Essay Abstract

What is the fundamental nature of reality ? After the development of the atomic theory of matter and nearly 100 years of quantum mechanics, we know that all objects in our world are made up of discrete units, namely atoms and molecules. Experiments in atomic, nuclear, and particle physics have shown that this discreteness (i.e. digital character) is replicated at shorter and shorter distance scales, to dazzlingly short ranges and almost unimaginably high energies. Thus, despite the superficial appearance of continuity at the macroscopic length scales on which we live and breathe, at its core reality is discrete in character, that is to say, digital. However the fact that this discreteness is correctly described by quantum mechanics means that it is a special kind of "digitalness" which we can express in the following way: we live in a world made of digital objects with the added complexity of a continuous quantum-mechanical phase. In this essay I address this idea and show how the historical development of first discrete and then continuous mathematics led to a classical physics which was based on untested assumptions of the continuity of matter. Ultimately these assumptions were unphysical, and had to be rejected in the face of experimental evidence from chemistry and atomic spectroscopy. The resulting development of quantum mechanics led to the correct modern digital description of matter but with the crucial addition of a quantum-mechanical phase factor.

Author Bio

Michael P. Bradley was born in Victoria, BC, Canada, in 1971. He received the B.Sc. (Honours) degree in Applied Physics from the University of New Brunswick in 1992, and the Ph.D. degree in Physics from MIT in 2000. From 2000 to 2003, he was a research scientist at Axcelis Technologies. In July 2003, he became a professor in the Department of Physics & Engineering Physics at the University of Saskatchewan. Dr. Bradley is currently a Research Fellow at the Bureau International des Poids et Mesures (BIPM), in Sèvres, France, working on BIPM's planned superconducting watt balance.

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Hi Michael, I found your style of writing very easy to read and liked your explanation of a 'special kind of digitalness'. Thanks and nicely explained. Alan.

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    Hi Alan,

    Thanks very much! Glad you enjoyed the essay.

    -Cheers,

    Mike Bradley

    5 days later

    Hi Mike, I've been asking a few authors about a new idea in foundational physics which I'd like you to consider please. At the time of Newton, why didn't anyone think about an Archimedes screw as a model for the graviton, a particle responsible for his force of attraction or spooky action at a distance?

    Best wishes, Alan

    Michael,

    I find that your essay was one of the few advocating a 'digital AND analog' answer that made a serious effort to explain exactly in what way reality could be characterized by these two seemingly contradictory descriptions. It seems to me that your suggestion can be summarized as follows: our description of anything that exists in space must be digital because below a certain limit it loses its essential character, but because it is (by quantum mechanics) associated with a phase it gains a 'continuous' aspect. If I misunderstood, I'd appreciate a correction.

    Yours is the only paper (other than mine) that I have read so far which draws special attention to the quantum phase. You may find my effort to explicate its physical origin of interest.

    Armin

      Michael,

      Thanks for the fine essay, which makes some very good points about how continuity is non-physical in many ways.

      Below is some feedback on a few details of your essay which are admittedly minor.

      In your definitions you write,

      "Continuous entities are non-countable, and in this way they are like the real numbers; there are always more real numbers (in fact, infinitely many more) to be found between any two real numbers on a number line, whereas for countable digital entities like the integers this is not the case."

      This seems not quite correct. The rational numbers are countable, yet they also have the property, like the reals, that between any two rational numbers there are an infinite number of rationals. The distinction between the countable and uncountable numbers is more subtle than this property.

      Later on, you write,

      "continuous mathematics was first developed in the form of geometry, which however remained utterly disconnected from the mathematics of countable objects until Descartes"

      While geometry and algebra were not synthesized until Descartes developed analytic geometry, it does not seem accurate to say that geometry was 'utterly disconnected' from countable arithmetic before then. For example, the ancient Greeks certainly were able to count the sides of a polygon, and they studied Pythagorean triples (i.e., integers satisfying the Pythagorean theorem).

      But I do appreciate how you put the rise of continuity in physics in historical context, and enjoyed the essay!

      Regards,

      Tom

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        Hi Alan,

        That is an interesting idea which I have not heard of before, I will have to look into it before I could comment intelligently.

        Thanks for the comment!

        -Cheers,

        Mike Bradley

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        Hi Armin,

        Thanks very much for the comment. I'm glad you found the ideas interesting; I think your summary basically agrees with the point I was trying to make.

        I will indeed look at your paper on the quantum phase and its physical origins; that sounds really interesting!

        -Cheers,

        Mike Bradley

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        Hi Tom,

        Thanks for your comments, and glad you enjoyed the essay.

