Essay Abstract

In this essay I argue that the large discrepancy between the calculated vacuum energy density of the universe and the amount corresponding to the observed acceleration of spatial expansion places a lower limit on the wavelengths of elementary fields. I demonstrate how the lowest wavelength, highest-energy fields, which I call holons, could form the basis for a digital system akin to a structurally dynamic cellular automaton. I show how such a system could model the growth of form, and offer an increasing topological entropy corresponding to the forward arrow of time. I examine the points of commonality between the holon hypothesis and the holographic principle, but argue that the two are independent, as the former does not necessitate reference to a boundary. Finally, I comment on the development of interferometry tests for the graininess of space that could also point to a fundamental minimum wavelength.

Author Bio

Paul Halpern is a theoretical physicist specializing in general relativity, complex systems, and the history of physics. He is Professor of Physics at the University of the Sciences in Philadelphia. In 1996, he was a Fulbright Scholar researching evolutionary algorithms at the Humboldt University of Berlin. In 2002, he received a Guggenheim Fellowship to study the history of higher dimensional theories. Halpern has published twelve books, along with more than thirty research articles and forty scholarly presentations. In recognition of his science writing he was the recipient of an Athenaeum Literary Award.

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  • Post #2

Hi Professor Halpern,

It was a pleasure to read your essay, and thank you for bringing structurally dynamic cellular automata to my attention. My research is in the domain of such models and this was a particular variant of which I was not aware.

Out of curiosity, do you see synchronous update of the sort employed in cellular automata to be central to the success of such a model, or do you think something more like Langton's Ant would suffice if operating over the right structure?

(If you're interested in algorithms of this sort, I would draw your attention to my own essay, which outlines several, which I've used for modeling both particle phenomena and the generation of spacetime geometry.)

Alex

    Dear Professor Paul Halpern,

    Holoarchy of Holon is a good philosophy to elucidate a Hierarchical clustering in, Coherently-cyclic cluster-matter universe model.

    Thanking you.

    With Best Wishes,

    Jayakar Johnson Joseph

      Hello professor Halpern, I was lost by the complexity of your essay but wondered whether the Archimedes screw is a structurally dynamic cellular automata?

      Alan

        Hi Paul,

        I like the holon idea and your essay, holons are something like my "particles made by their properties" in my essay, so maybe the ideas there are not so strange as it appears to be (and I have to read something more about holons and related stuff :-)

        But, in my opinion, holons assumed to be "... a photon (or other fundamental field) of highest energy and lowest wavelength" should be highly "reactive", and a Universe filled up with such particles, permeating everybody and anything, would be an extremely dangerous place. A holon particle stream would be by definition far more destructive than cosmic gamma-ray bursts.

        What comes me to mind as a resolution to this problem is an idea of "holon confinement", e.g. in a string ? AFAIK, string confinement of quarks was proposed in the literature sometime ago.

        Best regards,

        -Joachim.

          Dear Paul,

          I find your proposal intriguing and intelligent. The analogy you draw, between the 'ultraviolet catastrophe' and the discrepancy between theoretical and observed values of the cosmological constant, seems apt. In that context, however, I would point out that Planck's "solution" (to the former) was purely a mathematical device--the beginning, not the end, of many unresolved issues.

          I also liked your "mailbox" metaphor. It might prove helpful in clarifying the nature of 'information', which seems to be a glibly misused concept these days. In a number of submitted essays, there is reference to information being 'stored' or 'encoded', when the author simply means that there is continuity within reality itself, and from one description of reality to another, (at another time, for instance). While organisms explicitly need to model their environment, encoding it in some representation, there is no reason to assume that physical reality in general does this. The information is encoded by physicists, not necessarily by the world they study.

          Thanks and best wishes,

          Dan

            Hi Alex,

            Thanks for your kind comments. Glad to see that you are interested in structurally dynamic cellular automata. I will certainly have a look at your essay -- sounds very interesting! In answer to your question, one of the advantages of cellular automata is their flexibility, so synchronous updates would not be essential to the model's success. CA that display highly complex structures, resembling universal Turing machines, such as Langton's Ant or a glider gun, represent promising steps forward in trying to link discrete models with the dynamics of nature.

            Dear Jayakar,

            I appreciate your kind comment! Many thanks!

            -Paul

            Hi Alan,

            The Archimedes screw is a mechanical device with repetitive motion. Structurally dynamic cellular automata are mathematical, not physical constructs. However it might be interesting to use the latter to try and model the former.

            Best regards,

            Paul

            Hi Joachim,

            Glad that you like the holon idea. Interesting point you raise. My intention, however is to suggest these as limiting particle states, meaning that the universe today would be filled with particles spanning a wide range of frequencies (and energies). The spectrum of frequencies would be consistent with the current frigid temperature of space. However, instead of an unlimited range of frequencies, holon states would constitute an upper bound. This would cap the vacuum energy density at a value consistent with the amount needed for the observed acceleration of spatial expansion.

            Best regards,

            Paul

            Dear Dan,

            Thanks for your thoughtful remarks! Yes you are absolutely correct that Planck meant his resolution of the blackbody radiation "ultraviolet catastrophe" as a mathematical device, rather than as a physical quantum. It was Einstein who brilliantly suggested in his theory of the photoelectric effect that the quantum is a physical notion. Glad you like the mailbox metaphor! Interesting what you write about the distinction between encoding information and maintaining continuity within reality.

            Many best wishes,

            Paul

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            • Post #12

            Dear Professor Halpern,

            Your essay provides much food for thought. I would like to know how in the scenario of a holon falling into a black hole this idea can be reconciled with the GR prediction that the holon becomes gravitationally blueshifted.

            Thank you,

            Armin

              Dear Armin,

              Thanks for your kind comment! That is a fascinating question. It is unclear if GR applies in its classical form down to such minuscule length scales. According to the standard line of reasoning, because of the proximity to the Planck scale, one would need to replace classical GR with quantum gravity. Alternatively, let us consider the discrete approach, with fields emerging from an evolving network of connections similar to structurally dynamic cellular automata. In that case gravitational blueshifts or redshifts would represent the impact of regions with different topologies upon the size (wavelength) of structures within the network. The holon size would remain the lower limit of such distortions, similar to a single stone representing the minimal structure in the game Go.

              Paul,

              Incisive argument for holons that led me with the weight of your argument in each direction you took including your holon thrust.

              I haven't heard many looks into a dark energy explanation that work.

              Quite persuasive and scholarly.

              Jim Hoover

                Dear Jim,

                I appreciate your comments. Thanks so much! I'm glad you found the essay persuasive.

                Best regards,

                Paul

                5 days later

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                • Post #17

                Only this Essay and my comment reminding about Holometer

                http://www.fqxi.org/community/forum/topic/946

                  Dear Yuri,

                  Thanks for your comment and the link to your interesting essay!

                  Best wishes,

                  Paul

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                  • Post #19

                  Hi dear Prof.Halpern,

                  Congratulations, the evolution is so important.....quantum spheres.....H....CNO..Hydrospheroids about 3.4billions......CH4 H20 HCN H2C2 NH3....time evolution rotating spinning proprotions.........UNICELLS....differenciation......pluricells.....sponges ..mmedusas.......humans................UNIVERSAL SPHERE.

                  The encoding is rational simply.

                  Best Regards and good luck

                  Steve

                  Dear Steve,

                  Thanks for the kind comments and for pointing me to your theory of spinning spheres!

                  Best regards,

                  Paul