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

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

Hi Ben,

Looks like I spoke just a bit too soon: The FQXI grant program was announced, as I'm sure you've heard. Surprise! :)

- Shawn

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.

sockpuppets-play....conclusion, anybody of the familiy has right.

Results....easy to see the truth.

You do not understand what is the universal love. So why you insist ?

Ben

At the risk of causing a riot, a problem with that Smolin/Magueijo paper is that it presumes SR includes gravitation in the first place. Which it does not. So in that sense, there is no issue to resolve. Einstein defined SR several times, and it is not 1905.

In 1905, the two postulates are "apparently irreconcilable". Which is a bizarre statement when juxtaposed against the assertion that "These two postulates suffice for the attainment...theory...electrodynamics of moving bodies". The irreconcilabilty is because light is presumed to be in vacuo, whilst everything else is not, because they are subject to dimension and momentum variance. And the cause of that is subsequently revealed to be gravitational forces. In other words, light and matter cannot be co-existent and so 1905 is not a singular, cohesive, theory. So in expounding GR, where everything (ie including light) is subject to gravitation, Einstein refers to a special/entirely theoretical circumstance where there was no gravitation, ie SR. This is why SR only involves uniform rectilinear and non-rotary motion, light that travels in straight lines at a constant speed, and rigid bodies.

Einstein: Relativity 1916 section 18: "...the special principle of relativity, i.e. the principle of the physical relativity of all uniform motion..."

Einstein: Foundation of GR 1916 section 3: "...the case of special relativity appearing as a limiting case when there is no gravitation"

Einstein: Relativity 1916 section 28: "The special theory of relativity has reference to Galileian domains, ie to those in which no gravitational field exists...In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity"

Einstein: Relativity 1916, section 22: "Let us further investigate the path of light-rays in a statical gravitational field... Let us find out the curvature which a light-ray suffers. [equation (74) refers] ...a curvature of rays of light can only take place when the velocity of propagation of light varies with position...

Paul

The relationship between position configuration variables and momentum can first be seen by looking at the diagram I attach. This illustrates a scattering process with 5 input momenta and 5 output momenta. The "blob" is the region with virtual or off shell processes, which can be realized by on shell processes by BCFW recursion. I will ignore that matter for the moment. The momenta labeled with number 1, 2, 3, ..., 10 must all add to zero if we reverse the sign of the outgoing momenta. This is a trick used in working out the S, T, U channels. These momenta can then form a polygon. It is tempting of course to think of the configuration variables as defining the momenta by p1 = x1 - x2, p2 = x2 - x3, and so forth. However, this polygon has a dual polygon, which may be constructed by drawing a line through the mid points of the momentum edgelinks and then finding where these lines intersect. This will be the dual polygon. This dual polygon is then the vectors which represent the position variables of these particles. This is the more sophisticated way of such a representation for it does not rely upon an explicit reference to either set of variables to derive the other, but rather depends upon a duality principle.

In three dimensional space the diagram is more complex and the polygon is replaced with a polytope in three dimensions. Further, since the diagram on the left is really a spacetime diagram, with time running to the right, the polygon is really replaced with a polytope in four dimensions. The fundamental polytopes in four dimensions are the 24-cell, which is self-dual and the 120-cell that is dual to the 600-cell. In order to construct a one to one self duality between momentum and position configuration variables the 24-cell is the obvious model. For systems with more particles than can be represented by a single 24-cell tessellations of 24-cells may then be considered.

The 24-cell is a representation in Hurwitz quaternions of the F_4 exceptional group. The F_4 group shares a relationship with the B_4 = SO(9)

F_4/B_4:1 --- > spin(9) --- > F_{52/16} --- OP^2 --- > 1

And of course spin groups have a double cover to orthogonal groups

1 -- > Z_2 --- > Spin(n) --- > SO(n) --- > 1

The group SO(9) plays an important role with string theory or holography. Physics on an infinite momentum frame, physics observed boosted enormously, reduces the relevant physics to one dimension less, and the observed physics by time dilation is effectively nonrelativistic by time dilation. I illustrate this briefly below. This reduces the 10 dimensions of supergravity to 9, and the symmetry group of this spacetime is then SO(8,1) ~ SO(9).

