Philip,

Many thanks for yet another interesting read. You have succeeded in provoking my thoughts.

You briefly mention that the particles that we observe are simply a manifestation of a stable state of the vacuum. Does this suggest that the vacuum is more fundamental than the particles that reside within it? I believe that it does.

I am intrigued by your notion of summing up histories. But doesn't this produce some type of integral? Wouldn't the thing that is being integrated be more fundamental and the resulting integral be emergent? And a history is itself a kind of integral. So you are really proposing a double integration.

You seem to have belief that information is fundamental although I did not read that explicit statement.

I thought your use of recursive thinking was very clever. In some ways, that is precisely how the scientific method works ... The analogy of using the Newton-Raphson method to calculate a square root gave me a little chuckle. I can tell you that in some systems, it REALLY helps if you have a decent first guess. You don't want to be on the wrong side of an inflexion point.

You placed a lot of emphasis upon different types of algebra. This tends to reinforce some of my own thinking. I have not yet tried to study the Lie algebra and such but I see that I need to do so.

All in all, a very good essay.

Lastly, allow me to thank you again for the website viXra.org. I continue to use this resource to post works.

Best Regards and Good Luck,

Gary Simpson

    Scott, thank you for your comment. I think there is a genuine concern that some directions are not being explored because the young academics are made to follow the direction set by the older physicists. I am not saying that they have it all wrong but where they are stuck we need more diversity of ideas.

    The FQXi essay contest is a rare opportunity for people to think for themselves. It should be flooded with essays from PhD students but we only get a few of those. Are they afraid to say what they think? There is a lot more diversity from us outsiders so I hope we have a tiny bit of influence this way.

    Garry, Thank you for reading my essay. You have understood its important points.

    I do indeed regard information as fundamental. This is a common idea that I am sure will feature in quite a few essays. It was something I was writing about 20 years ago and I have been influenced by Wheeler, Fredkin, Duff and especially Weizsäcker.

    In the hierarchy of fundamentalness the vacuum is one above particles, but if there are many possible alternative vacua and spacetime is also emergent, then it is still some way down from the most fundamental levels where information is the main entity.

    I am beginning to see how Weizsäcker's idea of an iterative process related to quantisation addresses some of the problems that fundamental theories face in terms of where do you start, so I am glad that part stood out. The question is then how to turn that into a theory that works. It is a task of matching philosophical ideas with what we know about how physics works. Lie algebras are important and based on a symple idea of composing small transformations.

    The free Lie algebra is a structure that physicists and even mathematicians have neglected. It properties as a hopf algebra are striking and clearly related to physics. If people worked on how to generalise its mapping properties I am sure there would be a breakthrough.

    I will be reading your essay soon.

    "It has always been my view that symmetry is not only fundamental, but there is a huge hidden symmetry in nature that unifies the symmetry of spacetime and gauge theory." My guess is that the huge hidden symmetry is the monster group.

    Monster group, Wikipedia

    If nature is finite and digital then my guess is that string vibrations are strictly confined to 3 copies of the Leech lattice. If nature is infinite, then my guess is that string vibrations are approximately confined to 9 copies (or more?) of the Leech lattice.

      A lot of truth in regards to new ideas not coming from within physics academia...

      Is this issue of deforming or breaking the symmetry of the hexagon related to a paper I think you wrote about moving an object through a maze? I think it was titled the moving couch problem. It addressed the problem of the range of shapes that can be moved through a hallway with a 90 degree turn in the hall. I have been pondering something similar. We know you can't tessellate a plane with pentagons. However, if you shave off sides in various ways you might be able to approximate a tessellation. The question then is what is the minimum amount of deformation required to do this. Also, how is this related to the topology of a dodecahedron, topologically a sphere, and the R^2 plane.

      Cheers LC

        David. I share your enthusiasm for the monster group. Its relation to physics via the Leech lattice is very intriguing. However, I am looking for a group with one dimension for every degree of freedom in physics. According to our current view of field theory there are several field variables at every point in spacetime, so I require an infinite dimensional Lie algebra with one dimension for each one. This itself is not so outlandish. In gauge theory there is an independent gauge group at each point in spacetime. These generate the gauge symmetry. However the gauge field has four of these at every point so there are not enough for my theory. If the final theory is something like string theory then it takes even more variables to describe the state space, so the symmetry has to be even larger. I don't know anyone who shares a belief in this idea but I bet that when they realise it is right they will say they knew it all along.

