Dear Steve,

It took me a long time to realize you had posted here because it is so high up in my thread!

I agree that "disorder" is not a very good description of entropy. In some important cases entropy is actually a measure of symmetry.

By the way, another place in which the sphere arises is in quantum information theory; the space of states of a single qubit is a sphere called the Bloch sphere in this context. It can be identified with the Riemann sphere which is obtained by adding the point at infinity to the complex numbers.

My feeling about dimension is that it is still rather mysterious why dimension 3 is so important. There are a lot of mathematical arguments for this, but I haven't yet seen a convincing explanation. Take care,

Ben

Mr Dribus,

The entropy principle is a concept so difficult to encircle in its pure generality but so simple also. This entropy is like an infinite energy. The steps of fractalization are so numerous inside the pure physical 3D sphere. If this infinite light has created a physical 3D sphere in spherization of mass-gravitation. So we have disponible steps of energy correlated with our principle of equivalence. The mass, it is the energy. It is so a pure mesure of symmetries between the gravitation and the polarized light(due to evolution spherization)and its steps. I beleive that the spheres of light in their pure serie of unqueness so are quantas of pure energy correlated with the infinite singularity without motion ,time and dimension. That said, and it is paradoxal, the physicality is a finite system in increasing of mass, so the entropy, physical increases.See that this entropy inside the physicality is so under the physical laws. The infinite entropy so is a reality for both of systems. But the real interest is to utilize the disponible energies.A kind of taxonomy becomes an essential. The volumes of entangled spheres are so essential.The gravitation polarizes the light. The correlated synchonizations seem porportional with energies ,the spherical volumes of stability so are relevant considering the main central sphere as the most important volume of the serie of uniqueness. The cosmological number of spheres inside the universal sphere is the same than an ultim entanglement of spheres.The finite groups are essential. My 2 equations become very relevant considering a closed isotropical and homogeneous Universal Sphere.

You say "By the way, another place in which the sphere arises is in quantum information theory; the space of states of a single qubit is a sphere called the Bloch sphere in this context. It can be identified with the Riemann sphere which is obtained by adding the point at infinity to the complex numbers."

The spheres are everywhere ,I beleive that the simulations of quantum informations can be optimized. The Bloch sphere seems relevant considering the qubit informations. It can be optimized in a pure 3D convergence with the spherical volumes furthermore of the serie of uniqueness and its pure finite universal number. The complexs at infinity seems relevant also.They are tools. T

about the dimensions.I beleive that it is very very important to consider an universal axiom for our 3 vectors implying a pure 3D sphere.The metric is a pure 3D. The proportions need to have these 3 vectors. If not we cannot have the pure thermodynamical correlations, universal between all rotating 3D spheres. A closed evolutive system in 3D is essential for our proprotions.

Furthermore, the fact that we have the special relativity implying c and its limits for bosons, show us the road of the perception of 3D creations. c is essential for our contemplations if I can say. The general relativity tell us that the mass curves the space.It is so still an essential this 3D. More the mass increases, more the physical entropy increases, more the spherization of the universal sphere increases. The SR and GR are ok if and only if we have these finite groups inside a closed evolutive sphere. The dimension 3 is at all scale, it is the reason why we have our planck scale in meter and our universal sphere and its bounded limit also in meter.It is essential for all our universal proportions. The fractal of scales is always in 3D.

I wish you all the best in this contest.

Regards

Benjamin

I noiced your essay is top of the list, so I read it.

The first step is to understand how we detect existence, and hence what our reality is and how it must occur. We can only know our reality, as we cannot transcend our own existence.

"The first few assumptions I reject are... that systems evolve with respect to an independent time parameter"

Not so. The two fundamental knowns in respect of our reality (ie not some metaphysical conceptualisation) are that a) it exists independently of the sensory systems that detect it, b) it alters. This means our reality is existential sequence. Which entails:

1 It is comprised of elementary substances, these having physical existence which is not further divisible (there may be more than one type thereof).

2 These elementary substances have at least one innate property each which has a propensity to alter, of itself &/or under external influence, in its existent condition.

3 In any given sequence of physical existence, only one physically existent state (ie a reality) can occur at a time, and this has a definitive physical presence.

4 No phenomenon can have physical influence and not have physical presence.

5 There must be a particular relationship between a previously existent state(s) and a currently existent state for it(they) to be the cause, in terms of sequence occurrence and spatial position, as physical influence cannot 'jump' physical circumstance.