It is easy to how an extremely boosted system appears nonrelativitstic. We consider the invariant momentum

m^2 = E^2 - p^2,

here with c = 1. The energy is then

E = sqrt{p_x^2 p_y^2 p_z^2 m^2}

We then consider the momentum p_z as enormous, and p_z >> p_x,y. We factor this out with

E = p_z sqrt{1 (p_x^2 p_y^2)/p_z^2 m^2/p_z^2}

Where binomial theorem gives us

E = p_z (p_x^2 p_y^2)/p_z m^2/p_z

The momentum p_z then acts as a time dilation factor approximating a Lorentz factor. We may group all of this to define a new energy or Hamiltonian

H = (E - p_z)p_z = p_x^2 p_y^2 m^2,

where the right hand side of this equation is a nice classical nonrelativistic Hamiltonian. The mass squared then plays the role of a potential energy.

Cheers LCAttachment #1: scattering_polygon.GIF

Lawrence/Ben

Bear with me while I put up what may appear like a simplistic comment, but sometimes a person without all the background sees the 'wood for the trees'. I have no idea how this could be represented as a model, let alone analysed in practice, but the logic of our reality must be:

In establishing what constitutes dimension, distance and space in our reality, it must be recognised that we are, in effect, conceiving of any given physical reality (ie physically existent state) as if it was being divided into a grid of spatial positions. And in order to deconstruct it to its existential level, the 'mesh' size of this grid would have to be equivalent to the smallest physical substance in our reality. [Note: there is no form of change within any given state of physical existence within our reality, only spatial characteristics, because it can only occur in one such state at a time].

Only physically existent states exist, being comprised of physical substance. That is, concepts either reflect that physicality, or are an artefact of it. By definition (ie what constitutes physical existence within our reality), any given physically existent state must have a definitive dimension/size/shape (ie spatial footprint), this being a function of its constituent physical substance. That, with reference to the conceptual grid, can be defined as spatial positions 'occupied'.

It could be argued that a direct comparison between states is possible, and therefore there is no need for the concept of a grid. But this is a fallacy, because logically the two circumstances are the same. The physically existent state used as a reference is just a surrogate grid. Indeed, in order to ensure compatibility with other comparisons, that state would have to be maintained as the reference (ie a de facto grid).

'Mapping' other states that were existent at the same given time, would reveal not only, obviously, both the spatial footprint of those states and their comparability with each other, but also, distance. That is an artefact, a function of the physicality of the particular existent states involved. It is a difference, defined by comparison. So, there cannot be a distance between physically existent states which existed at other times, because there cannot be a distance to a physically existent state which does not exist. Distance is usually measured between the two nearest dimensions of the existent states, but could include any combination of dimensions. And depending on the spatial relationship of the states involved, distance could involve a relationship in terms of separation of the states, or one within another, that again being with respect to specified dimensions.

Dimension is a specific aspect of spatial footprint (ie spatial positions 'occupied' when existent). It relates to the distance along any possible axis. So, three is the absolute minimum number of spatial dimensions that is still ontologically correct at the highest level of conceptualisation of any given physical reality. But is not what is physically existent. At that existential level, the number of possible dimensions that any given physical reality has is half the number of possible directions that the smallest substance in our reality could travel from any given spatial point.

Paul

Largely what Dribus connects with is causal net, where physica can be established within a minimal set of postulates and is based on the causal succession of events. There is the shape dynamics which involves polyhedra in space and their dynamics. One involves time (causal nets) and the other involves space (shape dynamics), where I think there is some possible duality here between these pictures. I have suggested this might have some categorical relationship to supersymmetry.

Cheers LC

Dr. Crowell, and Essay Author Benjamin F. Dribus,

Very interesting thread. I appreciate the opportunity provided by FQXi.org to follow it. I hope there will be additions to it. Thank you.

James

In respect of any given physically existent state, ie the existential state of our reality (or constituent parts thereof) at any given time, there are only spatial characteristics. These being a function of the physical substances which comprise our reality. Space, as in the meaning of not-substance (ie rather than spatial footprint), which is not to be confused with just a different form of substance, needs to be proven. By definition, since a physically existent state involves no change, ie it is one state in the sequence, it only has one set of spatial characteristics.

Any circumstance where there is 'time' involves change, ie sequence, sequence order and the rate of turnover thereof. That is, the characteristics revolving around what and how a physically existent state is altering, which is derived from comparison of more than one of them in the sequence. Alteration must function in accord with specific rules relating to sequence order and spatial position, ie any given physically existent state can only be the potential cause of another if it is physically possible. Causality only relating to direct physical influence, since, by definition, all physically existent states which comprise our reality at any given time are ultimately physically interrelated.

The issue is what constitutes a physically existent state. And given the logic of our reality, that must be associated with being in any one of the possible conditions that the properties of the elementary substances could attain. The problem is that we do not conceptualise our reality at its existential level, and therefore fail to identify the entirety of a sequence and confuse the relative timings at which any given state in a sequence occurred.

Paul