Paul,

I am rather intrigued by your paper. I will confess that I think this perspective on time may apply to quantum gravity. I will have to read your paper again to firm up my understanding. The two competing ideas are string theory and loop quantum gravity. In LQG gravitation is background independent. However, this is based ultimately on a classical formalism of general relativity where time does not exist. String theory on the other hand has time, but it is not background independent. It also works best in a holographic perspective where one dimension is reduced near an event horizon. The string/M-theory approach is also best looked at in a dual gauge approach with Yangians, which has some overlap with braid constructions in LQG. So there may be some duality here that has some bearing on your idea about time and entanglement.

Cheers LC

    Having read so many insightful essays, I am probably not the only one to find that my views have crystallized, and that I can now move forward with growing confidence. I cannot exactly say who in the course of the competition was most inspiring - probably it was the continuous back and forth between so many of us. In this case, we should all be grateful to each other.

    If I may, I'd like to express some of my newer conclusions - by themselves, so to speak, and independently of the logic that justifies them; the logic is, of course, outlined in my essay.

    I now see the Cosmos as founded upon positive-negative charges: It is a binary structure and process that acquires its most elemental dimensional definition with the appearance of Hydrogen - one proton, one electron.

    There is no other interaction so fundamental and all-pervasive as this binary phenomenon: Its continuance produces our elements - which are the array of all possible inorganic variants.

    Once there exists a great enough correlation between protons and electrons - that is, once there are a great many Hydrogen atoms, and a great many other types of atoms as well - the continuing Cosmic binary process arranges them all into a new platform: Life.

    This phenomenon is quite simply inherent to a Cosmos that has reached a certain volume of particles; and like the Cosmos from which it evolves, life behaves as a binary process.

    Life therefore evolves not only by the chance events of natural selection, but also by the chance interactions of its underlying binary elements.

    This means that ultimately, DNA behaves as does the atom - each is a particle defined by, and interacting within, its distinct Vortex - or 'platform'.

    However, as the cosmic system expands, simple sensory activity is transformed into a third platform, one that is correlated with the Organic and Inorganic phenomena already in existence: This is the Sensory-Cognitive platform.

    Most significantly, the development of Sensory-Cognition into a distinct platform, or Vortex, is the event that is responsible for creating (on Earth) the Human Species - in whom the mind has acquired the dexterity to focus upon itself.

    Humans affect, and are affected by, the binary field of Sensory-Cognition: We can ask specific questions and enunciate specific answers - and we can also step back and contextualize our conclusions: That is to say, we can move beyond the specific, and create what might be termed 'Unified Binary Fields' - in the same way that the forces acting upon the Cosmos, and holding the whole structure together, simultaneously act upon its individual particles, giving them their motion and structure.

    The mind mimics the Cosmos - or more exactly, it is correlated with it.

    Thus, it transpires that the role of chance decreases with evolution, because this dual activity (by which we 'particularize' binary elements, while also unifying them into fields) clearly increases our control over the foundational binary process itself.

    This in turn signifies that we are evolving, as life in general has always done, towards a new interaction with the Cosmos.

    Clearly, the Cosmos is participatory to a far greater degree than Wheeler imagined - with the evolution of the observer continuously re-defining the system.

    You might recall the logic by which these conclusions were originally reached in my essay, and the more detailed structure that I also outline there. These elements still hold; the details stated here simply put the paradigm into a sharper focus, I believe.

    With many thanks and best wishes,

    John

    jselye@gmail.com

      Dear Sir,

      We have replied to you in our thread. Before we comment on your essay, we must clarify that we do not assume or consider anything or any theory as given. We examine everything from empirical perspective using precise definitions. Thus, our views are usually different from others. We are confused after reading your essay. Kindly spare some time to clarify it to us.

