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.

    Philip,

    Thank you for answering my questions. Your answers were well thought out and went in a completely different direction from what I imaged. I was very surprised by the black holes created by crossed information beams. I would have bet against you stating that the second law of thermodynamics survives nearly to the plank scale. I am glad I asked these questions. It looks like your essay is doing well, remember us little people when you win.

    Jeff

    Philip,

    I very much enjoyed reading your essay. Your application of Lie algebras to formulate how spacetime emerges from quantized charges of the symmetry hidden in holography is very intriguing.

    It is also possible to consider the momentum/energy information in a black hole and the lost spacetime information as reciprocal measures of entropy. In this way spacetime emerges from the hidden symmetry of entanglement entropy via the conditional entropy of the local observer.

    Conversely, a compactification of spacetime leads to a dimensional collapse from 4D to 2D (CFT) to 1D in the bulk towards a point singularity. (See my essay "A Complex Conjugate Bit and It".)

    Best wishes,

    Richard Shand

      Hi Philip,

      Terrific to see a way to discretize String Theory. Now if only we could find proof of String Theory... :)

      You wrote:

      1. "The lesson to be taken from holography is that there is a huge hidden symmetry in physics that nobody has yet appreciated."

      What do you think of Bobylev and Vilasi's Projective Invariance as a candidate symmetry? Their paper is not well-known as they published in an obscure journal that soon went under. Luckily, it survives in cyberspace.

      2. "Some observational input on phenomenology of quantum gravity would help but for now everything we can measure is adequately explained by the physics of quantum mechanics, general relativity, thermodynamics, and the standard model of particle physics."

      Quite an optimistic view in the face of multiple foundational cosmological issues regarding Dark Matter, Dark Energy, Inflation, quasar energies, CMB anisotropy, etc! In my essay, Software Cosmos I work out a holonomic model (in the sense of David Bohm and Basil Hiley) that utilizes the Projective Invariance symmetry to address some of these cosmological problems. Hope you get a chance to take a look...

      Hugh

        Hugh thanks for your comments and questions.

        I had not seen the paper of Bobylev and Vilasi. It should be interesting in the context of the systems they describe. The symmetry appears to use 2D Mobius transforms which are part of conformal invariance. This is a very important symmetry in quantum field theories of massless particles. In super yang mills theory there is a dual conformal invariance which conbines with ordinary invariance to give a larger symmetry which can be used to solve the theory in the planar limit and perhaps beyond. In quantum gravity an even larger symmetry is needed to explain holography but projective mathematics surely plays its part.

        I agree that Dark Matter, Inflation etc are big issues that need to be solved but they have not been much help to quantum gravity and I do not mention in my essay.

        I will take a look at your essay to see how you use projective invariance in relation to these problems.

        Phillip

        the way I like to do physics is to have clearly stated and motivated principles, and derive all physical consequences from them, as in a mathematical theorem.

        My best regards

        Mauro

        Dear Philip Gibbs:

        You quote Wheeler: "Nothing else in our multifarious universe is fundamental, he conjectured. Space and time, locality and causality". It would be the same if "time" is just a remnant word, from which mankind forgot its meanings as Einstein suggested is one of the pre-scientific concepts, and become more real if we find out that it is "motion" a quality or property of every physical existing thing?.

        I am sending you a practical summary, so you can easy decide if you read or not my essay "The deep nature of reality".