Now, what these simple rules mean 'in practice', is another matter. But one fundamental characteristic of our reality is that it is sequence (or system), timing being an extrinsic measuring system which calibrates the relative speed of changes. It is also easy, on the basis of the above, to discern, generically, what dimension can be, and indeed what any of the other concepts mentioned can be, if anything.

Paul

Dear Paul,

Thanks for reading my essay and for your remarks. I think I can agree with part of what you say; the rest I am not quite sure about. Let me be more precise.

1. You say "we can only know our own reality." True enough; every observation is mediated by our interpretation, and every argument is mediated by our reason. But all of science is based on the assumption that there exists an external reality with characteristics accessible to any competent observer; i.e., that competent interpretation and reason will converge on objective answers. I don't dispute this assumption; there is no use in doing science if one does.

2. I am not sure if your "not so" means you don't believe this is one of the first assumptions I reject (I assure you that it is!), or that you believe it should not be rejected. I will assume the latter.

3. Your first "fundamental known" is part of what I said above, that there exists an objective reality. I agree.

4. Your second "fundamental known" is less clear. What does it mean for "something" to "alter?" Well, you must have two different states, one you call "before," and one you call "after," but that is not enough. You must have some way of identifying the two states as representing the "same thing, only having altered." At the very least, this requires a relation pointing from the "first" state to the "second" state. The family of such relations is precisely a partial order as I described in my essay.

5. I am afraid that your points 1-5 seem to include many imprecise concepts and implicit time-related assumptions. For instance, what precisely is an "elementary substance?" Is it a set, or an element of a set, or a field on a manifold, or what? What precisely is an "innate property," and how is it connected to its corresponding "substance?" What precisely is a "propensity?" If a "property" "alters," how do you identify it as an altered form of the same property rather than an unrelated property? How do you define and model "influence?" When you say "only one state can occur at a time," you must already have an assumption about what "time" is for the statement to mean anything. Later you say that time "calibrates the relative speed of changes," but what does "speed" mean, and what are speeds "relative" to? What does "spatial position" mean? What does it mean to "jump?" And so on and so on...

You refer to these points as "simple rules," but I don't think they're simple. They sound simple in English, but if one tries to make them precise, one sees that they are quite complicated and include assumptions about the very things they are intended to define. This makes it hard to evaluate what you are actually claiming, and this is before one can even begin to think about whether or not the rules are likely to be valid or useful. Perhaps you could explain the meaning of these things a bit more clearly. Take care,

Ben

    Benjamin

    Thanks for you prompt response, and the constructive nature thereof.

    Re 1: But this is not what I am saying. We can only investigate a specific form of existence. In short!:

    Any form of existence invokes the possibility of an alternative, (ie if A, there is always the logical possibility of not-A). But, any form of existence other than our reality is inherently unknowable, since we cannot transcend our existence. Therefore, we can only analyse our reality. That being existence in the form of what we can detect (either directly or indirectly), which is dependent on the sensory processes.

    Therefore, our reality comprises those physically existent phenomena which are potentially sensorially detectable by any organism, and the existent phenomena which are proven to have caused them. The caveat of potentiality referring to physical, not metaphysical, issues with the mechanics of the sensory processes, because there are known problems with them. That is, instances where sensory detection either cannot be effected, or not completely accurately and/or comprehensively.

    In which case, dependence on the sensory processes does not necessitate objective knowledge being limited to validated direct experience. Where there are known functionality issues, what occurred must be hypothesised, but still be based on, and assessment of consequent outcomes referenced to, validated direct experience. That is, objective knowledge of our reality must always be subservient to direct experience, ie either proven to be directly experienceable, or proven to be potentially so.

    Essentially, the problem arises when there is a presumption that we can know existence, which we cannot. The confusion being between what, while not directly validatable, is properly inferable from other direct experience, and what is based on no substantiated experienceability.

    Re 2: the "not so" referred to the fact that our reality must occur as existential sequence, and that means there is only one physically existent state at a time. That is, for the successor to exist, the predecessor must cease. So the assumption you rejected: 'that systems evolve with respect to an independent time parameter', is true. Or at least is so given the immediate grammatical meaning of the phrase. Frankly, I was not so sure about the others, and hence your view on them, and would need more understanding as to what they are meant to mean.

