Hello Ben,

Thank you again for your comments on my essay, which to me are among the most valued of all the comments I've had.

I saw your recent point about objects ageing, in relation to the point I made about the residual effects of time dilation. The emphasis in my essay is simply to set out the clues we have, and draw broad conclusions from them, rather than going into detailed attempts to interpret them. Because I think it's possible to arrive at a conclusion that way, and to reject block time via simple deduction, it seemed a good way of keeping the essay simple. But of course these questions can be examined in far more detail, and from there it's a case of choosing between two or three initial avenues.

I've read your essay today, will read it again, I found it excellent in a number of ways. The overview of the whole landscape of physics you give in the first half is important and very useful, particularly at a time when things are getting a bit fragmented. It not only helps that you've summed up the landscape as a whole, but - like myself and not too many others - you've included comments on the mindset of the physics community over the 20th century, which helps with understanding about attitudes, and how and why the general view has shifted over time.

In relation to the second half of your essay, what I'll say now is simply a personal opinion, not a criticism of your particular view. And I tend to agree on the assumptions you reject. But I suspect that the way forward, when we find it, rather than involving shuffling the underlying principles and making some go from fundamental to emergent, while others go from emergent to fundamental - which several essays here do, though none better than yours - will instead involve finding some truly new concepts. However, it may be that rearranging the bits of the puzzle we have will also be needed, and I do see that you bring in new principles, and that you may recover established physics from them. So it's certainly too early to tell, and I very much wish you luck with it, and with your essay.

Best wishes, Jonathan

    Dear Juan,

    I appreciate the kind remarks. I'm beginning to feel as if it is difficult to be a competent physicist or mathematician without being a rather avid historian! Your comments are particularly valuable to me because you evidently possess a rare grasp of historical context in regard to foundational issues. The phrase "before his time" is overused, but it undoubtedly applies to Riemann. In many cases, the most fertile period for an idea seems to occur shortly after its inception, before certain arbitrary choices have hardened into orthodoxy, and if the community is unready to use an idea at the time it is introduced, it may be many years before it is fully exploited. I believe this has occurred with many of the ideas of Gauss and Riemann, and I'm only dimly becoming aware that the potential seeds of new advances may be lying dormant not in the last few generations, but a hundred years earlier!

    I will certainly read your European Journal of Physics article with interest. For myself, I have several volumes of unpublished work on foundational topics in physics, but this is my first small effort to make any of it public. I prefer Gauss's philosophy of "few, but ripe" to the current creed of "publish or perish." Also, I am coming from the mathematical side, and don't yet feel comfortable with my grasp of what is already known.

    I was unaware of the close connection between Cantor and Riemann, but Cantorian ideas do arise unavoidably in the approach I have been working on. I even named an important counterexample the "Cantor graph." The axiom of choice and the continuum hypothesis also become significant.

    I will have to look at the early notions of causality you mention. One thing I have learned from reading Grothendieck is the importance of properly organizing local and global data, and in regard to causality, this has led me to define things somewhat differently from the usual notions. In particular, "interpolative" properties like "interval finiteness" and transitivity play less of a role than legitimately local properties.

    Thanks again for the helpful comments! Take care,

    Ben

    Dear Jonathan,

    Thanks for the feedback! I understand that your essay doesn't represent the whole of your thinking about fundamental physics, and I agree that the ideas you consider are sufficient for the point you are making. Conciseness and clarity are particularly important in the present context.

    Nevertheless, I am interested to know what your ideas about the fundamental structure of spacetime are. You say that you "suspect that the way forward, when we find it... will instead involve finding some truly new concepts." Do you have any favorite conjectures for what those "new concepts" might be? Take care,

    Ben

    Hello Ben,

    well thanks for asking - it's more a book that's needed to answer that. I saw you mention somewere the other things that you 'ought to be doing' at the moment, well I have the same... I would be putting the finishing touches to my book if I wasn't on this site, the publisher is expecting it - but am enjoying the discussion here and learning a lot from hearing other people's views. In the book I compare and explore some different avenues, and different kinds of answers to these questions, and try to use rational thinking to estimate what kind of answer is the most likely. It seems to me that I narrow down the possibilities well, but I'll wait to see what others say. I'd very much value your opinion when it's out, will let you know.

