Dear Philip

I vaguely remember hearing the name Weizsacker as a president of Germany, but not as a theorist of matters quantum. JAW was the one who led me into the labyrinths of quantum mechanics. It was through his contributions in "Some Strangeness in the Proportion", a book of essays from the Centennial Celebration of the Achievements of Albert Einstein that quantum mechanics became alive for me. Before that only the catechisms of Schrodinger Equation and Heisenberg Uncertainty Principle!

In my essay "Analogical Engine" I tried to draw the parallels between Analogy (as a thought process) and Quantum Mechanics (as a physical process) from a premise "What quantum is to classical" is similar to "What analogy is to rationality." With the help of a thought-experiment, I came to this conclusion: "Planck constant is the Mother of All Dualities, and a necessary condition for the existence of thoughts and things."

Then entering the FQXi Essay Contest I found your essay, and wow you are saying: "With multiple quantisation the values of the probabilities themselves are replaced with further wave-functions ad infinitum." and "Bringing together different theories often forces almost unique conclusions."

Very deep and very interesting I said to myself. Unable to jump the maths huddles, I can feel only the resonances that I can barely articulate. I do not like to impose, but I am curious to know what do you see from your side of the fence if you were to look at mine.

Good luck!

Than Tin

    Dear Philip,

    It is clear you have worked long and hard on remarkable essay, but I have a few comments and questions:

    A clear and concise definition of the "holographic principle" was never given. What I get from context: the holographic principle - all information within a closed surface can be reproduced by knowing the flux of all the fields going through that same surface.

    A clear definition of "information" is needed.

    Is the same information bit used for all fields? If there is just one type of bit then how does one know which field the bit is producing? If there is a different bit type for each type of field then how does saturation in one field (gravity as seen in a black hole) saturate another field such as the electrical field?

    Why do we not see a black hole-like saturation due to other types of fields?

    Any volume of space could have many streams of information going through it at any given moment. At the shopping mall, you can buy glass paperweights with an imbedded pattern of tiny bubbles made crossing laser beams which over-drive phonons in the material. Over-driving phonons is many orders of magnitude less than the Plank density, but in theory, we could reach that information flow density. Could we create a black hole by beam crossing?

    Pions violate chiral symmetry. We have more matter than anti-matter, so charge symmetry is violated. Symmetry breaking is sometimes said to define a field, yet you declared that entropy is declared not fundamental because it violates time-reversal symmetry. Entropy might not be fundamental, but violation of symmetry cannot be the reason it is not fundamental.

    All the best,

    Jeff

      In ancient Greek philosophy acatalepsy ( http://en.wikipedia.org/wiki/Acatalepsy )was the antithesis of catalepsy ( or Katalepsis to avoid confusion with the medical condition http://en.wikipedia.org/wiki/Katalepsis ) catalepsy was the philosophy of the stoics such as Plato who thought there was an absolute reality that we experience through our senses but existing independently. The skeptics contested this an proposed the acataleptic philosophy instead. It is sometimes defined to mean that reality is incomprehensible but I dont think that is accurate. I think what they meant is that reality is uncertain. It is not fully knowable but to say that it is completely unknowable or incognizable just contradicts our sesnes.

      In the Bayzian worldview we only know things by probabilities that are never zero or one. There is always some doubt no matter how small. Our a priori probabilities are continually updated as more information reaches our senses. According acataleptsy precise reality is not just unknown, it is unknowable. The standard view of quantum mechanics supports this view. The Heisenberg uncertainty principle tells us that if know some things with a high level of certainty then other things are fundamentally unknowable with any degree of accuracy.

      The Greek skeptics said more than this, They also said that even the amount of uncertainty is uncertain. It is true that we do not really carry Baysian probability values around in our head. We have a more vauge sense of how certain or uncertain things are. In my interpretation of acatalepsy I assume that this is also true of physical reality. The wavwfunction amplitudes that give us levels of probability must themselves be quantised and replaced with wavefunctions that describe the uncertainty of their state. This must be repeated ad infinitum through a process of iterated quantisation.

      This does not lead to a reality which is completely unknowable or incomprehensible. On the contrary it is this process of multiple quantisation that builds the emergent structures of physics that we experience. At the macroscopic scale of our ordinary experience the world seems very real and almost completely certain. It is only when we look at microscopic scales that the acatalptic nature of reality is apparent.

