Essay Abstract

I bring forward some arguments to support the thesis that nature is fundamentally discrete, and present my own thoughts about the direction in which one could look for a possible, consistent "theory of everything" describing gravitation and quantum particles.

Author Bio

Daniel Canarutto is a researcher in Mathematical Physics at the Faculty of Engeneering of the University of Florence (Italy). His main research interests deal with the geometric structures underlying physical theories. He has published papers, on various international journals, on spacetime singularities, spinor geometry, and the geometry of distributional bundles applied to quantum physics.

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Dear Mr. Canarutto,

I was charmed by your short and clear, but deep essay. Although my essay argues for fundamental continuity (in relation to singularities in General Relativity), I must say that your arguments for discreteness are probably the most convincing I saw so far. I think that the image of a quantum world you presented captures some essential aspects, which indeed can be related to General Relativity in the way you said. As a matter of fact, my own vision of unity is somehow similar, but backwards than yours: I see the same kind of network of particles, but obtained from the topology of spacetime (probably the simplest idea of this kind is represented by the topological charges - Einstein-Rosen, Wheeler). Nevertheless, I am not able to tell yet how this relation is obtained.

Best regards,

Cristi

    • [deleted]

    Dear Dr. Canarutto,

    I fully enjoyed reading your essay, as my essay supports your thesis and Penrose's comments! In it is derived 'the Light' which cannot be differentiated, thereby showing calculus may be of limited validity when applied to certain physical concepts.

    Hopefully, you will have time to read my essay.

    All the very best to you,

    Robert

    Dear Daniel Cannarutto,

    I enjoyed your essay and have a few remarks.

    Two of your references are Penrose and Verlinde.

    Your interest in Penrose, if I understood you correctly, is his focus on angular momentum. I tend to agree with you on the significance of this, and invite you to read my essay, in which the C-field (my name for the Maxwell-Einstein gravito-magnetic field) is seen to be closely related to angular momentum.

    You did not employ the ideas of Verlinde, but you do reference him as indicative of approaches being taken in the direction of discrete physics. You do not seem to actually use his work, so this remark may be inappropriate, but I have commented on my page and elsewhere about the assumptions that Verlinde need to 'derive' Newton's gravity. He makes 19 assumptions, some of them very questionable, before 'deriving' Newton's law.

    In contrast, I make one assumption, that a universe consisting of only one (continuous) field can only evolve by interacting with itself. Applying Maxwell: energy=field squared, and Einstein: energy = mass, my master equation immediately reduces to Newton's law, then produces many other physics results. The details are on my comments page, if you're interested. I think this is an indication of the work necessary to impose a discrete interpretation on a continuous universe, as opposed to the ease of a continuous description. [Of course it may be easy for us only because of hundreds of years of mathematical development, who knows?]

    You also state: "Furthermore, we may note that saying that the foundations of physics are continuous implies seeing the real numbers as a primitive concept."

    I am not sure that this is the case. Mathematics is a descriptive language, and the language used to describe reality does not, in my opinion, influence reality, only our perceptions of reality. Nor is it necessary that reality enforce conventions on language, though that may be the case in practice.

    Finally, I found your Feynman-like diagrams interesting, and wonder if they might not apply to a continuous world as well?

    Good luck in the contest,

    Edwin Eugene Klingman

    6 days later
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    Noetherian currents are described by continuous groups and their representations. It is not possible to have these conservation laws in a completely discrete setting. One can construct conserved charges though. The question here is funny, for in a way I fail to see how one can construct a consistent theory of physics based completely on continuous or discrete settings. Quantities that we measure, which are bits or quantum bits, are discrete. However, there is an underlying continuous formalism required to adequately describe conservation laws.

