A Physical Theory based on Sets, Not Vectors

Hi Tom, Steve,

I've just come across what is for me a new concept, quasiparticles, and in particular, fractons, described in two recent Quanta articles. I was immediately intrigued to read that the fractons do not move, though composites of them can move in sub-manifolds (of the overall space). I think that there may be a connection between my set-based formalism and fractons and have reached out to those mentioned in this article (https://www.quantamagazine.org/fractons-the-weirdest-matter-could-yield-quantum-clues-20210726/?utm_source=pocket-newtab), in particular, the authors of this paper (https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.235136). I'm trying to work through this paper and am getting some glimpses of the analogies between their model and mine. It seems that they are extending the existing vector-based formalism of QT to describe these fractional particles, whereas I may have an alternate (set-based) formalism that might be able to describe the phenomena. We'll see.

BTW, Tom, I tried to read your paper. That's actually kind of hard for me. I'd need close help to understand it.

Sorry, here are the links:

[link:www.quantamagazine.org/fractons-the-weirdest-matter-could-yield-quantum-clues-20210726/?utm_source=pocket-newtab[/link]

and

[link:journals.aps.org/prb/abstract/10.1103/PhysRevB.92.235136[/link]

-Rod

Doh! here they are:

Quanta article

[link:journals.aps.org/prb/abstract/10.1103/PhysRevB.92.235136]fracton paper/link]

Thanks for the links, Rod.

If you follow the Quanta article, you can follow my paper--that's what I mean by radiation without annihilation.

Fractons--stable, motionless--can actually be described by a soliton standing wave. Quoting from the article: "To see what's so exceptional about fracton phases, consider a more typical particle, such as an electron, moving freely through a material. The odd but customary way certain physicists understand this movement is that the electron moves because space is filled with electron-positron pairs momentarily popping into and out of existence. One such pair appears so that the positron (the electron's oppositely charged antiparticle) is on top of the original electron, and they annihilate. This leaves behind the electron from the pair, displaced from the original electron. As there's no way of distinguishing between the two electrons, all we perceive is a single electron moving."

From my paper: "Wave-particle duality, however, cannot explain space and time, which we don't think of as physical quantities--and shouldn't, said Einstein and Minkowski--because only the unity of the two, as spacetime, is physically real. We want to demonstrate a more subtle consequence of that unity--a 1-dimensional spacetime field that grows and decays locally as a function of its global topology. That is, taking infinity mathematically as a growth rate and infinitesimal as a decay rate, we find a point that should be absolute--where motion is null, and mass is created and destroyed continuously. Radiation without annihilation."

(4) (PDF) Dynamic spacetime imposes matter-wave continuity. Available from: https://www.researchgate.net/publication/353495811_Dynamic_spacetime_imposes_matter-wave_continuity [accessed Jul 30 2021].

If these guys aren't destroyed by the "crank" label, maybe my proposed neutrino experiment has a chance of actually being performed.

It's good news for you, too, Rod -- your model (which I have now digested) based on set self-similarity, and fractons seem to fit the bill. A physically real spacetime field gives it continuity--I think you have already described such a field in different terms. More on that later.

All best,

Tom

Hi Dr Rinkus, It is very interesing all this. I have considered the ranking of quasiparticles in my model with these 3D quantum spheres with a kind of hopf fibrations on 2D surfaces of these spheres . That could be relevant to consider so the interactions with the vacuum. We must that said differenciate the fermions and bosons . A sure thing seems that it is an emergent phenomenon from causes. These causes can be ranked also ,and it seems that if we have the 3 ethers merging to create the satble baryonic matter, so these causes are complex, outside, inside, on fermions, on bosons, with the fields and excitations. The volumes and the densities and oscillations vibrations so seem relevant to analyse and the life time. Regards

Hi Ulla, the info processing theory is "Sparsey". The physical theory has no name yet. The key idea was described in my 1996 thesis.

The first pub describing the core learning (storage) algorithm, in the simplest case of purely spatial inputs, was in my 2010 paper.

The 2014 paper describes the generalization to the spatiotemporal input case (even though that was the case originally treated in my 1996 thesis).

The 2017 arXiv paper is the most up-to-date description.