    Your contribution here has been enormous, I find your posts in many places, helping to pull people's thoughts together, and helping to focus the general attempts to crack these puzzles. Thanks again, and good luck to you.

    Best wishes, Jonathan

      Dear Ben,

      Your comments all over the place have been a joy to read. I particularly admire your habit of asking 4 to 6 detailed and relevant questions on each essay, and am most impressed with the mental power and will power that drives your output.

      In most cases I find myself in agreement with you, and certainly when you state:

      "...in any case, the physical ideas ought to come first, and the math ought to be whatever is necessary to get the job done..."

      And in another comment to Peter you said:

      "My view is that simple physical ideas do sometimes lead to horribly complicated mathematics ... the less you assume, the more you have to explain."

      Despite my fascination with your prolific comment trail, it is scattered over a hundred or so essays, so I can only comment on my general impression, which is that you several times stated something to the effect:

      "the continuum is too good to be true."

      while qualifying this by saying that its mathematical definition (manifolds) is quite complex.

      Yes, the simplest physical possibility, the continuum, can understandably lead to horrible mathematical complexity in trying to "capture" this simplicity. In my view simple mathematics (can) lead to horribly complex physics. Integers and binary relations are "unnatural" compared to the continuum, although both can fall out of it.

      In prior essays I make the fundamental assumption that the universe began as ONE thing, and therefore any possible evolution (which must have occurred to get to where we are today) could only have come from the one thing interacting with itself. It's easy to turn this into a symbolic equation and, with a few known facts, translate it into a physics equation that leads to the world as we know it. I won't belabor the point here but think that you might find my previous FQXi essay to be of interest.

      One point in particular that might interest you is that, while no discrete or quantum value of space, time, or mass falls out of the master equation, a quantum value of 'action' does fall out [which I of course set equal to Planck's constant] in a very simple way.

      You are probably way too far down your own path of causal binary relations to reconsider things, but I think that you are spot on when you disentangle the complexity of math from the complexity of physics. If anything, they may be inversely related!

      Anyway, thanks again for your wonderful comments. They've made this FQXi event even richer than usual. And, having done my undergraduate work there in the early 60's, I have fond memories of LSU. I hope you're enjoying it.

      Best,

      Edwin Eugene Klingman

        There was a discussion last week comparing shape dynamics with causal nets. I am rather new to both of these approaches to physics. The comment was made that shape dynamics involves symmetric relationships, while causal set theory anti-symmetric relationships. Time evaluated from the Jacobi variational principle

        δt = sqrt{m_iδx_iδx_i/(E-V)}

        is related to a proper time, or an interval. I might then say that if we multiply by E-V on both sides we get

        (E-V)δt = sqrt{m_iδx_iδx_i(E-V)}

        where the left hand side appears to be a Lagrangian times an interval of time. This may then be written as

        ∫d^3 δt sqrt{-g}R = sqrt{m_iδx_iδx_i(E-V)}

        We may then break out the Ricci scalar R = R_{ab}g^{ab} and the left hand side exhibits this symmetry. On the right hand side again there is symmetry with the interchange of δx_iδx_j δ_{ij}. This probably needs to be firmed up of course, but I think this captures the idea.

        Causal dynamics on the other hand is ordered by events with the idea of building up geometry. So there are orderings such as x < y so that in some product we have xy = -yx. This seems to have some connection with Penrose tensor space theory, where for every symmetric tensor there is an antisymmetric tensor. The relationship between the two is a graded algebra similar to supersymmetry. The symmetric interchange between spatial coordinates in shape dynamics is similar to the symmetric interchange between boson fields. The antisymmetric interchange of events in causal sets is similar to the interchange between fermions ψ(x)ψ(y) = -ψ(y)ψ(x). Hence a causal set is potentially identical in form to a Slater determinant. This then opens the door to a type of functor or category theory which maps elements of geometry to elements of field theory.

