On the Foundational Assumptions of Modern Physics by Benjamin F. Dribus

Loop variable quantum gravity, causal sets or nets, causal triangulation theories and related ideas are themselves I think constraint systems. For instance, loop variable theory is a spinor, or spinor field, form of the 3 space plus 1 time form of relativity which has the Hamiltonian constraint NH = 0 and the momentum constraint N^iH_i = 0. The Wheeler DeWitt equation HΨ[g] = 0 is a canonical quantization form of the Hamiltonian constraint, and loop variable theory is a spinor form of this type of theory. The vanishing of the Hamiltonian NH = 0 or the canonical quantization HΨ[g] = 0 is due to the fact the manifold is global and there is no boundary from which one can compute with Gauss' law the mass-energy of the entire spacetime, or universe. It further have to be pointed out that loop quantum gravity (LQG) has yet to compute a one loop diagram properly. The reason is that if you have HΨ[g] = 0 it means you have ∂Ψ[g]/∂t = 0, and there is no dynamics! Computing a scattering amplitude, particles in --- > process --- > particles out, on a T-channel is not possible.

What do these constrain? Frankly I think they constrain string theory. Ed Witten has found that within string/M-theory there is a form of twistor theory. This is the so called twistor "mini-revolution" that started a few years ago. Twistors are in some ways related to loop variables, but they have more spacetime content. I think this segues into thinking about these non-string approaches to quantum gravity as constraint systems. String theory uses a "time" τ that is a string time parameter along the string world sheet with the parameter σ along spatial extent of the string. This permits one to construct Hamiltonians of the form

H = (T/2)[(∂X/∂τ)^2 (∂X/∂σ)^2], T = string tension,

for X the string variable. This contrasts of course with the LQG which has no explicit concept of time, because there is no way to define mass-energy in a global context. A Hamiltonian is the generator of time translations, which means the energy defined by the Hamiltonian is conserve (Noether's theorem). In string theory this corresponds to level matching of string modes, but in LQG E = 0 and there is no time translation. However, the spacetime is a target map from the string, which should correspond to HΨ[g] = 0 for a wave functional over the spacetime metric. LQG is then some type of constraint system.

There are also some interesting possibilities for duality principles. Barbour and Alves have proposed a form of shape dynamics, which is a symmetrical theory. The spatial relationships between elements that define a shape in space are symmetrical. Causal sets involve asymmetrical relationships between nodes that are connected by lines or into graphs. These represent temporal ordering. The two approaches seem to represent something similar to Penrose's tensor space of symmetric and anti-symmetric tensors in a type of duality. The duality in some work by Sparling and others is supersymmetry. I then conjecture that the correspondence between shape dynamics and causal nets (sets) is then a form of this duality or is a categorical equivalence to SUSY. This may then be another form of constraint, in particular the SUSY structure which exists in the AdS_n ~ CFT_{n-1} correspondence.

Cheers LC

The scalars for example cannot be utilized without a kind of universal 3D axiomatization. Let's take the equations of Friedmann Lemaître and the correlated metric. The 3D sphere and its intrinsic quantum spheres and cosmological spheres are all in 3D. We cannot insert extradimensions. The 3D is essential.The Universal sphere is in evolution spherization in a pure 3D. The scalars at my humble opinion are not vectors. the spherical coordonnates inside a closed system is essential. That's why the number of the universal uniqueness(see the fractal of spheres of light from the main spherical volume).It permits to quantize the mass polarizing the light in a pure 3D general point of vue.The quantum scale is in meter, the cosmological scale also.That's why a closed evolutive sphere is essential for the universal sphere. We arrive at an optimization of the model, isotropic and homogene. Like for Einstein. The spherization can bee seen with the help of equations of friedmann Lemaître. The space is curved by this mass and more this mass increases due to evolution, more the spherization acts, the spherization is general due to the increasing of mass due to the polarization mass/light.If we have not the number of uniqueness, it becomes more difficult for the quantization and the understanding of the spherization. The fact that this light is infinite in this Aether without motion, dimension,and times, shows us that this physicality is light in motion,so spheres in rotation. G c and h can be seen in a pure 3D spherization. the series of uniqueness of quantum spheres imply an interesting road for the quantization of evolution correlated with informations. The curves of spacetime are in fact coded by the singularities. The expansion is just a step, a maximum volume is an evidence. a contraction appears so when the density is ok for this contraction, the spherization in 3d is an evidence. The energy is correlated .The bosons and fermions can be seen like turning in opposite sense. The variables and parameters are relevant....sorry I must go,until soon

Regards

I will write more on the Penrose tensor space, or what I think is also called a modular space. Shape dynamics is really a form of Regge calculus. One could think about this according to light rays. In this way there is no matter of time involved with the "motion" of a shape, for null rays have no proper time. I illustrate this with two diagrams I attach to this post. The first is a flat spacetime description. This is also pictured in 2-space plus 1-time spacetime in 3 dimensions. Two points on a spatial surface emit light pulses. These converge on three points on a subsequent spatial surface. These then define a triangle on that spatial surface. The two points then emit subsequent light pulses and map the triangle onto a third spatial surface. In Minkowsk spacetime this continues indefinitely.

In the curved spacetime situation null rays are curved. Since the metric

ds^2 = g_{00}c^2dt^2 - g_{ij}dx^idx^j

is such that for ds = 0 we can have

U^iU^j = (g_{00}/g_{ij})c^2dt^2,

and the optical path change due to curvature has a c^2 term. Hence we can assume the triangles on the spatial surface are flat. The deformation of null rays will then map the first triangle on the second diagram I attach into the second. The picture here is then completely described by null rays which have no proper time.

The time evaluated from the Jacobi variational principle

δt = sqrt{m_iδx_iδx_i/(E-V)}

is related to a proper time, or an interval. In the case of a null interval the spatial δx_i may be evaluated according to g_{00} and g_{ij} as above. The time computed by the Jacobi variation is then an "emergent" or computed quantity. This is a parameter which emerges from the "motion" of the triangle, or the map from the first to the second. This is related to Desargue's theorem, where null geodesics are projective rays and these are used to "lift" a shape from one spatial surface to another.

The causal net or set approach is stranger to me. However, the ordering principle behind it seems to demand an antisymmetry due to one ordering A > B not equivalent to B > A. I ponder whether the two approaches have a relationship between each other. These two should have some matter of equivalency if they both predict the same spacetime physics. If this is so this seems to categorical relationship to this and supersymmetry. Penrose's modular space of tensors is one way one can look at supersymmetry. The problem is that as yet I do not see a tensor structure to causal net theory.

Cheers LC

I forgot to attach my diagrams in the post above

LCAttachment #1: 1_light_rays_and_triangles.JPGAttachment #2: 1_null_rays_and_triangles_in_curved_spacetime.JPG

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

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

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

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