Probably easiest to look at algorithm in 2010 paper. An underlying goal of the model is to achieve constant time complexity storage AND constant time complexity BEST-MATCH retrieval. No model formally achieves that, in particular, locality sensitive hashing might come closest, but it does not. In fact, Sparsey also does not formally achieve both, but it effectively does. I realize I need to explain that in detail, but the key is that when the overall information processing system is organized as a hierarchy of modules (each running Sparsey's algorithm), constant time complexity storage and best-match retrieval can be realized over arbitrarily long lifetimes. The argument is sketched in this short paper.

Hi Tom,

Well I've read through a good bit of the fracton paper. I get some things, but I definitely need to get more background in the basics of TQFT to fully understand it. Nevertheless, I do suspect a deep connection. Even just the idea of fractional charge suggests to me a set-based underpinning. In my terms, the fermionic state, X, of a corpuscle is a set of Q active fermion-planckons. Suppose X corresponds to the presence of one particle in some config. The corpuscle's universal set of fermion-planckons is >> Q. Suppose there is some subset, C, of the corpuscle's fermion-planckons that represent charge. Let C be of size 1000. Then the X can have intersection size of from 0 to 1000. The overall dynamics (physical law) governing the evolution of the corpuscle (and of any corpuscle) might be such that only intersections of certain sizes are possible. Some of them might correspond to integer charges and some to fractional charges.

Yes, I noticed the quote you cite too. In my model, the the initial electron-positron pair, at T, is just one set of Q active fermion-planckons; the remaining, displaced electron, at T+1, is just another set, though (as described in Fig. 4 of the essay), the two sets would have some significant intersection. And, as the article suggests, the two instances of the electron are only thought of as being the *same* electron because the two positions are along a line of travel (e.g., from T-2, T-1) and delta T is small. A key question then is: is the corpuscle's codespace (number of unique sets of size Q) large enough to represent any arbitrary path of movement through the corpuscle? More generally, is the codespace large enough to represent a very large set of quantum state sequences, where (I'm assuming) the vast majority of those states will actually be ensembles of multiple particles. While this might seem like a tall order, note that I'm assuming the corpuscle is very small, e.g., 10^12 planck lengths on a side. In that case, maybe only ensembles of quite limited size might actually need to be modeled (in order to explain all known larger scale (though still quantum) phenomena. In particular, while I said above, the codespace needs to be large enough to represent *any* possible path through a corpuscle, maybe the actual number of possible paths that need to be represented in such a tiny portion of space doesn't actually need to be that large. That is, even if only 6 paths were represented (one for each face of the cube directed inward across the corpuscle), looking from our much higher scale, we'd see all particle paths that span multiple corpuscles, as essentially straight lines. That is, at our high observational scale relative to the actual mechanics, we don't see antialiasing. BTW, the same principles apply with respect to a particle "moving" from one corpuscle to the next as well. The first state in which the particle appears in the next corpuscle is such another set of Q active fermion-planckons, just chosen from that next corpuscle's universal set of fermion-planckons.

Regarding your quote from your paper, I think I agree with you and Einstein and Minkowski about not seeing space or time as physical quantities. But what do you mean by "..grows and decays locally as a function of its global topology"? I realize the answer might be long. But maybe you can point me to an appropriate tutorial for that, or I'd be happy to vchat some time if you want.

What do you mean by the "crank" thing?

I'm happy that you have put time in to understand my theory. As you can see by now then, it is really extremely simple. The big thing I figured out (in my thesis) is that all you need to do, in order to statistically preserve similarity (of all orders, not just pairwise) when learning an input space, is organize the coding field as a set of WTA modules, and bias the distributions from which winners are chosen (one in each WTA module) based on a global measure of the familiarity of the input (my G measure). The great thing is that computing G is trivial and the whole algorithm runs in fixed time (does not grow as the number of stored items increases). And, then the one other, crucial thing, is that once the items have been stored in this way, retrieving the closest-matching item is also trivial (in fact, in simpler than the learning algorithm). I know that this is a better way of achieving the functionality of locality-sensitive hashing. I've reached out to many of the leaders of that field, but never gotten them to listen. Not giving up.

Anyway, it gives me a big boost that a person with your knowledge of QT sees some value in what I've done.

Rod

Hi Rod,

I don't hold myself out as an expert in quantum theory. I've got all three Steven Weinberg (RIP) books on quantum field theory, and haven't cracked one yet. I should read now to honor his memory, but at my age, that's a promise I can't keep.

I do know a little topology, though. So when Ed Witten came up with TQFT, I walked in through the back door. So I believe your instincts are guiding you straight.

