discrete models. Your work deserve more impact. I hope that here, it will convince our FQXI community that Lorentz invariance is not incompatible with discrete models. We just have to see your youtube videos.

      All the best

      Ray