      In the statistical method, observation remains non-deterministic because it is not related to individual measurements, but only to the minimal and maximal boundary conditions like the position of an electron in orbit around nucleus. You cannot apply this idea to "reality is timeless inside entangled systems, i.e., it continually evolves and cycles through its recurrence, defined by the available number of states", because your description shows sequence, which is used to perceive time. Unlike mass, space and time have no physical existence. We designate the interval between objects as time and that of events as time. Since they do not have physical reality, we designate them through alternative symbolism of objects and events, which are different from space and time or spacetime. Thus, the concept of sub-time is absurd, though reversible information exchange is frequently used. The velocity of photon is neither smooth, nor monotonic or irreversible background in time.

      How do you assume "information is associated with the propagation of a photon?" Information is not data that is transmitted. Information is specific data reporting the state of something based on observation (measurements), organized and summarized for a purpose within a context that gives it meaning and relevance and can lead to either an increase in understanding or decrease in uncertainty. Perception is the processing of the result of measurements of different but related fields of something with some stored data to convey a combined form "it is like that", where "it" refers to an object (constituted of bits) and "that" refers to a concept signified by the object (self-contained representation).

      Similarly, how do you "postulate sub-time is inextricably intertwined with space along the one-dimensional path defined by the photon traversal between emitter and absorber atoms?" Transverse waves are always characterized by particle motion being perpendicular to the wave motion. This implies the existence of a three dimensional medium through which the two dimensional reference wave travels and with respect to which the transverse wave travels in a perpendicular direction. In the absence of the reference wave, which is a longitudinal wave, the transverse wave can not be characterized as such. All transverse waves are background invariant by its very definition. All motions take place in space and time. Thus, how do you "dispense entirely with the notion that a background of time exists, along with any sense of future or past, between isolated entangled systems?" After all, the two waves are entangled.

      Photon exchange indicates the change in direction of the application of energy. Consider an example: A B → C D. Here a force makes A interact with B to produce C and D. The same force doesn't act on C and D as they don't exist at that stage. If we change the direction of the force, B acts on A. Here only the direction of force and not the interval between the states before and after application of force (time) will change and the equation will be: B A → C D and not B A ← C D. Hence it does not affect causality. There can be no negative direction for time or cause and effect. You also subscribe to this view later in your essay while talking about entanglement. Only there you start a reverse cycle with C and D in place of A and B. Then how do you claim "Only when the entangled system decoheres into the environment of other entangled systems (through the exchange of photons) does time emerge as progressively irreversible, providing persistent evolution of information at the macroscopic scale"?

      The result of measurement is always related to a time t, and is frozen for use at later times t', t'', etc, when the object has evolved further. All other unknown states are combined together and are called superposition of states. Hence there is an uncertainty inherent in it, which Shannon calls entropy. Indiscernibility such as the difference of time in the observation of an object, its description through a language and the perception of the object as described by that language can sometimes be designated as a superposition of states. Entanglement of quantum states of composite systems of two or more atoms cannot be a consequence of the principle of superposition. Contrary to the descriptions of EPR, entanglement does not physically last over long distances. Entanglement always indicates confinement, which means they are in a well defined boundary or state. Hence it cannot be a superposition. Further, since they are continuously changing their states ('a state of reversible change' - as you put it), which are 'events', it happens in the background of time (interval between events).

      Can you show us something that does not change at all? Everything is made up of elementary particles and fundamental energies, which always change their state. How can time stand still? Time may stand still only outside the Universes, which cannot be perceived at all. We measure analog time by observing some fairly repetitive (cyclic) and easily intelligible events and taking it as the scaling constant (unit). Generally we use the duration of the day or year, which are natural units and subdivide it to get the duration of second. Even atomic clocks, which define a second as the duration of 9192631770 cycles of radiation corresponding to the transition between two energy levels of the caesium-133 atom, retain the natural duration by averaging many readings of the cesium clocks in GPS, as they are individually not accurate. While the analog time is smooth and monotonous, the digitized time, when used to measure the intervals of events, is not so.

      The rest of your essay is extension of these ideas and other's ideas with pictorial representation. Hence we are not commenting on those.

      Regards,

      basudeba

        A post was made on this site by Basudeba Mishra when I woke up this morning. I prepared a response, but now find that the comment is missing. This posting is in response to Basudeba's original comments from this morning.