        Re: your points:

        (1) Yes you are absolutely right about the rational numbers being countable and yet there being arbitrarily many between any two points on a number line.

        So although there was a good point to be made my explanation is not exaclty correct.

        (2) Yes I was perhaps too theatrical in my contention that there was an "utter disconnect" between continuous and discrete mathematcis until Descartes. Nonetheless I think the real synthesis of the two only happened at that time, and was hugely important for future developments.

        Thanks for these useful comments!

        -Cheers,

        Mike Bradley

        7 days later

        It's great for a change to read an essay staying with the facts and not drifting off into wild speculation. The historical perspective has been enlightening! One thought I've had while reading the essay is this: while matter is made of atoms, atoms are made of a nucleus and electrons, the nucleus contains nucleons, which in turn are composed out of quarks... what if this hierarchy would just continue without end? Then at each level, the world would be discrete. But however, there would be no most fundamental discrete level, so in this sense the world would not be discrete. Surely philosophers have thought about this option...

        A small fine print about the issue of complex phase: in principle, complex numbers are not inevitable in quantum theory. While being physically unrealistic, quantum mechanics with purely real numbers is a mathematical possibility having many phenomena in common with ordinary complex QM, in particular interference.

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          Hi Tobias,

          Thanks for your comments and glad you enjoyed the historical narrative, I do think it is useful to consider these questions in that context.

          Re: your first question, if there are infinitely many layers of discrete buliding blocks, then yes we have the philosophical problem you posed. In that sense you then have to impose a cutoff or coarse-graining to get a truly discrete "fundamental" description.

          RE: your second comment, that is interesting, I didn't know about purely real QM-- can you provide a reference for that ?

          -Cheers,

          Mike Bradley

          Hi Mike,

          unfortunately, I'm having trouble finding a good reference--there's more literature about "quaternionic quantum mechanics", which goes beyond even the complex numbers. The original work seem to be contained in here:

          Ernst Stueckelberg, "Quantum Theory in Real Hilbert space", Helv. Phys. Acta 33, 727 (1960).

          but this paper I couldn't find online.

          You can think of wavefunctions in real quantum mechanics as analogous to water waves. A water wave is described by a single real number at each point, but nevertheless there is interference between water waves.

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          Hi Tobias,

          OK great-- thanks!

          -Cheers,

          Mike B.

          17 days later
          • [deleted]

          Sub: Possibility of manipulation in judging criteria - suggestions for improvement.

          Sir,

          We had filed a complaint to FQXi and Scienticfic American regarding Possibility of manipulation in judging criteria and giving some suggestions for improvement. Acopy of our letter is enclosed for your kind information.

          "We are a non-professional and non-academic entrant to the Essay contest "Is Reality Digital or Analog". Our Essay under the same name was published on 29-12-2010. We were associated with Academic Administration as a part of our profession before retirement. From our experience, we were concerned about the problems and directions of current science. One example is the extended run and up-gradation given to LHC, (which was set up to finally prove that Standard Model and SUSY were wrong), even when Tevatron is closing down. Thus, after retirement, we were more focused on foundational works addressing, in one of its many facets, our understanding of the deep or "ultimate" nature of reality.

          Specifically we were concerned about the blind acceptance of the so-called "established theories" due to the rush for immediate and easy recognition even on the face of contradictions raising questions on the very theories. One example is the questions being raised on the current theories of gravitation after the discovery of Pioneer anomaly. While most students know about MOND, they are not aware of the Pioneer anomaly. Most of the finalists of this contest have either not addressed or insufficiently addressed this question. We hold that gravity is a composite force that stabilizes. This way we can not only explain the Pioneer anomaly and the deflection of the Voyager space-craft, but also the Fly-by anomalies.

          Similarly, we were concerned about the blind acceptance of some concepts, such as inertial mass increase, gravitational waves, Higg's boson, strings, extra-dimensions, etc. Some of these are either non-existent or wrongly explained. For example, we have given a different explanation for ten spatial dimensions. Similarly, we have explained the charge interactions differently from the Coulomb's law. We have defined time, space, number and infinity etc., differently and derived all out formulae from fundamental principles. There are much more, which we had discussed under various threads under different Essays. We are the only entrant who defined "reality" and all other technical terms precisely and strictly used this definition throughout our discussion.

          Though our essay was on foundational concepts and we derived everything from fundamental principles, it was basically alternative physics. Moreover, we are not known in scientific circles because we did not publish our work earlier. Hence it is surprising that even we got a community rating of 3.0 and (12 ratings) and Public Rating of 2.5 (2 ratings). We have no complaints in this regard. However, we have serious reservations about the manner in which the finalists were chosen.

