Are there really unbreakable particles?

[Mighara Sovmadhi]

Or other units of matter/substance/stuff?

We know, roughly speaking, of molecules down through atoms down through protons and neutrons and electrons down to quarks, and alongside all these, in principle in some cases anyway, their (super?)symmetrical partners in the Menagerie, and so on. However, here, it's the quarks that don't divide, as far as the series of divisibles goes. (Throw in quantum field theory and everything's way more interesting; throw in string theory, though, and read on...) But there is in fact speculation or theorizing or at least maybe hypothesizing going on in some quarters, that maybe quarks (and antiquarks?) are composite, composed that is of things on average referred to as "preons."

Now, as a devotee of Kant, I have myself thought for a long time that we have no a priori reason to expect the possibility of division in matter to ever end. That is, since the intuition of space in the pure imagination is subject to infinite division, everything in physical space admits of being composed from subtler and subtler substance, else space would at some point not be filled and presto, the principle of the Anticipation of Perception would be violated. However, I doubt a Kantian argument, here, is going to do a great deal of solid dialectical work. Hence, a different proposal.

The question of geometrodynamics is at once a matter of genuine physics, it appears, yet with a strong relationship to philosophical inclinations in methodology or conception, affinities shared also with, say, quantum information theory (if from a syntactic rather than topological(?) direction, so to speak). Another random physics article I found recently reported on a mathematical discovery of a geometrical structure that maps all the Feynman diagrams for QM or something---the implication being that this hyperdimensional crystal or whatever they described it as, corresponds to the graph for the fundamental quantum functions of the world. That is, the geometrodynamical question just is the physicist's question: what is the function for the graph of the fundamental changes in physical reality (what functions graphs the unified action of the four forces, or even what function graphs that action as the action of a single force)?

But now suppose that we are also set with the problem of filling space, of making sure there is no vacuum. QM seems to solve the problem with notions like virtual particles or zero-point energy or the like. Space gets filled as the wave-function overlaps it indeterministically. Now actually there's nothing wrong with this as far as I or, I suppose, most anyone else can tell; or at least I am certainly not in a position to argue the merits of this solution to the space-filling problem.

However, one thing is that the waves of wave-particle duality, and the fields of QFT, and the like, don't quite reduce to the point-particulate description of matter. For example, the Higgs boson, if my understanding of the topic is correct, is a "scalar field," like a temperature map but for mass itself or something. Maybe there are in some form little spherical/point-like Higgs boson quanta pulsing about but I don't get the impression that that's really what's supposedly going on.

Another thing to consider is the motivation behind string theory. Now on the one hand there's all that "the elegance of mathematics" stuff, which again hearkens back to or anticipates at least aspects of the geometrodynamical question. But basically, the shift from point-particulate to string-theoretic descriptions of matter is much more than broad theoretical drift.

So, let's allow that space does have to be filled. If we are Kantians or whatever, we'll go a step sideways and say that it is not "intrinsically" filled but only so far as we have actually experienced its division, so that in a way the quantum foam might really be the "end point" for our knowledge of the substructure of matter and yet this is only in a proto-positivist sense true. But if we are more Platonistically minded geometrodynamics theorists, we will look for a function for a graph that can be used to fill space at all magnifications, at a glance, and which does seem to be manifest in much of the natural order---and which, due to the role of recursion in ideal mathematical structures across the board, is perhaps to be expected anyway, in the concrete expression of mathematical reality in the physical universe.

I'm talking about fractals, that is. What do you do if you want to fill space to infinity, but also to capture the proto-positivist sense of things, here? You fill it with two fractals, or rather you assume that there are two substances for the fractal, one for the figure, one for the "gaps." Well actually this is just speculation on my part; maybe it would take more; but the gist of it is, some set of fractals would be sufficient to fill in all of space, very efficiently it seems to me. Just watch a 3d-fractal video on YouTube and you'll have some sense of why it seems so to me, then.

If this is true, then the quantum foam, and even the preons that might precede this, are but the capstones of their own infinitely ascending series of material substructures. That is, every single atom that we know of, contains as much detail, as one divides its structure down and down, as does the entire observable universe, on the macrolevel, and in fact much more detail, but then everything would be much, much more detailed, on this scheme of things.

