Essay Abstract

G枚del's undecidability results showed the incompleteness of formal axiomatic systems.聽 A more concrete demonstration of incompleteness is predicated on Turing's work on uncomputability.聽聽Perhaps the most illuminating reason for incompleteness can be seen through algorithmic information theory where Chaitin used incompressibility.聽 Rather remarkably, incompressibilty聽highlights that incompleteness can be treated to be pervasive phenomenon throughout pure mathematics.聽 Using this work, Chaitin has pointed out that compression can be generalized to a universal concept.聽 In align with this, we argue to embrace compression as a primary method in physics akin to the geometrization of physics in the 20th century.聽 To warrant such a direction, we examine聽how compression already聽exists聽at a foundational level in current information theories associated to physical systems (both classical and quantum).聽 We proceed to argue that applying the concept of compression to the structure of spacetime provides us with a novel path forward in fundamental physics, which includes addressing the conceptual problems in quantum physics where "God plays dice."聽 We provide speculative聽mathematical ideas for how such a spacetime-information theory could be developed.聽 This alludes to the notion that time itself is intrinsically random.

Author Bio

Del Rajan is a quantum information scientist at the Victoria University of Wellington in New Zealand.

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Respected Professor Del Rajan,

Your well understood and well studied words...... Theoretical problem: What do the complex amplitudes represent?..........

That is a real question. Can we avoid fully those complex numbers? as the results will be complex and can not be physically placed.

Hope you will have a look at my essay " A properly deciding, Computing and Predicting new theory's Philosophy" ---- which described Dynamic Universe Model ; where complex numbers are avoided and got many nice results, and many predictions came true....

Best regards

=snp

    Thank you for your message and your thoughts. I will have a look.

    Cheers,

    Del

    11 days later

    Dear Del,

    I read with great interest your essay with deep ideas and conclusions aimed at overcoming the crisis of understanding in the philosophical basis of fundamental science. First of all, I want to note these thoughts, which, in my opinion, are important for finding a way to understand the structure of the Universe, the nature of the phenomenon of information:

    "Crudely stated, progress was measured in every parameter except understanding. It is our view that an understanding of quantum physics is necessary for genuine progress. "

    "Mathematically modeling the physical world without deep understanding can be compared to machine translation without comprehension. Only with the addition of understanding in our physics can we regard ourselves as an advancing intelligent species. "

    "...we want to harness compression as a primary mathematical technique for the aim to make deeper discoveries of the physical world."

    "Our view to resolve the confusion is remove the focus on information in information theories. Rather it is compression in these theories that is fundamental, and whose character we imagine will be found in the deeper laws of the Universe."

    I believe that in order to overcome the crisis of understanding in the basis of fundamental science, it is important to remember the philosophical covenant of Paul Florensky:. "We repeat: worldunderstanding is spaceunderstanding." My high score. I wish you success!

    I invite you to see my ideas .

    With kind regards,

    Vladimir

      Dear Vladimir,

      Thank you for your message.聽 To elaborate on the points you mentioned:

      Modern derivations of incompleteness are found in algorithmic information theory (AIT).聽 Central in these derivation is compression.

      Furthermore both classical and quantum information聽theory state compression as the fundamental result through their coding theorems. Information theories seem to be about compression, not information.

      If we assert that the Universe is made of information, then an educated guess is that compression is to be found in its deeper laws.聽聽

      Perhaps the advancements on incompleteness (namely AIT) provides a better scaffold for fundamental physics than harnessing the frontiers of geometry/topology.

      I will read your essay. Thank you again for your time and your most kind comments.

      Cheers,

      Del

      Dear Del (if I may),

      thanks for a grat essay, well-argued and full of inspiring ideas. I liked your didactical crystal clear introduction to quantum theory and information theory. I appreciate very much your motivation for "understanding" as opposed to the notorious "shut up and calculate" (I have myself written several works about this, also from the historical point of view). Also, your genius idea is to abond the widespread "conventionalism" (as Popper colled it) of "wonder at the austerely

      beautiful simplicity of the world as revealed in the laws of physics" as a research program, and substitute it by randomness. If you will have time to read my essay, you will see that my research program with Nicolas Gisin make use exactly of Kolmogorov complexity to find fundamental limits in physics and propose suitable alternatives. I will be most interesed in your feedback.

      Meanwhile, I give your essay a top rating, being among the best I read this year.

      All good wishes and good luck with the contest!

      Flavio

        Dear Del Rajan ,

        A truly excellent and enjoyable essay!