          A set of thirty-five finalists (the "Finalists") have been chosen based on the essays with the top Community ratings that have each received at least ten ratings. The FQXi Members and approved Contest entrants rate the essays as "Community evaluators". Since many of the FQXi Members are also approved Contest entrants, this effectively makes the contestant as the judge for selection of the finalists. This process not only goes against the foundational goals of the Contest, but also leaves itself open for manipulation.

          Most contestants are followers of what they call as "mainstream physics". Thus, they will not be open to encourage revolutionary new ideas because it goes against their personal beliefs either fully (like our essay) or partially (like many other essays that did not find place in the final list. One example is Ms Georgina Parry. There are many more.) The prime reason for such behavior is cultural bias and basic selfish instinct of human beings. Thus, truly foundational essays will be left out of the final list.

          In support of the above, we give a few examples. While there are some really deserving contestants like Mr. Julian Barbour, who really deserve placement in the final listing, the same cannot be said for many others. Mr. Daniele Oriti, who tops the list of finalists, says that whether reality is digital or analog "refers, at least implicitly, to the 'ultimate' nature of reality, the fundamental layer." He admits that "I do not know what this could mean, nor I am at ease with thinking in these terms." Then how could he discuss the issue scientifically? Science is not about beliefs or suppositions. His entire essay exhibits his beliefs and suppositions that are far from scientific descriptions. He admits it when he talks about "speculative scenario". Yet, his essay has been rated as number one by the Community.

          The correspondence between us and Mr. Efthimios Harokopos under his Essay and our comments under the various top ranking finalists show the same pattern. One example is Mr. Paul Halpern. We have raised some fundamental questions under the essay of Mr. Hector Zenil. If the answers to these questions are given, most of the finalists will be rejected. If the idea is to find out the answers to these questions, then also most of the finalists will be rejected.

          The public that read and rated the essays are not just laymen, but intelligent persons following the developments of science. Their views cannot be ignored lightly. Mr. Daniele Oriti, who tops the list of finalists as per community rating, occupies 35th place in public rating. Mr, Tejinder Singth, who is 7th among the list of finalists as per community rating, occupies 25th place in public rating. If public rating is so erroneous, it should be abolished.

          Secondly, the author and interested readers (including FQXi Members, other contest entrants, and the general public) are invited to discuss and comment on the essay. Here personal relationship and lobbying plays an important role. An analysis of the correspondence between various contestants will show that there was hectic lobbying for mutual rating. For example: Eckard Blumschein (Finalist Sl. No. 15) had written on Mar. 15, 2011 to Mr. Ian Durham (Finalist Sl. No. 3) "Since you did not yet answered my question you give me an excuse for not yet voting for you." There are many such examples of open lobbying. One of the first entrants visited most contestants and lobbied for reading his essay. Thus, not only he has received the highest number of posts under his Essay, but has emerged as one of top contenders.

          The above statement gets further strengthened if we look at the voting pattern. More than 100 essays were submitted between Feb.1-15. Of these 21 out of 35 are the finalists. Of these the essays of 14 contestants were published in 5 days between Feb. 14-18. Is it a mere coincidence? For some contestants, maximum rating took place on the last day. For example, on the last date alone, Mr. Paul Halpern rose from 14th place to 5th place, Mr. Donatello Dolce rose from 35th place to 14th place, and Mr. Christian Stoica came into the top 35. All these cannot be coincidental.

          Thirdly, no person is allowed to submit more than one essay to the Contest, regardless if he or she is entering individually or as part of a collaborative essay. Yet, we suspect that some have indulged in such activities. For example, we commented below the essay of one contestant on March 4. We got a reply from the next contestant the same day. The correspondence continued. The original contender has not replied to us. In fact he has only replied twice in 20 posts. This is surprising.

          In view of the above, we request you to kindly review your judging process and forward all essays to an independent screening committee (to which no contestant or their relatives will be empanelled), who will reject the essays that are not up to the mark and select the other essays without any strict restriction on numbers to the final judges panel. This will eliminate the problems and possibilities discussed by us. This will also have the benefit of a two tier independent evaluation.

          Our sole motive for writing this letter is to improve the quality of competition. Hence it should be viewed from the same light".

          Regards,

          Basudeba.

          2 years later
          • [deleted]

          Hi Mike,

          Have you read Communication in the presence of noise by Shannon?

          - Shawn (s'toon)

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