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

          Ben,

          The best thing about these contests is they give an opportunity to brain storm on a range of possibilities. The questions concerning physical foundations, particularly with respect to cosmology and quantum gravity, require different ways of thinking. I sometimes think that our educations have a disservice. While of course a graduate student needs to know classical and quantum mechanics, electromagnetic fields and so forth, I sometimes think these cement in our thinking so as to prevent successful consideration of deeper problems.

          I sometimes think that we often suffer from some of the difficulties seen in elementary students with basic mechanics and F = ma. Our brains are predisposed to thinking in certain ways, and though we may learn the breakthrough physics of the past, this learning often serves to foster thinking that is erroneous on deeper foundations.

          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.

          Fields on a Cauchy surface separated by spatial intervals define the "shapes." Intervals separated by null or timelike intervals define causal sets. The first of these is symmetric, while the next is antisymmetric. This is similar to Penrose's tensor space, which axiomatizes spaces. If you have a space in n dimensions one can represent the positive tensor dimension as ||| ...|•ε = 0, where | represents an element such as a vector or spinor and the set |||...| means an exterior product of these. The ε means a Levi-Civita symbol and this is a skew product. This can be seen equivalently as a skew symmetrization of the |||...| in a higher dimensional space. If this is zero, then the space of tensors is symmetric. This system however requires there to be the |||...|•g, where g is a symmetric tensor. Again this is equivalent to a symmetric trace in a higher dimensional space. The "dimension of these tensors" are n and -n respectively. They correspond to the symmetric and antisymmetric sets of tensors, which have a duality.

          This duality between symmetric and skew symmetric elements, or for two tensors products of the sort

          {ψ^a, ψ^b} = g^{ab}

          [φ^a, φ^b] = ω^{ab}

          involves supersymmetry. In the case of spacetime the generators of supersymmetry Q_a and \bar-Q_b construct Lorentz boosts

          {Q_a,\bar-Q_b} = iσ^μ_{ab}∂_μ.

          where the momentum boost operator p_μ = -i∂_μ constructs the Lorentz group. Meanwhile {Q_a,-Q_b} = 0. The anticommutator of the super generators seems to have a categorical relationship with the antisymmetry of causal nets. The rotation operator M^{μν} and the super-generator obey

          [Q_a, M^{μν}] = 1/2σ_{ab}^{μν}Q_b,

          and the commutator between the momentum p^μ and the generator Q_a is zero

          [Q_a, p^μ] = 0

          The relationship between the symmetry and antisymmetric approaches, say shape dynamics and causal set theory, might then have functors to Fermi-Dirac fields and boson fields, and a system which includes both might then have a graded Lie algebra with Grassmann generators that connect the two.

          Cheers LC

            Dear Roger,

            Thanks for the kind remarks. I took a look at your website, but unfortunately only the top of the page would load; I don't know if this is a site issue or a browser issue.

            In any case, even if some of the mathematical content was a bit unfamiliar, it seems that you understand quite well what I am trying to do conceptually. In particular, I'm trying to give a precise description of something very like what you mentioned in your point 5, with the clarification that I think each "element" generally has multiple "parents." In particular, by "causal relation," I mean almost exactly what you said.

            One difference we might have is that I think dimension (like "space" and "time" themselves) is just a "way of talking about what actually happens." For instance, in three-dimensional space you can "go in six different directions," forward, backward, up, down, left, right. If you turn this around and start with a bunch of events that are related to each other in this way (each having "six neighbors" in an obvious sense), then you would get a "three-dimensional network." This is all a very rough and imprecise way of describing things, but hopefully gives the right picture. I think that the dimensionality of the universe is telling us something about how interconnected the structure is at the fundamental scale: how many "direct neighbors" each "fundamental element" has, and how they are arranged. All this ignores the quantum-theoretic version, of course.

            Anyway, thanks again for the feedback! Take care,

            Ben

            Lawrence,

            Not to butt in here and while we have discussed this before, I usually avoid getting in the conceptual ring with you, but;

            You make the two observations that prior knowledge can blind our thinking and that physics treats time as an interval.

            That goes to my repeated observation that by treating time as a measure, physics only re-enforces the effect of sequence, rather than considering the cause of change, that is action. That it is not the present moving from one frame to the next, but action replacing configurations of the same material. Not the earth traveling a fourth dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates.

            Duration doesn't transcend the present, but is the state of the present between observations, so there is no physical extension, only action.

            If time were simply a dimension consisting of those intervals, wouldn't a faster clock rate move into the future more quickly, yet the opposite is true, as it ages/burns quicker, it moves into the past faster. Witness the twin in the faster frame has died, when her twin in the slower frame returns.

            I feel like a frog on the road when I make this point, but while it only seems to be ignored, no one bothers to refute it.