    Re 3: But, as said at 1, this is not what I am saying. In short (again):

    Being reliant on these sensory processes limits, it has to be assumed, the form of existence we can know, but not what occurs within that. Because the sensory systems receive, not create, physically existent phenomena in their detectable form (albeit these result from interactions between other existent phenomena, which is what is usually meant by reality), and create information. So the sensory processes can have no influence on our reality, only on information about it.

    Re 4: See 2 above concerning sequence, and then:

    Change concerns how realities differ, and is therefore not an attribute of any given reality. It is not existent, and neither is the difference. Only physically existent states are existent, it being comparison of these states which reveals difference. Logically, change involves: 1) substance (ie what changed), 2) order (ie the sequence of differences), 3) frequency (ie the rate at which change occurred). The latter being established by comparing numbers of changes occurring over the same duration. This could involve realities in any sequence (including different aspects of the same sequence), and have either occurred concurrently, or otherwise. This is timing.

    Re 5: There are no time related assumptions, what is being said is a function of what must be the fundamental nature of our reality (remember, we are trapped in an existential loop). So, to answer one specific question as an example, I do not know what could actually constitute an elementary substance. It is just that, given how our reality is constituted, there must be one, or indeed probably several types. Etc, etc.

    On time and timing. The phrase "at a time" refers to occurrence, not time/timing. In respect of the latter: timing compares the number of changes, irrespective of type, in different sequences. This can be done directly, or with respect to a common denominator. So if you are using a quartz watch, it is crystal oscillations. In other words, what is being established is the rate (speed) of a rate (change). And it is all about change, which concerns difference between, not a feature of. There can be no change in whatever constitutes a physically existent state, because otherwise it would involve more than one such state, and physical existence can only occur in one state at a time.

    Finally (well I could expand on dimension and space, but have said enough for now!), in respect of: "but I don't think they're simple". You are quite right, but not in the sense you mean. At the generic level, these are precise, when applied, not only is it difficult to discern what, within our reality, they could be, but their simplicity belies their significant consequences. In simple terms, physics has failed to understand the fundamental nature of what it is investigating.

    Paul

    Dear Paul,

    Thanks for the clarification. I believe I understand much better now where you are coming from. Also, your view does not seem to be quite as much at variance with mine as I had thought from your original comments. In particular, I think we completely agree that time is a way of talking about sequence (i.e. order). However, each event (or observer) has its own local sequence, so the order is a partial order, not a single linear order.

    You seem to be suggesting that it is the reality we perceive, not your principles, which is complicated, and this seems to be a valid contention. What I should have said is that it's complicated to translate your principles into meaningful statements about physics, but the same could be said of mine.

    You write, "physics has failed to understand the fundamental nature of what it is investigating," and you're quite likely correct. My causal metric hypothesis is a guess about that fundamental nature. Likely it's too simple, but I hope it can explain some current conundrums when properly developed.

    I chose not to write about observational and measurement-related issues not because I regard them as unimportant, but because there was simply not enough space. Also, these issues verge on the interface between consciousness and the physical world, which is something I regard as far beyond our abilities at present. I certainly don't feel confident writing about it! A few other brave contestants (Janko Kokosar, David and Julie Rousseau, Sara Walker, etc.) touched on some of these issues. Take care,

    Ben

      Ben

      I am not sure we do agree on the nature of time. Because you say, "However, each event (or observer) has its own local sequence, so the order is a partial order, not a single linear order". And you reject the principle "that systems evolve with respect to an independent time parameter".

      But, the entirety of our reality is an existential sequence, one can, to maintain sanity! conceptualise constituent sequences. However, there is no time in a reality, because this concept is about the calibration of change anyway and is therefore non-existent, but more importantly, there is no change in a reality, otherwise it cannot exist, and then alter. Changes are occurring at different speeds, but that is irrelevant. Timing is an extrinsic measurement system, time being the unit of measurement. For this to function properly there can only be one time/one system, which is applicable to the entirety of reality. Put simply, there is only ever in existence what is commonly known as a present, ie our reality is only in one physically existent state (a reality) at a time. Timing just provides a reference to establish what that was, and a means of relating various disparate rates of change.