        I am convince you would be interested in reading it. ( most people don't understand it, and is not just because of my bad English). Hawking, "A brief history of time" where he said , "Which is the nature of time?" yes he don't know what time is, and also continue saying............Some day this answer could seem to us "obvious", as much than that the earth rotate around the sun....." In fact the answer is "obvious", but how he could say that, if he didn't know what's time? In fact he is predicting that is going to be an answer, and that this one will be "obvious", I think that with this adjective, he is implying: simple and easy to understand. Maybe he felt it and couldn't explain it with words. We have anthropologic proves that man measure "time" since more than 30.000 years ago, much, much later came science, mathematics and physics that learn to measure "time" from primitive men, adopted the idea and the systems of measurement, but also acquired the incognita of the experimental "time" meaning. Out of common use physics is the science that needs and use more the measurement of what everybody calls "time" and the discipline came to believe it as their own. I always said that to understand the "time" experimental meaning there is not need to know mathematics or physics, as the "time" creators and users didn't. Instead of my opinion I would give Einstein's "Ideas and Opinions" pg. 354 "Space, time, and event, are free creations of human intelligence, tools of thought" he use to call them pre-scientific concepts from which mankind forgot its meanings, he never wrote a whole page about "time" he also use to evade the use of the word, in general relativity when he refer how gravitational force and speed affect "time", he does not use the word "time" instead he would say, speed and gravitational force slows clock movement or "motion", instead of saying that slows "time". FQXi member Andreas Albrecht said that. When asked the question, "What is time?", Einstein gave a pragmatic response: "Time," he said, "is what clocks measure and nothing more." He knew that "time" was a man creation, but he didn't know what man is measuring with the clock.

        I insist, that for "measuring motion" we should always and only use a unique: "constant" or "uniform" "motion" to measure "no constant motions" "which integrates and form part of every change and transformation in every physical thing. Why? because is the only kind of "motion" whose characteristics allow it, to be divided in equal parts as Egyptians and Sumerians did it, giving born to "motion fractions", which I call "motion units" as hours, minutes and seconds. "Motion" which is the real thing, was always hide behind time, and covert by its shadow, it was hide in front everybody eyes, during at least two millenniums at hand of almost everybody. Which is the difference in physics between using the so-called time or using "motion"?, time just has been used to measure the "duration" of different phenomena, why only for that? Because it was impossible for physicists to relate a mysterious time with the rest of the physical elements of known characteristics, without knowing what time is and which its physical characteristics were. On the other hand "motion" is not something mysterious, it is a quality or physical property of all things, and can be related with all of them, this is a huge difference especially for theoretical physics I believe. I as a physician with this find I was able to do quite a few things. I imagine a physicist with this can make marvelous things.

        With my best whishes

        Héctor

          Hi Philip,

          What I understand when you say the projective or conformal symmetries are not "large" enough is that they could not be dimensionally reducing in the way holography is.

          So let me make another suggestion for a "hidden symmetry"... how about a kind of "fractal invariance"?

          The idea is to postulate that space (and not just the contents) is self-similar. It would not necessarily have to be a regular fractal, like a Koch snowflake, but could be a brownian fractal (in the sense that Mandelbrot used the term) or even some kind of Julia set. Restriction to a fractal subset can be dimensionally reducing.

          In fact, if I remember correctly, the measurements of the fractal dimension of luminous matter in the cosmos is about 2, instead of 3. It is also worth noting the efficiency of the fractal compression algorithm on various kinds of data, and that the wavelet packet algorithm is surprisingly effective on natural spatial and temporal signals. Laurent Nottale has explored some of the consequences for microphysics of assuming fractal structure.

          Hugh

            A scale factor symmetry is included in conformal symmetry. I think the scale relativity is more about symmetry seen in cosmological structures rather than symmetry of the underlying physics but I am not an expert.

            When I say that the symmetry is huge I mean that the symmetry algebra has many dimensions. A scale invariance may sound like a big symmetry in some sense but it is only one dimension of symmetry. We need an infinite number of them.

            However, scale relativity and projective symmetry are important parts of it so it is good that you are looking at thst.

            Thanks for your comments. I am working my way through all the essays

            Dear Philip, Congratulations. I sincerely hope you win this contest. Apologies if this does not apply to you. I have read and rated your essay and about 50 others. If you have not read, or did not rate my essay The Cloud of Unknowing please consider doing so. With best wishes.

            Vladimir

              Thanks Vladamir, I read your essay some time ago. Good to see you in a strong position.

              Dear Philip,

              Quantization is only an abstraction of infinity in that process of abstraction is infinite for absoluteness. Information paradox indicates that the nature of information is continuum rather than discrete and thus the nature of matter seems to be as string-matter continuum rather than as particles, that is realistic rather than probabilistic with observational information.

              With best wishes

              Jayakar