        Paragraph 1:

        We have replied to you in our thread. Before we comment on your essay, we must clarify that we do not assume or consider anything or any theory as given. We examine everything from empirical perspective using precise definitions. Thus, our views are usually different from others. We are confused after reading your essay. Kindly spare some time to clarify it to us.

        A1 Dear Basudeba - I no longer see my comments or your reply on your page. Thank you for your time in reviewing and responding to my essay. I am sorry to hear that you were confused after reading my essay. I appreciate that new ideas can seem absurd at first and that precise definitions can be difficult in the English language. I will attempt to respond to your comments by paragraph number:

        Paragraph 2:

        In the statistical method, observation remains non-deterministic because it is not related to individual measurements, but only to the minimal and maximal boundary conditions like the position of an electron in orbit around nucleus. You cannot apply this idea to "reality is timeless inside entangled systems, i.e., it continually evolves and cycles through its recurrence, defined by the available number of states", because your description shows sequence, which is used to perceive time. Unlike mass, space and time have no physical existence. We designate the interval between objects as time and that of events as time. Since they do not have physical reality, we designate them through alternative symbolism of objects and events, which are different from space and time or spacetime. Thus, the concept of sub-time is absurd, though reversible information exchange is frequently used. The velocity of photon is neither smooth, nor monotonic or irreversible background in time.

        A2 My essay begins with a description of entanglement as a Poynting/Shannon relationship between two atoms, not within one. Instead of a universal background for time, I made a distinction between subtime (ts) which is reversible in all ontological respects, and classical time (Tc), which "appears" to exhibit monotonic and irreversible order at large scale according to Maccone [7]. I see many statements of opinion in your writing which makes it difficult for me to discern questions and formulate a response, so I will confine my response only to actual questions in the remaining paragraphs. Also, your restatement of my words in the last sentence of this paragraph confuses me too. Could you please quote the precise sentences from my essay? And specify an actual question - for example, when you mention "time" are you referring to ts or Tc? That way we can both be more precise and spare our audience further confusion.

        Paragraph 3:

        How do you assume "information is associated with the propagation of a photon?" Information is not data that is transmitted. Information is specific data reporting the state of something based on observation (measurements), organized and summarized for a purpose within a context that gives it meaning and relevance and can lead to either an increase in understanding or decrease in uncertainty. Perception is the processing of the result of measurements of different but related fields of something with some stored data to convey a combined form "it is like that", where "it" refers to an object (constituted of bits) and "that" refers to a concept signified by the object (self-contained representation).

        A3 It is a well established in science that information is associated with photon propagation. See for example, Neil Gershenfeld's excellent book [1] or the references cited in my essay [2,3,4,5,6] (citations at the bottom of this page).

        Paragraph 4:

        Similarly, how do you "postulate sub-time is inextricably intertwined with space along the one-dimensional path defined by the photon traversal between emitter and absorber atoms?" Transverse waves are always characterized by particle motion being perpendicular to the wave motion. This implies the existence of a three dimensional medium through which the two dimensional reference wave travels and with respect to which the transverse wave travels in a perpendicular direction. In the absence of the reference wave, which is a longitudinal wave, the transverse wave can not be characterized as such. All transverse waves are background invariant by its very definition. All motions take place in space and time. Thus, how do you "dispense entirely with the notion that a background of time exists, along with any sense of future or past, between isolated entangled systems?" After all, the two waves are entangled.

        A4 I believe the answer to your question is in the dictionary definition of a postulate. I state this as a premise to my argument and follow it with a logical and diagrammatic argument, concluding with implications should the postulate be true and the argument impeccable. This is to honor individuals in this community who are not mathematical virtuoso's; and for those who are, to illuminate issues regarding assumptions (such as a background for time) hidden in conventional formalisms. I am far from alone in this concern. Lee Smolin in particular has been a legendary figure in exposing many deep issues in modern physics. I dispense entirely with the notion of a background of time, in exactly the same way that we dispensed with the luminiferous aether: as a superfluous assumption not needed to explain the workings of the universe.