        The monster group is the largest sporadic finite simple group. It has a huge number of elements, but it is tiny compared to the invariance group of any gauge symmetry. It is really answering a different sort of question to the one I am thinking of. However, the intricacy of its structure is remarkable. I would not be surprised if it has a part to play. In contrast, the groups that I consider most fundamental are a little boring. These are the free groups where you just multiply and invert group elements without imposing any structure apart from associativity

        Hi Lawrence. Yes the Lebesgue universal covering problem is in the same class as the moving sofa problem. They are both geometric optimisation problems like a minimax problem in game theory. The interest is in that simple questions lead to complex, but comprehensible answers. It seems to be the nature of the type of problem that this happens. The state of the physical vacuum is also an optimisation problem, but we don't know the question we have to answer yet. What we can say is that the complexity of the vacuum could emerge from a much simpler starting point.

        I am sure you are aware that the problem of classifying pentagonal tessellations with a single (non-regular) pentagonal shape was solved this year Pentagonal Tilings but there are still lots of other problems to solve in this area.

        If we are instructed by your essay we may stray from scientific methods. Why should governments and universities fund endeavors if nature is relative to the view of each observer? They can just say "tens of thousands of people have been trained in the sciences and you guys are more confused than you were a hundred years ago". But you say some very important things. There is a structure to consciousness and it draws on information. The information it uses is not always relative. For example most believe that atoms and the quarks they contain are the same every time they are measured. Electronic structure may be probabilistic and complex but it is consistent. I believe you would say that some symmetry causes this. I couldn't tell for sure but you might also believe that the structure of consciousness may cause this consistency. This is a very productive line of thought. I associate what MIT calls the unitary operator 1=exp(iet/H)*exp(-iet/H) with the structure of consciousness. My essay deals with the quark "quantum circles" that this operator describes. The quantum circles can be either information based or real time and energy based. The operator and its quarks are a symmetry. The consciousness that contains quarks, atoms and electronic structure has access to consistent information that it can shape into what it pleases including relative thoughts.

        Thank you again for creating viXra (but I notice that you are able to use arxiv). My December 2017 paper vixra: Information and Reality, viXra:1602.0219v2 follows the line of thought above.

        Phillip, I posted the above with too much haste. I re-read it and want to clarify that I meant no disrespect to you or your fine, thought provoking essay. I was reacting to only one of your thoughts, not your essay in general. I am sorry if it came across wrong. I don't know if you saw Tyson's concern that we have some leaders who ignore science as "fake news". I was thinking about damage control if there is criticism that science doesn't appear to be converging.

          I was aware of the Bagina results and Mann, McLoud, Von Derau, but not the complete set by Rao. I suppose I should have done more of a heads up on this, but I have this small stack of drawings with calculations that are almost high school level.

          This seems in some ways a bit similar to the covering problem. If I want to tessellate a plane with pentagons I have to deform them. If I have a dodecahedron I can form a plane by sending a point to infinity and the pentagons are deformed and I have an icosian. This gives metric data near the origin, but far out there is little data. I might think of then piecing icosians together to create a regular pentagonal tessellation of the plane, What then are the deformations necessary? I have to perform transformations on the pentagons, and what are transformations or deformations are required?

          The vacuum is I think a sort of quantum time crystal. Wilzcek worked this up, where there is a periodicity of a discrete system in not just space but time. I make mention of this in my paper that will be coming soon. It is a part of my question with respect to tessellation of space with pentagons.

          Cheers LC

          Hi Gene, thanks for your comments. I have not been following the latest from Tyson, but I did submit an essay to the Global Challenge New Shape essay contest about how we could deal with these kinds of problems. The last thing we need to tackle fake news is fact checking organisation or any brake on free speech on the internet. I think peer review needs to be more open, not less open, but that is another subject. Nothing I have written is meant to be anti-science. When I say that reality is relative to the observer I am not saying we should accept alt-facts. I am talking about observers in different universes.

          You say that I have access to arXiv but actually my access is very limited. I can only post to a small number of categories and my papers have often been moved to different ones. All my submissions are held for moderation. It was better in the past but now I prefer to submit my work to only viXra and researchgate. I have not submitted to arXiv for nearly four years

          I noted your comment to Gene Barbee's comment in Scott Gordon's essay.

          Yes. We independents do it for our amusement. But, if one of us does get the beginning of a TOE a breakthrough, society and science will not know it. Or, will they?

          A breakthrough means a new paradigm which the money people (the powers that be in science funding) wold consider it a challenge to their authority. So, society suffers because an advance means the society gains.

          How does society become aware of the new paradigm? There are so many out there (just look at viXra) and most have almost no data or solved problems let alone predictions made and found.

          I've been published in peer reviewed journal, on arXiv. But Now my model is just too radical (apparently). I no longer try.

          But the model (STOE) has made predictions that were later found, explained problems standard models consider problems, the STOE suggested 2 experiments that were performed and it rejected wave models of light (a photon model produced diffraction and interference). Well, I still talk about it when I get a chance.