      Furthermore, I noticed the sentence: "The fundamental structure of spacetime is the central focus of both the rejected assumptions and the new principles". Now, as a representational device of our reality this model is invalid. As stated above, time is in no sense (ie even when properly expressed in terms of change) a factor within any given reality. This means that a reality has purely spatial properties. But, dimension has been misconceived. Three spatial dimensions is the absolute minimum number conceivable whilst maintaining ontological correctness at that level of conception, but not what is physically existent. In effect, dimension involves the concept of reality being divided into a spatial grid, the smallest unit of which equates with the smallest substance. The dimension, ie spatial footprint-size/shape, of any given entity being the relative spatial positions 'occupied' at any time (ie in its physically existent state). The number of possible dimensions in reality is half the number of possible directions that the smallest substance could travel from any given spatial point, because dimension relates to direction, either way.

      I could ask rather superficial questions about the causal metric hypothesis, ie why are there two versions when there is only one reality, why a binary relationship in causality, but the more important issue is what is the model of reality which underpins this. Because that comes first, and then everything else follows, ie those 6 principles, once understood in grammatical terms, can then be translated into what they can mean in reality, given how that is fundamentally constituted.

      Finally, one does not need to know about consciousness, etc, as such. These are just unfortunate(!) interference factors. The physics of our reality is unchanged. We, and all sentient organisms, receive a physical input. This exists whether we receive it or not. We create (ie the output) knowledge of reality, not reality. The trick is to discern (ie eradicate the interferences) what was received, and hence what caused that, given knowledge as to how the phenomena involved behave physically.

      Paul

      Hello Again Ben and friends,

      On the subject of Lorentz invariance; a couple of brief conversations with Gerard 't Hooft about the Fermi results at FFP10 in 2009 gave me a lot of food for thought. Initially I simply asked how his newest CA-based QG theory fared, in light of the recent results, and his response was "it's too early to tell" and that considerable work still needed to be done (to make experimental predictions). But then I had another chance to speak with him later, and revisited the topic - naively stating that the microscopic time reversibility of any cell in his formulation avoids the local time arrow problem cited above (for CDT) - and he reiterated that Lorentz invariance is not that simple.

      However, at FFP11 the following year; he had added 4 or 5 slides to discuss how desirable Lorentz invariance is to achieve, and how hard it is to accomplish with a CA-based theory. But many of his comments also apply in the case of CDT and likely Causal Sets. I still have not completely digested the Sorkin papers I downloaded, but one in particular directly addresses this issue, and says that instead of CauSets being Lorentz invariant, that type of graininess in spacetime induces a fuzziness to measurement instead. I think I like your approach better still, but I need to keep reading and digesting to be sure I understand. But there is one important matter you mentioned on George's thread.

      The significance of action and reversibility thereof, was noted. Some of what was said there reminded me very much of ideas expressed by Phil Gibbs in his book Event-Symmetric Space-Time, which is worth checking out. Event symmetry may be important to developing Lorentz invariant formulations. I should also mention once more that I think that octonions hold a special place owing to their connection with projective space - and thus with the basis of object-observer relations in general. It seems that generalizing the ability to put things in perspective affords or possesses a natural embedding space that is octonion. Maybe that's part of the special magic of S7.

      But again it is late, so I'll save further comments for another post. Sorry I have been too busy to post sooner. There is much to do.

      Have Fun!

      Jonathan

      Dear Paul,

      Let me ask a few questions, since we seem to be at terminological cross-purposes...

      1. Would you say, roughly speaking, that "time is a way of talking about change?"

      2. How are the two statements "our reality is an existential sequence" and "there is no time in a reality" not contradictory? If time is unreal, why talk about it? In particular, why insist on its existence as an external parameter?

      3. You say "Timing is an extrinsic measurement system, time being the unit of measurement. For this to function properly there can only be one time/one system, which is applicable to the entirety of reality." Why? Why make this assumption? What does "function properly" mean? In particular, how does this not contradict the relativity of simultaneity and everything we know about physics at large scales?

      4. Regarding the reason for "two versions" of the causal metric hypothesis, the answer would be the superposition principle; i.e., because a single quantum-theoretic reality is built out of configurations we call classical alternatives. But what I can't understand is why you need both "sequence" and "time" in a purely classical picture. The sequence is what actually happens; your notion of "time" seems merely an artificial redundancy. Why not throw it out?