        Paragraph 5:

        Photon exchange indicates the change in direction of the application of energy. Consider an example: A B → C D. Here a force makes A interact with B to produce C and D. The same force doesn't act on C and D as they don't exist at that stage. If we change the direction of the force, B acts on A. Here only the direction of force and not the interval between the states before and after application of force (time) will change and the equation will be: B A → C D and not B A ← C D. Hence it does not affect causality. There can be no negative direction for time or cause and effect. You also subscribe to this view later in your essay while talking about entanglement. Only there you start a reverse cycle with C and D in place of A and B. Then how do you claim "Only when the entangled system decoheres into the environment of other entangled systems (through the exchange of photons) does time emerge as progressively irreversible, providing persistent evolution of information at the macroscopic scale"?

        A5 I do not quite see the relevance of your example. My essay is about "Information, Entanglement and Time", not forces. I would be happy to engage in a discussion regarding forces in a different forum (your web page perhaps?) so that our audience are not taken off track regarding the essential properties of photon entanglement in this forum. As far as your last question is concerned, please refer to the excellent answer to this question in [7] and [8].

        Paragraph 6:

        The result of measurement is always related to a time t, and is frozen for use at later times t', t'', etc, when the object has evolved further. All other unknown states are combined together and are called superposition of states. Hence there is an uncertainty inherent in it, which Shannon calls entropy. Indiscernibility such as the difference of time in the observation of an object, its description through a language and the perception of the object as described by that language can sometimes be designated as a superposition of states. Entanglement of quantum states of composite systems of two or more atoms cannot be a consequence of the principle of superposition. Contrary to the descriptions of EPR, entanglement does not physically last over long distances. Entanglement always indicates confinement, which means they are in a well defined boundary or state. Hence it cannot be a superposition. Further, since they are continuously changing their states ('a state of reversible change' - as you put it), which are 'events', it happens in the background of time (interval between events).

        A6 Please, Sir. The whole point of my essay is that there is no t, t' or t'' (a classical/background view of time). If you can relate the question to ts, or Tc, then I think we might begin communicating on the same page. I cannot prove a negative - that a background of time does not exist - only that it is not necessary, like the luminiferous aether, to explain how the universe works. I will leave the remainder of your paragraph to be judged by other readers on this page relative to verifiable experimental science.

        Paragraph 7:

        Can you show us something that does not change at all? Everything is made up of elementary particles and fundamental energies, which always change their state. How can time stand still? Time may stand still only outside the Universes, which cannot be perceived at all. We measure analog time by observing some fairly repetitive (cyclic) and easily intelligible events and taking it as the scaling constant (unit). Generally we use the duration of the day or year, which are natural units and subdivide it to get the duration of second. Even atomic clocks, which define a second as the duration of 9192631770 cycles of radiation corresponding to the transition between two energy levels of the caesium-133 atom, retain the natural duration by averaging many readings of the cesium clocks in GPS, as they are individually not accurate. While the analog time is smooth and monotonous, the digitized time, when used to measure the intervals of events, is not so.

        A7 Subtime describes precisely something that (after each recurrence) does indeed "not change at all". The point is this: you can have a process that repeats indefinitely in subtime (ts) but will appear "frozen" because it is uncountable in classical time (Tc).

        Paragraph 8:

        The rest of your essay is extension of these ideas and other's ideas with pictorial representation. Hence we are not commenting on those.

        A8 I took the time to read your whole essay through from beginning to end twice before I commented on it. I would appreciate the courtesy of reading mine through to the end just once. I believe you will find that many of your questions are more fully covered in the essay, and that you will find many aspects later in the essay perhaps more agreeable to you because they coincide with some of your own insights into nature, for example in bipartite relationships and atomic clocks.

        Kind regards, Paul

        References:

        [1] N. Gershenfeld. The Physics of Information Technology. Cambridge, New York: Cambridge University Press, 2000.