          Hodge

            It is going to be very hard to get people to notice a new theory of fundamental physics from an outsider. Sometimes the sociology lines up and there is some short-lived media attention (think Garrett Lisi or Eric Weinstein) but the main problem is that a worthy theory needs to be very complete to be recognised. It may be that what I or you are saying is correct, but it is hard to see that now. It may become clear much later but even then we will get little credit because they will say that we did not have much influence and that is what counts. There is some truth to the "challenge to authority" claim, but a really clear breakthrough would get past that. Some of the essays here are mathematically sophisticated, but their correctness would need to be overwhelmingly obvious in some way to grab immediate attention.

            I now prefer to work on mathematical problems because if you solve an interesting unsolved problem in mathematics it is much more likely to get noticed and appreciated. In physics I just do he FQXi essays because I find that the questions I get help push my ideas along a little each time

            "... a group with one dimension for every degree of freedom in physics ..." If nature is infinite, then it is plausible to assume that physics has infinitely many degrees of freedom. If nature is finite, then nature might have only 78 degrees of freedom. Consider 3 copies of a model of 26-dimenional bosonic string theory, yielding 78 dimensions of bosonic waves. There might be a boson/fermion duality theorem derivable from Wolfram's cosmological automation. There could be 6 "barks" or "big quarks" each carrying a barkload of 12-dimensions of information, yielding 72 dimensions controlled by Fredkin's 6-phase clock, thus 78 dimensions of fermionic information. Each 12-dimensional barkload might represent 4 dimensions of spacetime, 3 dimensions of linear-momentum density, 3 dimensions of angular-momentum density, 1 dimension of quantum-spin density for matter, and 1 dimension of quantum-spin density for antimatter. By redundant representation of information, it might be possible to derive an 11-dimensional model of M-theory and a 12-dimensional model of F-theory -- the idea is that the interior of the multiverse would be 72-dimensional in terms of "barkload" data, and the measurable universes would all be 71-dimensional and located on the boundary of the multiverse.

            Phil,

            "I expect to find this symmetry in a pregeometric meta-law that transcends spacetime."

            That says it pretty well. Like the shape of a Lotus petal bespeaking the whole form of the opening blossom. In spite of the possibility that not even the universe always works perfectly. Merry Christmas and a Happier New Year. jrc

              quote

              The biggest difficulty faced by theoretical physicists of this generation is that positive experimental

              input on physics beyond the standard models is very hard to come by. That situation could change or

              it could continue for much longer. Without empirical data how is it possible to tell if the answer is

              string theory, loop quantum gravity, non-commutative geometry or something else? The theorists

              can still progress by working with the few clues they have, but success will depend on guessing

              correctly the answer to questions like 'what is "fundamental"?' If they don't know then they must be

              prepared to consider different philosophical options, letting the mathematics guide the way until the

              experimental outlook improves. If young researchers are all corralled into one pen it could turn out

              to be in the wrong place. The chances are they are going to be influenced only by the highest profile

              physicists. If those leaders say that symmetry is unimportant because it is emergent or that

              geometry is more fundamental than algebra, other possibilities may be neglected. It appears to me

              that there is a clear program that would combine the ideas of algebraic geometry with quantum field

              theory. It just requires mathematicians and physicists to bring their knowledge together.

              You nailed it !!!!

                Dear Phillip,

                I knew there's a reason I always prioritize reading your contributions to these contests. Excellent work, and you certainly succeeded in your aim of provoking the readers' minds.

                I particularly like this sort of theory-independent view in terms of events: whatever the fundamental theory may turn out to be, it has to have events within it in some form, be those worldlines crossing, particles of all conceivable kinds interacting, string splittings or whatever. So let's not worry about those details for the moment, but rather, think in terms of those events, and the stories that can be told with them.

                One tiny bit of criticism I have is that there's many deep and possibly controversial ideas that aren't developed in the way they deserve (although that is likely owed to the length restrictions, and I'm also aware that this is a criticism you could probably lob straight back at my own essay if/when it gets posted). In particular on topics where I perceive some confluence with my own thinking---like the relative nature of reality, or the idea that in terms of information, 'nothing' and 'everything' are really the same---I would have liked more discussion, just to see how somebody like you develops these notions.

                But these are the complaints of one having been hooked by your ideas, and now finding themselves jonesing for more. Which, as you said, is really all you intended with this essay.

                All the algebraic stuff has re-awoken that curious sense that if you could just take one further step back, you'd just see the big picture pop out. There are so many tantalizing hints and connections, it's hard to believe that there isn't some fundamental story to be told in these terms.

                But I think that's for someone smarter than me to discover. I may get back to meddling with this some day (although my love of the octonions means that I'm skeptical of requiring associativity---alternativity is really all you need!), but for now, I'll concentrate on other matters.