      You have me more than a little confused! Take care,

      Ben

      Ben

      Congratulations. Well earned. You said of mine; "Your ideas sound interesting" and "I'll be sure to have a careful look at your essay when I get back from my trip." (Sept 11th) . But seem not to have yet managed to do so. I do hope you can.

      One thing I suggest is a limit to the domain of vector space for evolving kinetic systems, arising from the invalidity of motion as a concept in geometry. A simple and self apparent solution emerges, though from the viewpoint of current assumptions it seems not at first apparently simple at all!

      You have to 'self built' an ontological construction from a kit of new elements, just like a dynamic Chinese puzzle, but with instructions and precisely following the structures of logic (from the basic 'nested' hierarchical structure of compound propositions in TPL upwards).

      I think it represents the 'simple idea' Wheeler anticipated. But it needs help. I greatly look forward to your comments.

      Very best wishes for the final judging.

      Peter

        Dear Peter,

        You're absolutely right... I did neglect to post my remarks on your thread. Things got a bit chaotic there for a while, and my own thread became rather busy, though not quite a busy as yours! In any case, I see you are near the top for the second year in a row, so I congratulate you.

        I read your essay a couple of times before, but I should read it again before attempting to address you seriously. I do recall having a couple of questions about the scenarios involving multiple media in your scene 2, and the exact implications of the optical axis rotation on page 7. Also, I'm not quite sure in what context you refer to the "invalidity of motion in geometry," both in your essay and in your remark here. For instance, timelike curves in Minkowski space certainly "represent" motion in an obvious sense. I happen to agree that motion is derivative, but then of course I view geometry itself as derivative!

        Anyway, thanks for the gentle reminder... I will certainly take another look at your work. Take care,

        Ben

        Ben

        Re 1: Yes, but that answer would need an awful lot of caveats.

        Re 2: Because the common assumption is that time is a characteristic of reality (specifically, a dimension), so one can end up using the same incorrect phraseology in refuting that!

        The underlying point here being that, in terms of existence, there are only physically existent states (or realities) of whatever constitutes our reality. When compared, difference is revealed, which indicates alteration/change. Difference is not physically existent, neither is alteration/change. But these concepts reflect physicality, they are not an illusion. What they refer to are the characteristics of the difference between realities, not features of any given reality. So timing can only be an extrinsic measuring system, as its purpose is to calibrate the relative rates at which changes occur (by comparing numbers thereof within different sequences against a duration reference, ie time).

        Re 3: It is not an assumption. By definition, ie given how our reality must occur, the identification of any given physically existent state (ie a reality) involves establishing what existed at any given time. There is no change in a physically existent state, otherwise it cannot exist, and then alter, because the incidence of change means there is more than one state involved. The choice of what time is irrelevant in that it does not determine the state, just what happened to exist then. But, as with any such form of comparison, having selected a reference this must be maintained in order to ensure comparability of different measurements. In other words, that same point in time would have to be used to discern what other physically existent states occurred at that time in other sequences. They do not have their 'own time'. Only different times if they existed at different stages in the sequence.

        [Just for the record! This misconception lies in Poincare's flawed concept of simultaneity, and became the surrogate variable for dimension alteration (usually referred to as length contraction), which Lorentz, et al, were uneasy with, ie time variance seemed more rational. So the tail got pinned on the wrong donkey, so to speak. In repeating simultaneity in 1905 (the A-B example, 1st section), Einstein went a step further, thereby compounding a felony, by using light speed to assess distance, but this was effected in terms of A to B, and then (ie subsequently) back (B to A), thereby, again, reifying time as a feature (a variance) within a reality. Apart from inadvertently attributing light speed with some relationships which are non-existent. In the meantime(!) Minkowski reified time with his spacetime model, following through the flawed concept of simultaneity.

        t = x/v is an expression of what timing is. The number always equals the sum on the other side, and the property is the same on both the top and bottom of that side. So it is an expression that timing is rate of change (1/t, per time). Which it is. Having understood this, one then has to be very careful how alternative variables are introduced into this 'equation'.]