        You make so many wonderful observations, connecting lack of physical evidence to support various views and inability to derive the Born Rule, lack of evidence to support the assumption that non-locality is false, and finally, "nobody knows what quantum information is." that I must restrain myself from expounding on each of these. Instead I will focus on what seems to be your main hypothesis, that, at a deep level the Universe is random. Several current essays relate to,this assumption.

        First, John Bell stated

        "No one can understand this [deBroglie] theory until he is willing to think of psi as a real objective field rather than just a 'probability amplitude'."

        If one assumes, as I do, that this physical field is self-interactive, then it is essentially non-linear. Bill McHarris's essay points out that:

        "the behavior of simple but non-linear classical dynamical systems...can be startlingly similar to quantum mechanical systems in multitudinous ways."

        This implies an essentially non-algorithmic system, and Schultz's essay claims that the limitations on knowability [the 'no-go' theorems] do not apply to non-algorithmic patterns.

        Your compression ideas are fascinating, and require some digesting. In the mean time I invite you to read my current essay, Deciding on the nature of time and space, and welcome your comments.

        Best regards,

        Edwin Eugene Klingman

          Dear Del,

          Great essay. One of the most interesting ones for sure.

          I find it interesting how you made the connection between compression and the structure of spacetime itself. In my essay (https://fqxi.org/community/forum/topic/3523) I use similar notions of compression in a slightly different way, combined with finitist notions. You might be interested in taking a look at it.

          All the best,

          Rafael

            Dear Flavio,

            Thank you for your time to read the essay and your most kind comments.

            It is quite interesting that the technological aims of the 20th century provided a basis for 'shut up and calculate' whereas聽in this century the technological development associated to quantum information makes it difficult for this attitude to be unchallenged.

            I am very interested to read your work on integrating the Komogorov聽complexity with physics.聽 It certainly sounds like an innovative path and an exciting聽exploration.聽 聽

            I will most certainly read your essay and good luck with the contest.

            Cheers,

            Del聽

            Dear Edwin Eugene Klingman,

            Thank you for your time and for your kind feedback.

            In regards to your comments regarding non-locality and aspects on quantum information, a further interesting point would be the PBR theorem.聽 It is profound in that it looks at the reality of quantum information, or alternatively introduces a non-locality far more stranger than Bell non-locality.

            Thank you for pointing me towards your essay.聽 I will read it and good luck for the contest.

            Cheers,

            Del

            Dear聽Rafael,

            Thank you for your time to read the essay.聽 I appreciate the kind feedback.

            Yes I am very interested in the connection.聽 What I imagine would be interesting (in relation to spacetime) would be looking at the concept of compression in relativistic quantum information (RQI).聽 Whether an RQI version of Schumacher's coding theorem would give a novel insight into spacetime.聽

            I will most certainly be interested to read your essay and its utilization of compression.聽 聽聽

            Cheers,

            Del

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            • Post #12

            Dear Del,

            Congratulations for your interesting and very well written essay.

            I completely relate with your argument that an esthetic principle, as the one of Dirac's, is not enough. And your ''principle of mathematical randomness'', i.e. taking randomness as fundamental, seems (to me) to be one of the best tracks to move forward. I also enjoyed your proposition to focus on compression rather than information, and your proposal on typical and atypical time is really interesting. Working on quantum causality on quantum indefinite causal orders, I would have liked to have an analysis of these compared to your ideas.

            "The emergence of time in this intrinsic random manner suggests that God not only plays dice but plays dice all the time and with time itself." My essay aims at arguing for the fact that quantum "paradoxes" might emerge from self-referential issues (i.e. God does play dice, and this fundamental randomness in quantum theory as a source which might be analog to the undecidable propositions in mathematical logic). As an epilogue, I propose a (not very developped) intuition that time itself might emerge from self-referential structures. If you have the time to read it, I would be very interested to have your feedbacks on it.

            All the best,

            Hippolyte

            PS : Correct me if I am wrong, but it seems to me that you identify the Copenhagen interpretation with "shut up and calculate". However, there are rather Copenhagen interpretationS (nuances between Bohr, Heisenberg, Pauli... views) and they do not defend the "shut up and calculate" view, but rather refined forms of realisms, that could be said to be carefully based on structures and relations (cf. the section "The Heirs of Copenhagen" in my essay).

              • [deleted]

              • Post #13

              Dear Dr. Rajan,

              Your essay is beautifully written and a pleasure to read. You ask all the good questions about quantum mechanics - whether randomness is fundamental, the origin of the Born probability rule, the possibility of there being randomness in time, and the deep foundational issues that plague quantum gravity research.