      German President Richard von Weizsacker was the younger brother of Carl. They came from an incredibly successful family who made their mark in politics and a wide range of academic fields. see http://en.wikipedia.org/wiki/Weizs%C3%A4cker_family

      Thank you for your comments. I will read your essay.

      Thank you for your good questions

      The definition os the holographic princple I used in the essay is "The

      amount of information in any volume of space must be limited by the area of a surface that encompasses it" Stringer and weaker version of the principle exist.

      Information is just answers to questions we can ask about the world around us, such as the state of a particle.

      Ina unified theory there are not really different fields. They are all different aspects of one field, so the type of information is also unified.

      The gravitational field seems special because it is connected to geometry of space-time. All fields interact with gravity to information is all fields is limited by the holographic principle. A black hole must form when informnation density exceeds the holographic bound no matter what form it takes.

      P and CP symmetry are broken in nature but CPT symmetry is always valid.

      Breaking T symmetry is therefore the same as breaking CP symmetry but this is a very small effect and probably cannot account directly for the arrow of time. Some people might dispute that and we do not know enough to be sure.

      However, the bigger point is that space and time themselves are emergent and the second law of thermodynamics cannot make sense at a level more fundamental than the emergence of time.

      I hope this answers your questions. If not please ask again.

      Dear Philip

      Thank you for explanation.

      Do you know Who is Warren McCuloch?

      Dr. McCulloch's researches uniquely exemplify the modern interdisciplinary approach. During his long and distinguished career in neurology

      and related disciplines he has also applied his talents in modern

      mathematics, symbolic logic, information theory, cybernetics, medicine, the classics and the history and philosophy of science.

      This is one among his many interesting articles.

      http://www.vordenker.de/ggphilosophy/mcculloch_what-is-a-number.pdf

      Yuri

      Philip,

      Thank you for your reply.

      What is "holographic" in the holographic principle?

      Just to be clear, you confirmed that a volume of space with enough signals passing through it could become a black hole.

      if this volume has a material in it could this information be sound as well as EM? Could this space be a vacuum?

      Jeff

      Hello Philip,

      You are right: «What we need is a consistent theory built on mathematical logic that accounts for all known observations». Your revolutionary ideas and revolutionary open vixra - the highest grade.

      Good luck and best wishes, Vladimir

        As I go on to explain in the essay the entropy bound means that the information in a volume of space must be described by states on the boundary. This is the sense in which it is holographic, just as a hologram can build a 3D picture from a flat surface.

        The information can indeed be included in sound waves but the information in the medium carrying the sound waves will be much more than the information in the sound waves themselves.

        Whether it can be a vacuum depends on what you mean by vacuum. If you mean an absence of matter then electromagnetic radiation can travel through a vacuum but sometimes in particle physics we take the vacuum to mean flat space with no matter or radiation of any kind. In this case it contains no information.

        Thanks and its good to see you well up in the rankings.

        Hello Philip, What an excellent essay! Very deep and elemental in nature with a lot of killer maths. I learned from you about Carl von Weizsäcker and his theory "that builds infinite dimensional symmetries using layers of quantisation from information" I have similar idea that in KQID, our Ancestor FAPAMA Qbit can split itself up infinitely without cost to itself and to our Multiverse. However, I concluded that Wheeler did not go far enough that not only "it from bit" but also that "it is bit and bit is it." I did rank highly of your essay, if you have time please look at and rank my essay Child of Qbit in time. Best wishes, Leo KoGuan

          Thank you, yes I see some n ice parallels between our essays

          Philip,

          "However, the bigger point is that space and time themselves are emergent and the second law of thermodynamics cannot make sense at a level more fundamental than the emergence of time." By more fundamental do you mean smaller scale of size and larger energies? Quantum Mechanics is statical in its results as is statical mechanics. We can run particle interactions very high energy densities; we currently cannot run something like a stream engine at gamma ray blackbody temperatures. The law of thermal dynamics should hold at the scale of nuclear reactions in the core of stars were temperatures and densities are at this level.

          Jeff

          Dear Philip,

          I completely agree with your overarching point that we need consistency to guide our approach to help us gain further insights into the fundamentals of nature. It struck me, though, that when you gave the examples of Maxwell, Einstein and Dirac, these were in a sense completely different situations from the one that relies on arguments pertaining to black holes to derive new consistency-based insights.