        [2] J. P. Torres, Gabriel Molina-Terriza, and Lluis Torner, "Twisted photons: new classical and quantum applications", 2005, vol. 5958, SPIE Publications.

        [3] G. Molina-Terriza, Juan P. Torres, and Lluis Torner, "Twisted photons", Nature Physics, vol. 3, no. 5, pp. 305-310, May 2007.

        [4] J. P Torres and Lluis Torner, Twisted Photons: Applications of Light with Orbital Angular Momentum, Wiley- VCH, Weinheim, Germany, 2011.

        [5] A. Afanasev, Carl E. Carlson, and Asmita Mukherjee, "Excitation of an atom by twisted photons", arXiv e-print quant-ph/1304.0115, George Washington University, Mar. 2013.

        [6] J. Bahrdt, K. Holldack, P. Kuske, R. Mller, M. Scheer, and P. Schmid, "First observation of photons carrying orbital angular momentum in undulator radiation", Physical Review Letters, vol -, no. -, pp. -, Accepted for Publication June 2013.

        [7] L. Maccone, "Quantum solution to the arrow-of- time dilemma", Physical Review Letters, vol. 103, no. 8, 2009.

        [8] M. Schlosshauer, Annals of Physics 321, 112 (2006).

        .

        • [deleted]

        • Post #42

        Jenny - I finally got to your paper early this morning and I must say, I really enjoyed it. My favorable review appears on your page.

        I replied briefly to your question regarding eternity in my earlier response (above). I do appreciate you pointing me to Sir Roger Penrose's concept of Quanglement [1, p 603]. This is one of my favorite books on my bookshelf and yet I never realized (or more more likely didn't remember) his introduction of this concept.

        I believe Sir Roger is clearly showing us the answer to the paradox of entanglement and non-locality in this concept; but even he doesn't realize that he's pointing his enormous intellectual gun to an answer -- hidden in plain sight.

        If you check the various sections in his book that mentions quanglement [1. p 407, 578, 603-7] you will notice that he still maintains two principles: (a) that quantum behavior cannot be explained classically, and (b) that time, once having gone forwards, never goes backwards. This is manifested, for example, in the statement on p 603 "I am not trying to give support to the idea that ordinary information can be propagated backwards in time (nor can EPR effects be used to send classical information faster than light);"

        However, he then plainly states further down the page that "quanglement links have the novel feature that the can zig-zag backwards and forwards in time.".

        Sir Roger continues to commit the background of time fallacy in figure 23.7 on the previous page, describing quantum teleportation as "acausal propagation of quanglement". And then having a single direction (upwards) for an irreversible, monotonically increasing classical concept of time (what I refer to as Tc in my essay). This is strongly reminiscent of Wheeler & Feynman's Absorber Interaction paper [2] who also commit this fallacy.

        I think we have a smoking gun! I will leave our readers to follow up with Sir Roger's various other publications where he appears oblivious to having committed this fallacy.

        I truly hope that (after reading my essay) that he or someone else will educate us by pointing out where we are wrong about the relationship between subtime and quanglement ;-)

        [1] R. Penrose. "The Road to Reality. A complete Guide to the Laws of the Universe". 2004.

        [2] J. A. Wheeler and R. P. Feynman, "Interaction with the absorber as the mechanism of radiation", Reviews of Modern Physics, vol. 17, no. 2-3, pp. 157-181, Apr. 1945.

        Kind regards, Paul

        • [deleted]

        • Post #43

        Peter - thank you for your kind comments on my essay.

        I have found I have to be careful when talking about the notion of proper time. It is convenient to say that proper time for a photon is zero, but that depends on which Lorentz frame you choose.

        Besides the references to works on orbital angular momentum in my essay, you can find pointers for downloading Poynting's early work on the following site: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3390789/

        I have copies of all his papers from jstor, but I am uncertain about the copyright status and don't want to run afoul of the terms of use for the fqxi contest by attaching them.

        Thank you for your good score. I am hoping that there is more to this than just an original idea. If I am even remotely correct, there are many profound implications and follow-on ideas; but I wanted to try and get this one idea over first and see if it holds water after examination by my peers before exposing my other ideas.