        Re 4 To which I would say, does the concept of superposition have any existential substance? Sequence is different from time, and neither is this to do with a 'classical picture'. The differentiation of classic/quantum is a false dichotomy, there is only one form of our reality, with distinct generic features. Sequence is how change occurs, ie one at a time. It is like a film. Time is about the speed of change. At the existential level, it might be that all change is a function of the same feature, or different features which function at the same speed. So however change eventually manifests, it is, at that level, occurring at the same speed, which then makes the concept redundant, at that level. But this needs to be proven first. And anyway, deconstructing physical existence to this level is probably impossible to achieve, and certainly does not help in understanding most situations. Try describing one physically existent state of the 'object' known as The White House. Trillions of dollars worth of equipment and a million years later, we would probably still be at it!

        Paul

        Ben

        In scrolling down I noticed the post above on symmetry. After our first exchange I did have a think about those 6 key principles you refer to, and came to the immediate conclusion that symmetry (amongst others) was a meaningless concept, given the fundamental nature of our reality, but did not want to 'overload' the exchange. However, since you indicate above that this is important, I looked at your post (19/9 17.29) to David Alves. In it you say:

        "Shape dynamics deals principally with symmetric relations, since the separation between two points has nothing to do with their order; X is a distance D from Y if and only if Y is a distance D from X"

        Indeed, but this is just a truism determined by how existence occurs. There is no symmetry, or relations, involved. [Incidentally, this happens to relates back to my point about the AB example, which I threw into my last post]. Distance is a function of the relative spatial footprint, and the relative spatial position, of the physically existent states involved. It is an artefact and has no physical presence. One has to presume, until proven otherwise, that as at each subsequent point of time, a change will occur to one or more of the physically existent states involved which will impact on distance. But, in reality, the distance has not altered, the physically existent states have. In other words, it is no longer X &/or Y, it is a distance being different states. So, yes, by definition, X to Y must be the same as Y to X, but it is not a case of "only if", because what must be under consideration here is an existent state which involves no change. The distance is just the distance is just the distance, as are the physically existent states which determine it.

        Then you say:

        "Spacelike separation in relativity is similar. However, two events may also be causally related, and in this case the relation between them is generally asymmetric because the order matters; X is in the causal past of Y if and only if Y is in the causal future of X. In all but extreme cases, causal relations correspond to timelike separation"

        Indeed, but again this is just a truism determined by how existence occurs. There is no asymmetry, just a sequential order of different states. Neither is there asymmetry in the sense that the other circumstance had symmetry, because there was none. In the first circumstance there was no sequential order, only one state within such an order. Now the circumstance involves more than one state of the order.

        And, by definition, for any given physically existent state to have had a physical influence on any subsequent one, there must have been a specific relationship between the two in terms of both sequential order and relative spatial position. So, in terms of sequential order, a potential causal state must have been one of the immediate predecessors, because physical influence cannot 'jump' sequential order. Then in terms of relative spatial position, for any given state to be a potential causal factor, it must have been adjacent to, or in, the spatial position of the successor, because, again, physical influence cannot 'jump' spatial position. Given these criteria for potentiality of being a causal factor, in any given circumstance the causal factor could have stemmed from a) a previously existent physically existent state altering of itself, b) any combination of influence from all the other previously existent states, c) any combination of a & b.

        Paul

        Dear Paul,

        I think most of our mutual difficulties come from different conceptions and uses of the terms "existence" and "reality." In particular, this leads you to insist on one hand that a particular entity "does not exist," or "is not real," and at the same time insist that such an entity has particular properties and must be understood in a particular way.

        For instance, you say, "Difference is not physically existent, neither is alteration/change. But these concepts reflect physicality, they are not an illusion." Similarly, you insist that time is "not real," yet insist that it is an "extrinsic measuring system!"

        What I am trying to do is propose a model that may be useful in describing the physical world. Trying to argue about whether or not certain aspects of this model are a priori "physically real" on philosophical grounds is a waste of time. Ultimately, nature is the judge of whether or not a theory is useful. For instance, it's useless to argue against the superposition principle on the philosophical basis of whether or not it has any "existential substance." The fact is, it seems to describe how the world works. Similarly, the classical/quantum "dichotomy" is not really a dichotomy, but just reflection of archaic language. Again, "E pluribus unum" seems to describe how the world works.

        Symmetry and asymmetry are not meaningless; they have very well defined meanings. The extent to which they are physically important is another matter. I argue that symmetry is slightly less physically fundamental than most physicists believe. To argue that it is physically meaningless, however, seems again to ignore the evidence of nature on philosophical grounds. Take care,

        Ben

        Dear all,

        Some time ago, Jonathan Dickau raised the question of what the correct formulation of path summation is in various contexts. He attached a well-written paper by Steven Kauffman advocating a Hamiltonian phase space path integral approach and deprecating the Lagrangian approach. I would like to make a few remarks about this.