An immediate objection that comes to mind is that since photons could not access the overwhelming majority of these lower material levels, or would overlap them in some unhelpful way, or whatever, no information about them could be effectively conveyed. Or something along this line. Now the Internet Encyclopedia of Philosophy article on infinity includes a discussion of a description of the electron as posited to be "infinitely small." Hence it would be a genuine point-particle. But are photons infinitely small, too? Are either, that is, anyway? I don't know what the most up-to-date summaries of the research say. So, anyway, then, though, to broaden the objection, the problem with fractal theory, so to speak, is that, like string theory, it does not appear to have observable evidence, irrespective of our theories of photon paths and information transmission more particularly or whatever. Even if some parts of the world exhibit fractal order, or are recursively geometrodynamical, or however you'd like to put it, the whole world doesn't strike many as being so.

So secondly, a different objection that comes to mind is that the theory would reduce the action of the four known forces to the action of one force, the fractal force. The category of a fundamental force is the category of a fundamental cause of a fundamental change in space, i.e. there is a function for the graph of all things changed by gravity, by the strong and weak nuclear forces, and by electromagnetism; and the GUT/TOE ideal is to find the function for a single graph that encompasses the others in the most fitting way. However, according to fractal theory, it seems, all the positions of all particles/units of matter are determined just so as to iterate the application of the axiom of the system's geometry, to infinity. Thus what appears to be gravity resulting from the curvature of space is really just space itself warping according to the fractal pattern, with its content appropriately warped as well. And where would gravitons appear in this description at all?

Since I am not a physicist except in some elaborately rudimentary way, I am not going to make a lot more in the way of detailed claims about the fractal picture of the cosmos. So, to pursue the immediate line of inquiry, why yes there would be a sense in which the curvature of the fractal determines the curvature of physical space. But more importantly, we are not to go about applying the fractal picture purely a priori but, to help test the theory at least mathematically---much as string theory is, then, to date more than less---it has to be shown whether there is indeed a given function, for a fractal graph, that maps on to the actions of the four known forces. Fractal theory then becomes a hypothesis and a research program, so to speak, and not a dogma: in the quest to find that function or similar ones, or to pursue new lines of relevant reasoning in this kind of light.

[peter]

As ever........

(I'm not even going to say it Mighara - you don't need me to: but I promise I did read every word of it! )

But one thing; in this are we not forever stuck in the realm of theory that can never be confirmed or refuted by experimentation? Are we not beyond the point where to investigate requires energy inputs that become part of the very results you observe? On the simplest level, that the energy you use to further split the particles is itself transformed into the particles that result from the splitting?

[Mighara Sovmadhi]

That does This does seem to be something of the impasse... but then again I am not familiar with how particle accelerators actually work or how their results are interpreted, and so on, so the scifi-writer in me wonders what might be gleaned from the world if we could construct much more massive PAs in outer space for instance?

Other than that, though, IDK. I guess at some point devising the experiments is going to depend to some degree on handling supervenient information indirectly. So maybe subatomic fractal theory will predict that if we adjusted some influx of energy on that scale, we could get a specific set of results, wherefore even if we didn't see the energy going "down to that level," so to speak, we'd see it "come back up" in a way that would be akin to how the fractal force in theory would affect it, maybe.

EDIT: For rizzle, though, you gotta watch some 3D fractal videos on YouTube or wherever you can find 'em. I recommend the work of Julius Horsthuis, Truman Brown, and schizo604 (I think is his "callsign") for starters. This stuff looks hella organic, like people thought Julian and Mandelbrot fractals seemed to be showing up in nature, well, hey, here we can easily get everything from mountains to galactic systems to churning molecular oils, to machines to monsters to deities. So the computer-simulation evidence, so to speak, for fractal-force theory (or whatever), is actually pretty good---which brings up the fact that computers are heavily used not just in pure mathematics (where their results are subject to a very peculiar epistemological paradox or similar problem) but in science overall, so that one might count computer simulations alongside experiments of a more classical caliber, as scientific evidence of some form.

[Vraith]

I recently posted somewhere about abstract infinity vs. material infinity...
Just because you can imagine cutting the smallest thing in half and creating something smaller is not sufficient reason to believe it is actually possible.

There are other factors in the physical realm.
It MAY be that there is a possible infinite splitting...but it seems unlikely, because of the energy involved in breaking.

I suspect at the bottom, if you hammer away at the unbreakable fundamental you won't get a breaking.
Instead, you'll get a phase/state change or fusion.

Fractals are fascinating for sure, though---and surprisingly useful.