        Cheers LC

        Dear Edwin,

        Thanks for the kind remarks. You are, I believe, even more prolific than I am on these threads, and you always maintain a high standard of reason, civility, and circumspection.

        I hope I'm not too far down the path of causal binary relations to reconsider things! I'm 32 years old, and have been working on this idea for about 2 1/2 years. As I've mentioned before, most of my mathematical work involves manifolds, varieties, schemes, and objects of that nature, so I am quite friendly with them in general. In addition, a lot of what I have read here has taught me features of manifold physics that I simply did not know. I have read about a lot of things, but my education in physics is not standard. I never had the usual graduate curriculum. Hence, there are bound to be gaps in my knowledge that most professional physicists don't suffer from, and the only way to fill them is to keep an open mind.

        I have your ideas filed away for further consideration, partly because I tend to suspect that you will be willing to continue to engage in conversation after the contest is over. I suspect that a number of authors will check out after the next few weeks, so I have been trying to gather information while everyone is still engaged.

        The action principle you mention does interest me. Besides your arguments, the specifically "pro-manifold" contributions that have made the biggest impression on me are those by Torsten and Jerzy involving exotic smoothness structures, those by the shape dynamics folks (Sean, Flavio, Julian, Daniel), the essay by Abhijnan Rej, and a few others. The questions I asked these people were serious, and the answers were quite convincing in some respects. There is no reason to limit oneself to working on a single idea.

        In any case, I appreciate your remarks and will always welcome any sincere effort to challenge my point of view. Learning which of my opinions are mistaken as quickly as possible saves a world of trouble! Take care,

        Ben

        Dear Juan,

        Thanks for letting me know. I will be sure to look out for that article.

        I feel silly for overlooking the distinction between t and tau causality in your essay. My only excuse is that I have read a lot of physics papers in the last few weeks! Of course you mentioned tau as the "fundamental concept of time" in the Liouville space at the very beginning. Many people do not associate time and causality so closely, so I did not put two-and-two together even though I view the two concepts that way myself. Oh well... if one talks or writes for long enough, one is bound to make a fool of oneself eventually!

        Thanks again for keeping me in the loop on this. Take care,

        Ben

        Lawrence,

        (Feel free to post at the bottom of my thread at any time; the comments up here are easier to miss.)

        The first part of your sketch seems right to me. Regarding the second part (involving causal dynamics), I am not sure about the meaning of the algebra with the antisymmetric product. I have thought a fair bit about path algebras in this context, and for path algebras acausal products (including anticausal products) are zero. The reason is that this algebraically encodes path sums. For instance, if you partition a "spacetime region" in a causal graph by a "Cauchy surface" (i.e. suitable antichain) then the path algebra element representing all maximal directed paths in the composite region is just the product of the elements representing all maximal directed paths in the subregions.

        The obvious thing is take the minus to mean "time reversal" in the obvious sense, but I will have to think about the physical significance of this. The pure causal philosophy is that there is never disagreement between "time" and the "direction of trajectories." In particular, in the causal configuration space, this would correspond to "un-evolution of the universe."

        In my original remark about symmetry and antisymmetry I was referring to the order-theoretic definition, not necessarily implying that an antisymmetric algebra is the appropriate vessel for containing information about phases of paths, etc. But perhaps I need to rethink this. The sketch you present is rather compelling. Take care,

        Ben

        Dear Hoang,

        I would not presume to propose a "Theory of Everything;" my belief is that all such attempts will look a bit silly a thousand years from now. Even if we succeed in developing a theory that seems to explain all natural phenomena of which we are currently aware, there is nothing to prevent us from making new discoveries in the future. Don't you think a "Theory of Everything" would be a bit depressing? What would be left to do?

