Atoms v. Particles

Important Note: In the following essay, I will be referring to things called "atoms." My only intention is to think of this word solely in the philosophically pure context of a spatially-extended, yet ontologically simple material body, rather than in the derivative context of the contemporary natural sciences—i.e. consisting of so-called sub-atomic particles. The atom is to be considered in contradistinction to the notion of the zero-dimensional "particle" of theoretical physics. Both of these entities are "indivisible," but in vastly different ways. While an atom may be conceptually subdivided for the simple reason that spatial extension itself is built upon the notion of the possibility of unlimited divisibility, each of the conceptual subdivisions are reciprocally dependent upon every other for its existence. In other words, there cannot possibly be separate existences of the subdivisions of an atom; an atom is ontologically indivisible. On the other hand, a particle is indivisible solely because it cannot even be conceptually subdivided—it is by definition unextended, and therefore "partless" in every sense of the term; a particle is logically indivisible, and not, strictly speaking, ontologically indivisible for the simple reason that it is not ontologically anything.

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In the common vernacular, all of matter (and energy) consists of "tiny particles." In the more rigorous context that is academic theoretical physics, however, a particle is a thing that occupies one and only one location at any given time; and a location ,furthermore, is just a zero-dimensional construct that represents the solution to a particular algebraic equation.

In the sensible world, a thing must at least occupy a finite volume of three-dimensional space in order for it to be considered to have any size at all, whether this size be considered small, large, or somewhere in the middle. Anything less than the occupation of three full dimensions banishes a thing into a state of nothingness.

Opposed to the mathematically localized particle, the concept of the atom relies upon the philosophically sensible idea of three-dimensional (i.e. "spatial") occupation. Such a thing as an atom, however, does not correspond very well (if at all) with rigorous algebraic calculability. That is, there is no easy way to cause a unified region of space to result from a mathematical equation.

It was for this reason that Newton "simplified" the concept of the space-filling material body, so that it would correlate exactly with his algebraic technique (i.e. "calculus"), by way of saying that a body can be located at its center of mass. But of course this simplification is nothing but a case of mathematical convenience that seeks to evade the much more daunting—and potentially embarrassing (and possibly career-threatening)—question of how, precisely, a material body is fundamentally structured.

Newton was thus able to abstain from taking an official position concerning the ontological "fundamentals" of physical reality. By asserting that a cosmic body could be mathematically "located," and that this kind of locatability through time lies at the heart of the scientific project, the implication is that the only important question about the theoretical fundamental elements of the material world—i.e. "atoms"—consists of their mere locations within universal space.

Perhaps the most notable attempt to come to grips with the way in which matter ultimately "looks" is in Plato's dialog, Timeaus. No matter how believable the final result, the fact remains that Plato at least tried to give a sensible explanation as to the ultimate forms of physical reality. Because of the inherent subjectivity of the Platonic project—being that it involves rational ideas rather than immediate experiences—the particularly empirically minded contemporary Westerner has seen fit to relegate all such enterprises into the dustbin of pointless metaphysics.

But we must not allow the apparent difficulty of the task at hand to cause us to forget about its profound significance! Instead, we must redouble our efforts to see if any progress can possibly be made...

First of all, let us reconsider the question of scale in terms of its theoretical significance. In the previous blog entry, I upheld that all of the fundamental entities are to be treated as existing on the "universal scale." This seems to be perfect nonsense—until we realize that the only reason that we consider something to be "microscopic" concerns the empirical fact that our senses only consist of a finite amount of resolving power. If, therefore, our eyes had the magnifying power of the world's most technologically advanced microscopes, then the line that divides the worlds of the small and large would exist at a vastly different place than it currently does.

The wise interlocutor, however, might very well object that it is not truly a question of the subjective visual appearance of a thing that determines its scale, but rather the way that it relates to an objective standard of measure, such as a meter stick. But of course, in what way is it meaningful for a thing to have a certain scalar relationship with another thing without our first being able to [subjectively] sense each individual thing, as it is?

The point I am trying to make here is very subtle, and a thorough understanding of it will go a long way toward helping us to find our way into the heart of my ultimate thesis. When it comes to our experience with everyday objects, we think of them as having definite (discrete), impenetrable bounding surfaces. But the empirically determined location of a given surface necessarily depends upon the sensitivity (i.e. the resolving power) of a particular sensory device. It is crucial to understand here that the sensitivities of our manufactured measuring instruments consist of just as much potential subjective error as do the instruments—such as eyes and ears—that are innate to the human body.

If only, therefore, it were technologically feasible to construct a device with an arbitrarily high resolving power, then there is no reason to assume that the effectively detectable surface of a given object would not exist at an arbitrarily greater distance (from the object's center) than what we had originally (and so crudely) surmised. Given this same line of reasoning, it makes sense that a measuring device of "perfect" resolving power would be able to register a surface distance that is as large as the entire universe.

But there is a hidden difficulty in gaining a full appreciation of the point that I am trying to make, and that involves the way in which we think about the problem of light (the signal of the thing) versus matter (the thing itself). The commonly accepted "solution" is to treat both of these entities as "particles," with the result being that they are both equally relevant to the locatability (exact solvability) of the standard algebraic treatments of modern physics. The acceptance of this scenario, however, leads us right back to the problem of the zero-dimensionality—and therefore the implied non-existence—of the entirety of physical reality.

The only reason why we require the concept of "light" (or any other force carrying mechanism) is so that we may understand how [localized] matter particles may be able able to affect one another.

Now that we understand 1) that the notion of the localization of matter is purely a function of a desire to "reduce" reality in a way so that it fits into the context of "easy" mathematical calculability, and 2) that the empirically determined sizes of objects is fully contingent upon the arbitrary sensitivity of the measuring device in question, then there is no longer any theoretical justification for the bifurcation of physical reality into the domains of matter and matter's indicator.

To continue down this line of reasoning, it is necessary to affirm the senselessness of a doctrine (such as is given to us by the scientific establishment) of pure mutual exclusivity—for, this doctrine is only possible if "all there is" comes in the form of zero-dimensional point-locations; thereby negating the physical sensibility of reality itself. Furthermore, given the philosophical untenability of a doctrine that includes arbitrary mixtures of mutual exclusivity and mutual inclusivity, the only alternative is to simply accept a doctrine of pure mutual inclusivity. And by "mutual inclusivity," I just mean that a material body actually fills three-dimensional space and that a device would therefore be able to sense this body directly if only it shared this same volume of space. The reason why a mixture of the two would be arbitrary (as previously asserted) is that the effective sensitivity of any possible device that exists to sense a material body is solely a [contingent] empirical fact.

We have, therefore, arrived at the unavoidable conclusion that the only philosophically tenable sense for the term "material body" is that it is some kind of a universally space-filling geometric form. (The descriptor "geometric" is wholly unnecessary here, because anything that occupies space in any manner whatsoever is necessarily geometric. The purpose for its use is to emphasize the fact that we need to recast our understanding of what it means to be "truly" mathematical within the context of the possible ways in which matter occupies space, as opposed to the standard modern treatment that understands mathematics primarily from within the realm of solvable point-location algebraics.)

After all of this, we have—in a purely philosophical way—come into an understanding why it is that the term "atom," in the sense of a universally extensive geometric form, serves as a much more robust template for the fundamental entities of physical reality than does the term "particle," which signifies nothing other than the ontologically (as opposed to logically) irrelevant solutions to the algebraic equations whose only purpose is the rather mundane task of detailing the trajectories of arbitrary material bodies (whether cosmic/complex or atomic/simple) as a function of time.