    Cheers LC

    5 days later

    Hi Daniel, thanks for your essay. I wondered whether you have considered the Archimedes screw as an analogy for the geometric structure of a particle/wave duality? T

    14 days later

    Dear Daniel,

    In your very lucid essay you write:

    -"According to one point of view, particles are an "epiphenomenon" and the fundamental theory is one of fields. [..] What is a quantum particle? "-

    This suggests that the field is the primary phenomenon, the cause of the particle. In my essay I start from the assumption that in a self-creating universe particles have to create themselves, each other. This means that (the properties of) particles must be as much the product as the source of their interactions and fields. As the same holds for the force between them, a force cannot be either attractive or repulsive (at least at quantum level) so there are no infinite interaction energies at infinitesimal distances. Since a universe which finds a way to create itself can hardly stop creating, this continuing creation process leads to effects we associate with a gravity which seems attractive at one scale, and repulsive at the other. Being as much the product as the source of their interactions, quantum particles then might be defined as particles which cannot be distinguished from their interactions, their function. being as much the cause as the effect of its interactions, a quantum particle has no reality, does not exist outside its interactions. For a massive quantum particle 'to be' then is not a state, a noun, but an activity, a verb.

    -"So we detect certain quantum events, the absorption of single particles, and we have good reasons to assume that each event is correlated to an event occurring at the source, the emission of one particle. It's then natural to view the particle exactly as this correlation between two observed events. Though our (classical) mental habits would suggest that 'something' has traveled from the first event to the second, this is not the right description at a more fundamental level. The two events and their (abstract) correlation are just everything that can be regarded as "real". Now suppose that some external Observer looks at our universe, not being subjected to our universe's time, and sees the whole spacetime at one glance (the cosmos from the beginning to the end). This object looks to the Observer as a [..] network of correlated events. Considering a particular photon, the Observer might see that a certain event, occurred at recombination era 400,000 years after the big bang, is correlated with an event occurred at a radio telescope on Earth 14 billion years after the big bang. He might say that a photon was emitted at the recombination era and detected 14 billion years later, but not that something was wandering all this time through the cosmos, waiting to be detected. For the Observer, only events and their correlations exist. " -

    Indeed: if particle A emits a photon which is absorbed by particle B, a transmission changing the state of both particles, then A sees the state of B change at the time it emits the photon, whereas B sees the state of A change as it absorbs the photon. (That is, unless B after absorbing the photon sends back a photon to A to confirm the receipt of the photon, a thank-you-note saying that A can from this moment start to see B in its new state, altered by its absorption of the photon.) So though an observer certainly measures a transmission time equal to the AB distance, the photon bridges this spacetime distance in no time at all. (see for a more elaborate discussion about the speed of light, the UPDATE 2 post at my thread).

    As to the 'external Observer': as any observation is a physical interaction, this would incorporate the observer into the universe he observes: he cannot see the universe from the outside, it doesn't exist to him. This is not an irrelevant philosophical point. If a universe creates itself out of nothing, then the sum of all things and events inside of it, including spacetime itself, must remain nil, so the universe can have no particular property as a whole. It also cannot evolve as a whole as this would require the existence of a clock outside of it the pace of which doesn't depend on whatever happens inside of it. A universe only can have properties as a whole if it has been created by some outside intervention, with respect to that creator, its evolution be timed using his/her/its watch. Though things inside the universe certainly keep evolving with respect to each other, a self-creating universe cannot evolve as a whole: if there's no time outside of it, then we cannot ask what causally precedes what, the photon emission by A or its absorption by B. The idea of photons buzzing trough spacetime, as tiny bullets, 'wandering all this time through the cosmos' is a classical way of looking at what in fact is a purely quantum mechanical phenomenon, that is, a non-causal phenomenon. It doesn't, then, make sense to ask how much energy it contains, how large it is or how old it is. Only in a big bang universe, which necessarily, implicitly must has been created by some Outside Intervention, we can ask such questions. However, the price we pay for this naïve, religious view on the universe is high as it affirms our classical notion of particles only being the source of their fields and interactions. By clinging to the bigbang scenario, to the idea that particle properties are independent from their interactions, we make them incomprehensible. The result is that we doom ourselves to invent unnecessary, nonsensical hypotheses and theories like cosmic inflation and string theory, and fictitious (Higgs) particles. Being the product of fundamental misconceptions, intended to reconcile the many inconsistencies of present physics, these theories and particles are part of the problem, not of its solution. I like to think that my essay offers a 'ansatz' to a solution of some of these problems.

    Best regards, Anton