The main concept remains with the field continuum of spacetime. When spacetime is accepted as physically real a number of problems, of unifying fields, disappear.

Radiation without annihilation provides the constraint on runaway (positive) feedback to the system, protecting it from annihilation radiation, and providing negative (control) feedback. I think the wave shape of this constraint is a standing soliton wave, sharing many properties with fractons, as already noted.

From your paper:

" ... a boson field completely connects any particular fermion field."

You might be describing spacetime.

If the boson field of massless particles interacts with the fermion field, you are begging a field continuum. If " ... we require that the matrix between any two Sparsey coding fields (including recurrently) and between a coding field and an input field (are) also complete ... " case closed. The fields are not discrete, only the associated particles. And the only measurement is between and among mass points, which are real, i.e., physical. If the superposed boson field affects fermion fields, it fits perfectly Einstein's definition of a physically real spacetime continuum: " ... independent in its physical properties, having a physical effect but not itself influenced by physical conditions."

All physics is local, Einstein asserted. A boson field is created locally from interacting mass, yet possesses no mass of its own, and thus "has a physical effect, but is not itself influenced by physical conditions." So what does give the field its effect?--I (and perhaps others) propose Time as the whole reason that space alone, and time alone, are real only if spacetime is real. And it's why time is identical to information. Physical information can be shown causative.

Now here's where the "crank" label comes in. It seems that every time an analytical, i.e., continuous, theory of nature gains momentum, self-appointed guardians of discrete physics go apoplectic. And they have the advantage of presently holding the power.

Prove that spacetime is real, and the tide turns.

"I suspect that the recent Bell inequality violation findings do not refute the type of 'local variables' explanation given here."

I'm afraid they do. Your weight matrix emulates a negative feedback (control) mechanism that regulates information (thus, time), measured at the completion of an event; say, the absorption of a photon or electron. And that's the only measurement constant in Bell-Aspect type experiments. It's just algebra, a count of the number of times particles were correlated or anti-correlated.

All best,

Tom

Steve,

Re Steve Dufourny replied on Jul. 28, 2021 @ 12:34 GMT:

Why am I a critic of the ideas of (male dominated) physics and a critic of the ideas of (male dominated) computer nerds? Because, unlike you and Tom and others, I actually DID study physics, maths and information (computer) science at university for 3 years, receiving a high distinction for one of my maths subjects, and I was a computer analyst and programmer for more than 20 years. Unlike some others, I am not an uncritical follower.

And Steve,

I might add that there is only one, ONE, thing you need to know about the world: is the world such that people genuinely make a difference to the world (i.e. is the world such that people change the numbers for the variables) or not? And clearly, people DO change the numbers for the variables.

Ps I was at university and I study all days the maths and physics of the best papers of best thinkers,don t try lorraine, try to be less vanitious and frustrated please

ps, stop to tell also ironical things about the members , Tom is a relevant thinker . And the persons that I have known on FQXi them are more general and skilling than you for me, they are able to speak generally , not you, you repeat the same always Lorraine like if you had something to prove, you prove nothing of really innovative and generally relevant you know. You just show us a frustration and anger.

You know Lorraine, Personally I am a nice guy and I am going to tell you an advice for your credibility, stop to be too much like this against the males, I can recognise that the hormonal testosterones can imply problems but it exists men respectable . And for your informations, I am obliged to tell it I am invited to many conferences to present my theory and many Phd from manu countries like my theory , and I improve it all days.They told me that I have found a general universal link and it is innovative in the sense that the spheres can be the answer and that there is probably a conjecture with the strings and fields. Instead to repeat these things about the variables, boolean algebras and computing, if you could speak about the geometrical algebras, the quantm gravitation, and others with concrete maths , it d be better becase there we don t learn nothing from you.We just see an odd comportment of frustration agianst the males.Make the peace with yor psychology and past please .

Steve,

I'm sorry to be such a pest. I'm laughing to myself when I write about "the men". But it is not just a joke: you can't deny its true: it IS men that have come up with particular types of ideas/ views about the world, and who continue to vigorously defend these ideas/ views as if the ideas/ views about the world were truth itself.

And you must admit that the ideas/ views of these men have a LOT of followers, mainly men, people who also never question that the ideas/ views are truth itself. E.g. people who never question the idea that a set of equations could represent a system, and then wonder why the equations never ever seem to represent a system.