        I would be happy to take a look at your essay, I am just wading through a pile of other fqxi essays now, but will see if I can get to yours in the next day or so.

        Kind regards, Paul

        Jayakar - thank you for your comment on my essay. The principle I describe is distinct from conventional concepts of "discrete-time". I identify photon traversals from emitter to absorber with what I believe EPR intended by the term "elements of reality".

        They are not discrete (fixed sized) entities as in chronon's, but finite (and variable) intervals of time/space traversed by a photon; bounded by the atoms on both ends. Not only do I eliminate the notion of a background concept of time, I eliminate the infinities also at both ends of the real line when talking about the concept of subtime (ts). Classical time (Tc) then becomes the vector sum of subtime through entangled systems as they grow from simple bipartite systems to an indefinite size all the way up to the macroscopic and beyond.

        So, this is why I disagree with your statement that subtime is linear and infinite.

        I have downloaded your essay on "Exclusiveness of Binary numeral system in Information

        unit is causal for Information paradox" and will make sure to review it in the next day or so and respond on your fqxi web page.

        Kind regards, Paul

        Dear Paul,

        You write

        "Two atoms exchanging a photon with each other in perpetuity comprises an entangled system (Figure1)."

        It reminds me the idea I published some time ago

        "Quantum Phase Locking, 1/f Noise and Entanglement",

        although I am no longer convinced that entanglement relies on this concept.

        You write

        "From this insight, we can now begin to formulate a new and logically consistent information view of the apparent non-locality revealed in violations of Bell's inequality without sacri cing the principle of locality."

        At the end you may be right. It may be that one forgot to introduce the right notion of time in the interpretation and that some kind of quantum phase-locking is at work. I would be delighted to see a following up of my 15 year quest

        http://xxx.lanl.gov/abs/math-ph/0510044

        and this could be checked with atomic clocks in the end.

        Good luck,

        Michel

          Paul,

          Both profound and paradigm shifting, if such is now possible.

          Thanks for the links, and kind comments on my blog.

          Do stay in touch.

          Hold tight for the roller coaster ride to the finish!

          Peter

          PS, I think I have Proper and co-ordinate (arbitrary) time well defined, but if you have a chance please read my last two (both top 10 but passed over) essays for the foundations and give me your views. Or fuller range of papers here; Academia.edu Papers.

          • [deleted]

          • Post #47

          Dear Paul,

          Thank you for your kind comments in my essay forum. I hope my vote gave your essay a deserved rating boost.

          When the recent kerfuffle over "faster than light neutrinos" was percolating, I expressed doubt that any one-way measurement could ever suffice to demonstrate the case, because any particle that exceeds the speed of light also exceeds the speed of time and therefore (like the hypothetical tachyons) could never have been shown to exist in the first place. So I appreciate your promotion in these discussions of Lev Vaidman's model, where (phi|psi) past and future states are entangled and reversible.

          We have a lot to talk about that is more complicated than I wish to engage in right now, because we are so close in our views. In the end, I would hope to convince both you and Lev Vaidman that if time is indeed identical to information, entanglement of wave functions is identical to classical orientation entanglement rather than quantum entanglement that entails superposition -- in any physical sense, I mean. My physical definition of time (ICCS 2006, 2007), "n-dimension infinitely orientable metric on random, self avoiding walk," meets the classical criteria.

          Thanks for a stimulating essay and all best in the competition!

          Tom

            Gaicomo - I have your essay printed out and will respond on your page.

            Kind regards, Paul

            Héctor - thank you for your comments. I will read your paper and respond on your page.

            Kind regards, Paul

            Joe - thank you for your message. I have your essay printed out and will review it later today.

            Kind regards, Paul

            Akinbo - you can find excellent accounts of Mach's principle in the books by Lee Smolin [1] and Brian Greene [2]. I think you will find them both a fascinating read. Brian's book has a specific description of the bucket of spinning water which I believe directly addresses your question.

            Kind regards, Paul

            [1] Lee Smolin. "The Life of the Cosmos. Oxford University Press. 1997.