[Mighara Sovmadhi]

Well like I said, the space-filling problem is only sharp enough to require a fractal solution if, like Kant, you think that the ability to imagine (not just conceive in the abstract---here we differentiate between material infinity, imaginary infinity, and conceptual (abstract?) infinity, perhaps) an unending division in space, is tantamount to space itself being endlessly divisible, and then if you think that an empty space is imperceptible and therefore not an object of physical reality (i.e. if you think that nature abhors a vacuum). Adjust or dispel those assumptions and the problem of filling space is more of a non-problem, I think.

[peter]

Is it down at this level that reality actually becomes mathematical: the reason why math actually works - because at the fundamental nuts and bolts level the universe is math?

[Vraith]

Is it down at this level that reality actually becomes mathematical: the reason why math actually works - because at the fundamental nuts and bolts level the universe is math?

I mostly don't even know what people mean when they say that.
Do they mean it has a, or some, geometry? But that doesn't mean it IS math...it means it has a shape that is describable via mathematics.
Saying it is math seems to me like saying the word bird and an actual bird are the same thing.
It also seems to me that the entire reason math "works" is precisely because it is abstract, not thingly.
The nature of things makes the math workable...the math doesn't make the nature of things.

[Mighara Sovmadhi]

Let's consider calculus for a second. This is basically an entire form of mathematics that was developed by Newton for the sake of physics (Leibniz had different reasons IIRC but the two independently formulated the method or w/e). So do we say that the mathematics describes the physics (of continuous change) or that Newton had an intuition about that physical continuity itself and then sucked it out of normal objects and projected the system of method through it (so to speak)? It's not entirely clear that we could separate calculus from (Newtonian) physics.

Some other ways this idea is meant:

• "Everything is mathematics," means, "Everything's a set."
  
  "Everything is mathematical," means, "Neutral monism about substances/properties is true and it is something like computation or information that consists in the underlying monistic force for mind and matter."
  
  "Everything is mathematical," means, "Everything exists in quantitative relations, and these relations are fundamental."

Now however it is somewhat difficult to see(!) how the colorfulness of a thing is a quantitative relation. That X is red does not seem like an arithmetical or algebraic or geometrical or calculus-related fact, does it? What branch of mathematics would it fall under? And yet on the other hand we have such things as the Munsel(sp.?) color solid (or whatever that map is known as). So perhaps colors are numbers, too, only with their shadings they map onto, IDK, some transfinite number beyond the Real Number Line (since Cantor's theory allows, for example, aleph.aleph.aleph-27923, for example; this will include the infinities we know, and countless others, and maybe one of them matches up to the colors.)

[Mighara Sovmadhi]

Physics might be described as the science of finding the functions for graphs of information that is configured below the chemical level. This is not to say that chemistry graphs don't ultimately emerge from physics ones, but the problem of the unity of science is a rather major one awaiting further attempts at solution. But anyway, when physicists talk about "an equation you could print on a T-shirt" when referring to a Theory of Everything or such-like, they mean something similar to "f(x) = T" where T = the expression for the theory that assigns points on the graph of x.

The notion of spacetime, for example, is to treat time like a fourth dimension of space. So just like 2D parts make up a 3D structure, so do 3D structures make up a 4D one, as its "sides." Each full 3D slice of an object's existence in time, then, is a "side" of a 4D "time-worm." Passage through time is something like the rotation of the 4D structure so that we perceive different slices, or different slices become perceptible, but in principle all the slices exist "above us" already (hence talk of time being sort of "illusory").

But then the problem is: what function graphs the points of the total 4D object? If all there were in the universe were a single inert sphere, the 4D object would be graphed just by the function for a 4-sphere (a spherical polychoron, I think they're sometimes called---at least I think the suffix -choron, or one like it, is the 4D-analog for -hedron in 3D). But our universe contains more than inert spheres so the trick is finding graphs for all the menagerie of particles and their configurations with which we deal.

[peter]

(Peter has to wait for V's response to Mighara's post out of sheer respect for his infinitely greater understanding of math than his own.....but thinking - is it not UP THERE or down there that stuff like the 'infinity hotel' actually becomes the reality that we have to deal with.)

[Vraith]

(Peter has to wait for V's response to Mighara's post out of sheer respect for his infinitely greater understanding of math than his own.....but thinking - is it not UP THERE or down there that stuff like the 'infinity hotel' actually becomes the reality that we have to deal with.)