              I wanted to mention here that there has been much progress on these questions, in a manner which moved away from `shut up and calculate'. It started with the Ghirardi-Weber-Rimini-Pearle theory of spontaneous localisation in 1986. They provided a falsifiable and dynamical explanation of the quantum measurement problem, and of the absence of macroscopic superpositions. The theory is currently being tested in a few labs in Europe.

              Subsequently, Stephen Adler sought to derive quantum theory from a deeper underlying formalism - his theory of trace dynamics. The deeper theory is a deterministic matrix dynamics from where quantum theory, Born rule, randomness, and spontaneous localisation are emergent phenomena.

              Recently, I have shown how to include gravity in Adler's framework, using the mathematics of non-commutative geometry. This has lead to the new theory of Spontaneous Quantum Gravity, where indeed God plays dice with time, but only in an emergent sense. Underlying quantum indeterminism is determinism at the Planck scale.

              I discuss these developments in my essay in this contest: The pollen and the electron. Since many of the deep questions you raise are addessed and answered in my work, I hope you will find it interesting.

              My best wishes to you in this contest,

              Tejinder.

              My apologies. The anonymous in the previous post is me...I forgot to log in. Sorry!

              Tejinder

                Dear Hippolyte,

                Thank you for taking the time to read my essay.聽 I appreciate your kind comments and critical feedback.聽 To elaborate on some of your points:

                1. Indefinite causal structures: The theory put forth with the process operator and its extension聽to graphs via quantum causal models is of great interest to me.聽 Besides the quantum switch concepts, I feel quantum causal models may provide a basis for novel information-theoretic applications (especially in distributed algorithms).聽 More fundamentally, the notion of unordered time which I briefly mention in the essay can be related to some formal concepts in their theory, and I do provide a reference to the recent Bell's theorem for temporal order.

                2. Copenagen interpretation:聽 As mentioned in the essay, there is no consensus on what the intepretation聽states (there are various versions) but that the overarching theme is that a description beyond quantum theory is not needed.聽 I mention 'shut up and calculate' as a refined version of the latter theme given it has the commonality of ignoring a desire for a deeper description.聽 I also provide a reference to聽David Kaiser's article on the historical inception of the 'shut up and calculate' mindset.聽聽

                I will be most interested to read your essay and the idea that time may emerge from self-referential structures.聽 Thank you for that and I will have a read.

                Cheers,

                Del

                Dear Tejinder,

                Thank you for your most kind comments and your time to read the essay.聽 To elaborate on some of the points you mentioned:

                Collapse models:聽 I have a basic undertanding聽of GRW collapse models as well as the one proposed by Penrose.聽 For me, the measurement problem is not so fundamental; it is only fundamental if one assumes quantum information (i.e. the quantum state) has a direct physical manifestation.聽 Whether it does or not is hotly debated and in the essay I do provide a reference to Leifer's review paper on this topic.聽 For me, the more fundamental question is what do the amplitudes themselves physically represent?

                Trace Dynamics:聽 I must admit that I am unfamiliar with this theory but it sounds very interesting and novel.聽 Hence I look forward to reading your essay.聽 Thank you for pointing that out.

                Cheers,

                Del

                Dear Del,

                A most interesting, dense and deep essay which I enjoyed reading.

                I was particularly interested in your conclusion re typical and atypical time intervals. In my theory of time (not covered in my essay) I also have typical intervals (relates to relative time, and flow rate of time) and atypical intervals (relates to expansion of aether, cosmological time - thus working at boyh the smallest and largest scales.

                In my essay I discuss the 3 Un's as they have affected me, and I cover another aspect of time from a new point of view - philosophical presentism.

                Good luck with the ratings - you deserve high scores!

                Regards

                lockie Cresswell

                  Hi Rajan. very important points you raise there on quantum spookiness in a very simple and elegant manner. very well done, you certainly earn my votes.Forgive me, but to be sincere this year's contest raised within me Questions which to date make me more than just suspicious about us as Quantum observers.When quantum event occurs in nature,Do quantum effects of an opposite Nature happen in our brains to counter observation ridding us access to Reality ?maybe you may please see my take on Anthropic bias here -https://fqxi.org/community/forum/topic/3525.all the best to you thanks.

                    Dear Lockie,

                    Thank you for taking your time to read my essay.聽 I appreciate your kind comments.

                    Yes in my essay, the typical and atypical time intervals are purely predicted on the notion that compression is perhaps the appropriate mathematical technique for fundamental physics.聽

                    Thank you for pointing out your ideas on the intersection of time and typicality. I look forward to reading your essay.聽 (The link above did not work but I have found your essay on聽https://fqxi.org/community/forum/topic/3397)

                    Cheers,

                    Del聽