            [2] Brian Greene. "The Fabric of the Cosmos. Space, Time and the Texture of Reality." Vintage Books 2004.

            Than - thank you for your comment.

            Kind regards, Paul

            Vladimir - I will take a look at Alexander Zenkin's work after I have finished with my reviews of the fqxi essays.

            I have your essay printed out and will review it shortly.

            Kind regards, Paul

            Antony - thank you for your comment. I'm pleased that you find it makes sense. I described only entangled photons as dark.

            I have your essay printed out and will take a look at it shortly and comment on your fqxi page.

            Kind regards, Paul

            Peter - thank you for your kind comments. If such a thing is possible, then it puts a whole new light (no pun intended) on some of the most vexing issues in physics today and a number of profound consequence follow.

            I started reading your papers from Academia.edu, and yes, I do believe you have proper and co-ordinate time well defined ;-) In fact, I was really quite impressed, you have done some outstanding work here. I am surprised I have not come across your work before.

            Would love to stay in touch.

            In the meantime, good luck in the contest.

            Kind regards, Paul

            Michel - I hope that by now you have forgiven me for not using the concept of entanglement in an appropriate way ;-)

            I intended to be provocative: if the concept of subtime and the mutual hot potato photon does indeed predict identical results in Bell experiments and yet it has explanatory power beyond the statistical-only Hilbert formalism, then we can begin a new conversation on the nature of entanglement and perhaps even the measurement problem itself.

            I looked at your paper on phase locked loops. This is an impressive piece of work. It reminds me of my first career in my teens and 20's as an electronics and telecommunications engineer and the old familiar PLL concepts came flooding back. Very enjoyable, thank you.

            The biggest distinction I see is that I have introduced a truly reversible local-only conceptualization of time. The principal argument is that subtime starts and stops with the emission and absorption of a photon, and is reversed in all ontological respects as the photon is returned in the hot-potato protocol. This is how I divorce myself from a background assumption of time, which is not (as far as I can tell) the situation in your otherwise excellent PLL paper.

            One possible further thought - to begin to unify the multiplicative Fourier transform approach applied to the tensorial products in your paper is to consider the path traced out by the photon, not as "terminating" on the atoms, but as a continuous path through each atom, a half orbit (Pi) change of direction at each end. This provides both a mathematical "pole" in the imaginary plane as well as a potentially appealing visualizable ontology which can be explored in its compatibility with Maxwells equations and Euler's identity.

            I would love to stay in touch.

            Kind regards, Paul

            Paul at Borrill dot com

            Michel - I hope that by now you have forgiven me for not using the concept of entanglement in an appropriate way ;-)

            I intended to be provocative: if the concept of subtime and the mutual hot potato photon does indeed predict identical results in Bell experiments and yet it has explanatory power beyond the statistical-only Hilbert formalism, then we can begin a new conversation on the nature of entanglement, and perhaps even the measurement problem itself.

            I looked at your paper on phase locked loops. This is an impressive piece of work. It reminds me of my first career in my teens and 20's as an electronics and telecommunications engineer and the old familiar PLL concepts came flooding back. Very enjoyable, thank you.

            The biggest distinction I see is that I have introduced a truly reversible local conceptualization of time. The principal argument is that subtime starts and stops with the emission and absorption of a photon, and is reversed in all ontological respects as the photon is returned in the hot-potato protocol. This is how I divorce myself from a background assumption of time, which is not (as far as I can tell) the situation in your otherwise excellent PLL paper.

            One possible further thought - to begin to unify the multiplicative Fourier transform approach applied to the tensorial products in your paper is to consider the path traced out by the photon, not as "terminating" on the atoms, but as a continuous path through each atom, a half orbit (Pi) change of direction at each end. This provides both a mathematical "pole" in the imaginary plane as well as a potentially appealing physical ontology which can be explored in its compatibility with Maxwells equations and Euler's identity.

            I would love to stay in touch.

            Kind regards, Paul

            Paul at Borrill dot com