        However, I will take a look at your essay! Take care,

        Ben

        Dear Benjamin,

        Your CMH opens a lot of new perceptions and universes. I liked it very much. You also mention : "The initial family evolves to the terminal family", so in your view every universe was in facto initial and becomes terminal, also the conglomeration of universes that forms our "reality".

        In "THE CONSCIOUSNESS CONNECTION" I go back to the initiality and limit our universe by the Planck length and time. So "reality" emerges from our consciousness, that is why I appreciate your "thought experiment".

        I also saw that Eric verlinde had your attention, his perception of gravity is also in accordance with my idea that only materialistic reductionism is not the only way to research our questions about existence.

        I hope that you will read my attribution in the contest, especially your opinion about my "causality" perception.

        best regards

        Wilhelmus

          Dear Wilhelmus,

          Thanks for the kind remarks. I have seen some interesting comments of yours on other threads, but so far missed reading your submission, probably because you are near the bottom of the alphabetical list! In any case, I will be sure to take a look. I do think that consciousness is a very difficult topic and one that I would not have attempted myself, though I have thought about it a fair bit. I'll be interested to see what you have to say. Take care,

          Ben

          Ben,

          Thank you for the nice comments over on my essay. I responded over there. While your essay is way over my head in terms of math, the points you made that I think (?) I understood were very good! A few comments are below, but take them with a grain of salt because, as I said, it was kind of over my head. Anyways, they are:

          1. I think your way of thinking as illustrated by this quote:

          "What I try to do is build up fundamental physics from simple principles like cause and effect. This leads to some rather thorny mathematics, but my view is that the physical principles ought to be simple and well-motivated"

          is exactly right, and I wish more physicists and thinkers in general would think this way. If we start at base principles like cause and effect, we have a better chance of building a working model of the fundamentals of the universe that can make predictions than by starting out with high level, assumption-riddled, current physics thinking and working down to more fundamental levels.

          2. I totally agree that the assumption that systems evolve with respect to an independent time parameter, and that the universe has a static background structure seem unlikely. To me, if the universe is the "system", time is just the same as a sequential chain of physical events occurring within the universe, with the earlier events in the sequence corresponding to earlier times. If the events A ->B->C are sequentially followed by the events C->B->A, this doesn't mean that time is going backwards because the events C->B->A still occurred after the A->B->C sequence of events. When I hear physicists say that their equations work fine when time is negative, this doesn't mean that time in the real world (not in the equations) can actually go backwards. Also, if time exists as this separate, independent dimension somewhere, I'd like someone to point it out to me now. Where is it?! I can't see it. Also, in regard to the second assumption, I think of the universe a little more holistically where matter and energy aren't occurring against a separate space background, but rather that they're interactions between the units that make up the universe/space.

          3. You mentioned on pg. 6 "This means, in particular, that spacelike sections are merely unordered sets, with no independent notion of distance or locality". If I understood this, I think I'd also agree because I think that location of something refers to its position relative to other things within a bigger set of things. That is, while a single existent state may "be" or exist as a location, it doesn't "have" a location within a bigger reference frame.

          4. My own view on volume is that to physically exist, any existent state must have three dimensions, and, therefore, volume. I have trouble imagining an actual physical state in which one of the dimensions is zero. Not just infinitesimally small but actually zero. At zero, it disappears. So, three dimensions, or volume, seems to me to be a requirement of an existent state and thus a requirement for whatever existent state makes up our universe.

          5. So, is a binary relation just a relationship between two elements in a set/ And, if one element causes the related element to appear, is this a causal relation? If this understanding is right, this makes a lot of sense to me because my own view of existence is that given a fundamental state of existence, whatever this is, this state will somehow cause the formation of identical states around it, these new units will cause the formation of new states around them, etc. and this expanding space of existent states is equivalent to our universe. So, in my view, I think I would say that there's a causal relation between each existent state and the existent states it causes to appear next to it. I have more on this at my website at:

          https://sites.google.com/site/ralphthewebsite/filecabinet/why-things-exist-something-nothing

          Sorry for the long response. Nice essay and good luck in grad. school!

          Roger