          In each of the historic cases, there was at least a prospect that the assumptions on which the consistency-based arguments rested could eventually be checked by experiment. What prospect do we have for that when it comes to black holes? The power of the consistency-based arguments we derive from these assumptions is only as great as the consistency of the assumptions themselves. It seems to me that if we cannot check our most basic assumptions about black holes experimentally, then there is a real danger that we could have overlooked inconsistencies in them, and will continue do so. This could then lead us to derive false arguments even though they are consistent with the assumptions. Instances like the recent firewall debate only strengthen my suspicion that this may in fact be the case.

          It seems to me that a more reliable way to use consistency as a guiding principle would be to apply it to a situation that has at least a fighting chance to be eventually subjected to experimental test. I agree that it is not easy to find such situations where both GR and QT come into play, but consistency-based arguments based on that kind of a situation would seem that much more compelling.

          As you may know, I am also pursuing an idea based on the notion that spacetime emerges from a lower-dimensional analog, namely that quantum theory tells us that pre-measurement states are spacetime manifestations of lower-dimensional objects and that a "measurement" is really the mechanism by which actual spacetime objects emerge out of these. Several people have told me that this reminds them of the holographic principle, although I am myself remain skeptical of that. It is good, though, that you explore the holographic principle from an angle that others have apparently neglected, as hopefully this will increase the chance the whole issue will be more clearly defined. Why do you think is it the case that over the last 20 years, the application of necklace lie algebras has not been taken up by the string theory community?

          All the best,

          Armin

            Thanks Phil, apologies if what I was saying was misunderstood, I wasn't posting to get you to read the essay it was more to illicit dialogue. In any case, I have always been impressed by your posts on the Higgs particle and for that will give you a 10.

            Jeff, I think that space and time will break down at temperatures and densities around the Plank scale. Theory suggests a Hagdorn temperature for quantum gravity analogous to the one for QCD at much lower temperatures. This is responsible for emergence of space and time. It is a temperature many orders of magnitude higher than those reached in stars or particle accelerators, even in neutron stars and gamma ray bursts. The second law of thermodynamics is safe for anything we are ever likely to observe but conceptually we need to understand how that works.

            Armin, I was coincidentally reading your essay today so I am happy to find your comment here.

            The examples of Maxwell, Einstein, Dirac and Higgs are some of the best examples from history of how logical consistency has been used by theorists. I agree that the circumstances have changed in that further experimental data is lacking for quantum gravity, but that is precisely why consistency is now so important.

            I do think that whatever we conclude will eventually be confirmed by observation but the time scale is goinf to be much larger because it is difficult to reach the energy scales required. Nevertheless there are people looking for possibilities in quantum gravity phenomenology.

            Of course it would be better if some theory could shed light on dark matter or inflation in a way that we could test, but there are people looking at that too. It is not a choice of one or the other. For some reason we seem to be able to make more promising progress on questions that relate to the highest possible energies at this time. Perhaps that will change.

            "Why do you think is it the case that over the last 20 years, the application of necklace lie algebras has not been taken up by the string theory community?"

            This is an interesting question but I think the simple answer is that I have not found a convincing enough case to get them interested. There are so many ideas around that might be important that it is hard to get people interested unless there is something really obvious that makes it look important.

            Sometimes a mathematical idea can hang around for years looking interesting before people find the right way to use it. A good example is twistor theory invented by Penrose years ago. Most people gave up on it but a few kept going. Andrew Hodges developed a complex diagramatic system for physics based on twistors but nobody paid any attention until Witten applied twistors to string theory a few years ago. A group of theorists then started to use it on super Yang-Mills theory. According to Nima Nima Arkani-Hamed they started to develop a new diagramatic approach for this and then noticed that some of their diagrams looked like the ones drawn by Hodges whose theory they could not really understand at that time. So they looked at some of his more complex diagrams and asked what they would mean in their new theory of super yang-mills. Suddenly everything made sense and they were able to move forward much quicker.

            Now they understand it all in terms of invariants of an infinite dimensional Yangian symmetry which had previously been used to understand integral models of spin chains. These things are tantalizingly close to my necklace lie algebras but so far no cigar. It would certainly be amusing if someone wrote down the same definitions as I used twenty years earlier as a solution to the corresponding problem in string theory, but it is more likely that it will be something else

            I don't think I had heard of him before, thanks for the pointer.