        1. In causal theory, the natural version of path summation involves paths defined by order morphisms from linearly ordered sets into the causal order. Assuming local finiteness and acyclicity, these may be identified with sequences of relations. In terms of acyclic directed graphs, such paths are just sequences of directed edges.

        2. The natural object to sum over in this context is a "relation function;" i.e., a map from the set of relations to a ring, which conventionally is the complex numbers, but may be some other algebraic object. Finite fields, quaternions, octonions, etc. are interesting in this regard.

        3. There is a technical information-theoretic reason why an "element function" won't work: "antichains of elements are permeable."

        4. This relation function doesn't correspond directly to a Lagrangian, but to a phase, which in Feynman's Lagrangian approach is the exponential of the classical action. The action comes from integrating the Lagrangian with respect to time, but in the locally finite case, the integral is a sum, and a single relation represents the smallest subdivision of a path. In this sense, the relation function is an "infinitesimal path functional," which is what a Lagrangian is in abstract mechanics. This is the sense in which the approach is "Lagrangian;" it need not have anything to do with conventional Lagrangians or actions.

        5. Path summation over a single classical universe violates background independence, so the path sums I have in mind are over causal configuration space.

        6. Conventional phase space involves "position" and "momentum" coordinates, and the Hamiltonian is an "energy function" on 2n-dimensional phase space. However, "momentum" is emergent in causal theory. As of now, I don't know how one would could carry out background independent "phase space" path integration in the context of causal theory, or if this even makes sense.

        So further thoughts on this would be appreciated! Take care,

        Ben

          Ben,

          Very wise to read again, and slowly. There are a whole related set of quite new assumptions to assimilate. The scene 2 (Act 1) media do have more different scenario's than we've assumed. I really needed a dozen more pages! Perhaps read my recent posts to Eckard & Pentcho.

          But the concept is simple and physical. Six buses and six clouds of electrons flying round in space all represent different and mutually exclusive 'inertial frames', and domains for Maxwell's (near field) equations. Each then has spatial limits, with a boundary state and mechanism that absorbs and re-scatters to the local c precisely like a fluid dynamic coupling (as an auto gearbox torque converter). It is variously, magnetohydrodynamic shocks, surface charge/fine structure, the far field transition zone, the heliosheath, galactic halo, etc. It contains Boscivitch's 'sphere of influence' Einstien's 'spatially extended mass' and represents Galileo's states of motion, so, yes, derives discrete space time geometries, and at ALL scales, from a particle to a universe.

          The structure is precisely that of Truth Functional Logic. Substitute 'frame' for 'proposition' and quantum relativity emerges. It's also continuous spontaneous localisation generalised to matter and systems in common states of motion at all scales.

          The whole 'concept' of motion is of course invalid in geometry. Descartes tried a solution, but space and matter are 3D. It is the 'whole geometry' that moves, as a frame, not some unreal 'wire frame' where the wires have to cross. 'Getting wires crossed' may assume a new meaning!

          Optical axis rotation was the last big piece that fell into place to complete the puzzle. If a plane wave in a medium hits ('charges') a beach ball or gyroscope (ion) at rest in the medium, which absorbs and re-emits it, the re-emission may be expected to be symmetrical (an ion/plasma is 'self focussing') and at c wrt the ion.

          But if the ion is in motion through the medium fings appen! (effects from causes). Motion on the x (source) axis causes change to lambda L and, inversely, frequency f, (new but entirely obvious) which conserves c (c = fL).

          Lateral motion v means the charge cannot be symmetrical. Ergo the re-emission is likely to be rotated, and in proportion to v. All of a sudden we find this maps atomic scattering direct to some of the most poorly understood physics we have; Stellar Aberration, Kinetic Reverse Refraction (the same thing). lensing, a whole host of related phenomena in optics and astronomy, and, yes, when we include harmonic resonance subject to f, and Huygens construction, apparently quantized refraction and 'curved space time.' Scary indeed. But it all needs clearer translation from English and logic into into physics and maths. It just needs someone who speaks both and also understands it.

          That's almost another essay! but just scraping the surface. Do just ask every question you think of. I'll then link you to more if you can take it.