Hah..funny peter.
But Mig, I didn't mean literally I don't know what they mean...I meant that what they mean cannot be true literally---only abstractly/metaphorically/analogically/descriptively.


Back to peter...even if there is a real physical analog of the infinite hotel, that doesn't make or require reality made of math.
And when he talked about tossing the trash he completely left out minor things like the infinite mass and infinitely multiplied energy required to do that in any material realm.

To bastardize an old phrase:
The Math is not the Territory.

[peter]

But am I correct in thinking V, that there are theoreticians out there who believe that ultimately the math is the territory (in some weird way I can't begin to grasp). Remember - most of my physics comes to me via Sky TV and I'm sure I saw a Horizon episode where one bod was propounding this as one of a number of theories about the ultimate nature of reality.

[Vraith]

But am I correct in thinking V, that there are theoreticians out there who believe that ultimately the math is the territory (in some weird way I can't begin to grasp). Remember - most of my physics comes to me via Sky TV and I'm sure I saw a Horizon episode where one bod was propounding this as one of a number of theories about the ultimate nature of reality.

I've seen a significant number of statements by various people that SEEM to say that at first blush and/or out of context. But situated properly, [at least the ones I can grasp] they really mean it other than literally.
Something more like "Math is the only tool that can draw a proper map, and the map illustrates everything that is there accurately."
The difference between being mathematical and being math...between adjective and noun.

I think [I've probably said before] there is a perfectly good reason for that:
Any universe that exists will be describable by some kind [[for most decent universes you'll need many different kinds, actually]] of mathematics.
The only case I've thought of where that might not be so is if the universe was absolutely random at every level. But I have a hard time imagining existence and total randomness together as something possible. They seem inherently irreconcilable.

[Mighara Sovmadhi]

Max Tegmark might be a non-metaphorical proponent of the idea, I think. His idea seems to be that the graph for the function of this world is an individual Platonic object, so that just as there are the Eternal Square and the Eternal Sphere and so on and whatever, there's the Eternal f(x) = Tx [sic?] for our world (universe/sub-multiverse?)... and that's all there is to it. There's no gap between the "laws of nature" and nature, the objects therein; they're the same thing. As long as the Eternal f(x) exists, and in its existence, is our world. Our perception of change is just due to a subsidiary function for the total map. But now anyway moreover, as many worlds exist as there are relevantly similar individual Platonic objects, on his view.

[peter]

Yuval Noah Harare's new book Homo deus culminates with a chapter on 'dataism' which (if I understand it) see's everything from the big bang onwards terms of simple data flow. As disorder increases (ala the 2nd Law) could it not be perhaps that the regularity of data increases in a sort of inverse relationship? Hawking's original work was I
believe involved with conserving 'information' at the edge of a black hole (the loss of which had prior to this had been a major problem with the theoretical work in the field) so clearly scientists and mathematicians are using the terms outside our normal usage of them.

More to the point in respect of the original post, would the limit of splitting not be reached if not before, then down at the Planck length where the very grainy nature of space-time is itself evident. In a program I saw earlier, a physicist working at the MAGIC telescope explained how this very grainyness could be the explanation for the five second time lag seen between photons of different energy levels arriving at the detectors following a seven billion year journey across the universe, an explanation that if confirmed would overturn that most fundamental of constants that underpins all of our understanding of the Universe in which we live, the very speed of light itself.

[Vraith]

Mig...Platonic objects aren't real, in the material sense.
All the Tegmark I've read on this seems to come down to the distinction I made---mathematical, but not math.
Descriptive, not causal or existential substance.

peter---the MAGIC thing failed to replicate, and in fact found contrary results afterwards. Other experiments have also.

Planck length doesn't mean spacetime is grainy. It's a measurement limit, not a grain of space. The problem is measuring smaller than that because the scale both A) is smaller than the uncertainty and B) requires too much energy in the "space." Black Hole, Law of Nature shredding amounts of energy. Not that there is nothing that can be smaller, [especially empty/smooth space] but that we can't look at it...not without transforming it to something else.
That doesn't mean spacetime ISN't grainy at that level...but the Planck length doesn't mean it HAS to be, and experimental evidence so far says it isn't.

[Mighara Sovmadhi]

@Vraith, I should probably just agree with you

[peter]

I'm lost for words!!!

[Vraith]

@Vraith, I should probably just agree with you

Well that's a shitty trick.
You think I come around here to be all AGREEING with people?
What kind of fun is that?

[Avatar]

Yeah, no fair...

--A