You and Tom are very smart people who can actually do the equations as well as, or better than, any physicist; and better than I can now. But I'm saying that the equations are only PART of the picture, and can never represent a whole system.

Importantly, for a person like you who wants to save the world (and who DOESN'T want to save the world?), physics does NOT allow you to act to save the world, or to act to do anything at all. According to the crazy ideas/ views of physics, its only the laws of nature that change the numbers for the variables. This is important: the ideas/ views of physics say that you CAN'T act to save the world: the only actors are the laws of nature.

Hi Lorraine, Lol I don t see you like a pest but like a rebel against the testosterones and the correlated vanity and power. I must say that can understand what you tell in the sense that indeed we are governed in majority by the mene and that indeed these testosterones can imply problem in the social interactions and that it is more difficult for a woman on this planet. But it exists also good men trying to fight these hormonal comportments with the consciousness.

For the project Global collaboration, I try indeed to make something for a better world. I know that it will not be easy. It is not to satisfy my vanity you know, I am sincere Lorraine , I find sad that we don t do it knowing that the solutions exist. The laws of nature Lorraine don t say that we cannot act to save the world, because the laws of nature have created this consciousness and that this tool can be utilised in finding solutions of adaptation in utilising the tools of this nature. We have created a specific global econonomical system and we have a sad common past and this system with the greed, the vanity, the individualism, the power, the unconsciousness...is not perfect and not harmonised where all lifes can find its place in being more happy. What I tell is that this system global can be improved , we need funds and a new global revolutionary industrialisation. We can give water, food,energy, jobs, hope to the majority and the humans globally need to be reasured and the world bank and the UN and all governments are the keys, they must simply take their responsabilities and improve what can be improved.The lazs of nature are complex and this consciousness and intelligence are results of evolution from these lazs of nature Lorraine. We cannot be fatalists or defeatists, because we can optimise, it is not an utopy, it is just improvements of the global system. Wer are actors of these laws of nature with a brain and a consciousness. Take care, regards, from a man trying to harmonise these testosterones wich indeed can sometimes imply problems lol :)

Hi Rod,

You wrote "Regarding your quote from your paper, I think I agree with you and Einstein and Minkowski about not seeing space or time as physical quantities. But what do you mean by "..grows and decays locally as a function of its global topology"? I realize the answer might be long."

Not too long, though I hope, satisfactory:

https://www.researchgate.net/publication/353644476_6_april_2017

Regards,

Tom

Hello Sir, since this is a set theory formulation, have you considered 'tearing' or 'stretching'? It seems to me that stretching might equate to Special Relativity. And tearing might equate with acceleration. Thanks

Hi Lloyd,

I have not considered those things. I'm wondering if your use of the word 'sets' here is that used in topology, i.e., where the sets are (I think) generally of 'points' in an underlying geometric space. In that scenario, I suppose such sets are generally of infinite cardinality (not sure). Anyway, my (sub)sets are over finite-sized sets (of binary elements). Specifically, the fermionic state of a corpuscle is a set of Q (e.g., 10^6) Planck-size fermion-planckons, chosen from a much larger ('master') set, e.g., 10^10 fermion-planckons. Moreover, there is no spatial ordering (topology) over that master set: they are just an unordered collection of elements. So in this case, I'm not sure 'tearing' and 'stretching' apply in the way you may intend. I have developing ideas on acceleration (and thus, I suppose on SR), that I hope to share at some point, but not ready yet. As described in the essay, in my theory, the notion of space itself (thus, the kind of of geometric space underlying a topological space) is emergent: specifically, the space, i.e., its dimensionality and its valuedness on each dimension emerges in the patterns of intersection over the sets (each of which represents a particular state).

Thanks

Rod

Hi Dr. Gerard Rinkus,

I skimmed over you essay about set theory as a basis for a physical theory and found it to be interesting. As a matter of fact your idea is very similar to mine but mine is more direct and its easy get results with simple calculations that match QM/QFT in a a very simple way. As I have always thought that my idea can be formulated in many other mathematical formalisms , one of which I was hoping to be set theory which I thought is very natural. So Please skim over my essays and see how much similarity there is. Thanks.

https://fqxi.org/community/forum/topic/2451

https://www.reality-theory.net/

you can run the simple modifiable JavaScript programs to confirm some of the results

https://www.reality-theory.net/a.htm