          Thanks

          Peter

          Ben

          I am not aware of any contradiction, although at times it is difficult to find an exact expression, because our very language incorporates a particular view as to how our reality functions. The differentiation is between something that is (or was) physically existent, and an artefact which reflects that, but cannot, of itself, be existent. Though your repeated reference to time is different from that, it being just a human devised measuring system, and therefore, obviously, has no physical existence.

          And whilst that might appear to be somewhat pedantic or philosophical, it is not because it highlights the crux of the problem. And this is contrary to your assertion: "Trying to argue about whether or not certain aspects of this model are a priori "physically real" on philosophical grounds is a waste of time. Ultimately, nature is the judge of whether or not a theory is useful".

          The argument is not philosophical, but physical. Because, before any analysis can get underway as to what (ie content) is happening, we must first establish how existence is detected, and then how that (ie our reality) must occur generically (ie form). Form comes before content. And our reality has a definitive, independent, physical manifestation of its own, and there are physical processes which enable its detection. All of which is discernable, and thereby invokes a set of pre-conditions which must not be contravened in the analysis, construction of representational devices, etc. For example, given the fundamental characteristics of our reality ("nature"), the question then becomes, does the concept of superposition have validity? And the answer is: no, because it contravenes how our reality must function.

          In respect of symmetry, again in the context of the form of our reality, I was pointing out that the first circumstance had no symmetry in it, there was nothing to be symmetrical with. And the second circumstance was not asymmetrical, it was just existential sequential order. Any concept of 'a direction of progress' (ie there is more than one possibility) is a fallacy. Which leaves me wondering, again, whether the concept of symmetry has any meaning. The more interesting point was about distance. This is another artefact. And there can only be distance between existent states which occurred at the same time. There cannot be a distance between an existent state and one that has ceased to exist, or indeed has not yet existed. All of which points to the necessity to understand the sequential order of the sequences and their relative status, otherwise we will have a jumble of hypothesised physical influences which actually could not have occurred. And since we depict a reality at a higher level than that at which it exists, and we have deemed that change (aka time) can be a characteristic of it, then it is highly likely we have that jumble.

          Paul

          ahahah learn french and read my poems ahahah uncle spherical gives you a lesson.and you know it.Don't try with the faith and the spherization. You are not really relevant in fact.a simple sockpuppet player is your name,in fact you are only good for the computing, the rest oh my god but what is your foundamentals. ahahah in fact you are only good for these kind of play.not for the gnerality.You repeat always the same in fact. ahahah frustrating no? me I have faith, you no.It is there your error sockpuppet inventing false names. Even your maths are always the same. In fact several people fear for their funds. They fear that their institute looses a little of their credibility.So they utilize the competition like excuse, but in fact they are just pseudos. They prefer the publicity instead of generalities. They are simply people lost in the meanders of the society. You confound a little the things in fact.You do not evolve, you just make a pub because you fear for your jobs perhaps I don't know.Or it is just the taste of monney who interests you.In all case, it is not a good parameter that you utilize. You have just simply profitted about a discovery, revolutionary and you try simply to prove to yourself that your hormons are ok. Have you probelms in the bed with women or What ? if you want I can give courses. I am understanding your hate.You can evolve, buy a bibble I don't know me. I can also give courses of maths, piano, physics, theaters,poesy,guitar,taxonomy of evolution,indeed I class all.You know animals and vegetals I suppose. And you try with what ? the spherization, ahahah let me laugh.I have quantized the mass me, you no. I am arrogant I agree but it is the reality. The story begions dude, you know the evolution and its optimization spherization, we are young, we are aged of 14 billions years dude, I have time to explain you the spherization.I am going to explain you what are the maths of spheres of light and its uniqueness giving the singularities. You think really that my soul of spheres of light is going to accept your play.You can even kill me you know.We are eternal my friend, you shall be head in the soil in front of the infinite light poor thinker. Uncle what? make surf dude, and pray for your soul. All is said in fact. Jesus Christ and Siddartha Gottama Buddah are with me.Ahahah I have the syndrom of the elected. and what ? what is the probelm, put me also on a cross also if you want, I will laugh in front of your face, I will resist with universal love and faith.you can even burn me if you want,I will resist poor dude.

          You are already in the bad boat.

          Spherically yours band of comics.