Monday, December 13, 2021

Answering Aristotle I.2 - There Is More Than One Thing I

This one was very confusing, especially in trying to figure out what Aristotle means by a "principle" -- or what the translator translates as "principle." Part of this section's difficultly (and the next) is that in arguing for a particular position, Aristotle isn't laying his argument down precisely, but is responding to other philosophers of the day. This makes it hard to pick out what is essential in his argument that ther is more than one thing and what is an accidental argument because it is meant as a refutation. My discussion will talk a lot about my understanding of qunatum field theory, which is certainly wrong, and propose that string theory is a counterexample to Aristotle's main assertion, even if I can't be sure if all of the arguments Aristotle puts forward here even apply.

The following is the best one sentence summary I could come up with for Physics I.2:

Physics I.2 There must be more than one thing because the ways in which all reality can be made of one thing each require there to be multiple things.


Aristotle is agnostic about the kind of thing that is the one thing. Is it a substance, a property, an element?* It doesn't matter. If there is only one of them, then he asserts there will be a contradiction. Although most of his arguments are directed against Parmenides and Melissus, they are of a kind: find what seems to be a logical contradiction, e.g. the skinny man is fat, that comes from some assumptions. One that he asserts are that something cannot be finite and infinite at the same time.

These do not feel very compelling. For example,"...so there will be a substance as well as a quality, in which case it is twofold..." feels, at least in the translation, as if there is some confusion here. The two things are of such different kinds that I don't know how you can call them "two things," really.

What this brings to mind, though, is string theory. In the standard model of particle physics, you have a number of fields corresponding to two kinds of particle: bosons and fermions. The fermions are leptons (electrons) and quarks, which constitute matter. The bosons, photons, gluons, and W & Z particles, constitute the fundamental forces of nature (sans gravity), the connections between matter particles, in a way.

String theory makes all of these particles one kind of thing.

And because we can envision these particles as excitations in their corresponding fields. That is, whenever the electron field gains energy, a new electron is born. This is a little bit weird to think about in fundamental physics, because we don't have an independent concept of an electron field. But in condensed matter physics, we do have strong classical ideas about the meaning of some of the fields that appear in matter. We know about sound waves, we know about spin waves (magnetization waves). These waves are continuous and extend through the body. They have standing states, just like the standing waves on a string or a membrane that you might be able to envision.

And they're quantum mechanical.

The physics of these waves are describes as excitations in their corresponding fields. A spin wave is an excitation in the local magnetic polarization (magnetization) of a ferromagnet, and these excitations can only happen for certain multiples of a fundamental oscillation mode, just like the vibrating string. However, unlike the vibrating string,** there is a minimum energy necessary to excite a single vibration, and increasing the amplitude of the vibration requires additional quanta of that vibration mode. The amplitude of the spin wave is an integer number of of these quanta.

How much energy is this minimum energy? A ferromagnet (like your refrigerator magnets) is a material whose atoms' magnetic moments tend to align so that there is a net magnetic moment of the material. The minimum energy of a spin wave is exactly the amount of energy required to take one of these aligned moments and flip it 180 degrees. If you flip a spin like this, it can propagate through the material by successive mutual flips between neighbors. And we can examine the behavior of these spin flips, and their interactions with defects and oscillations

The spin wave and spin flip are two aspects of the same thing: a magnon.

This is the kind of quantum mechanical dualism you're used to, but it also shows the dualism between particle and field. The spin wave is an excitation over the entire field of atomic spins and the particle is an excitation at a single point, and depending on what we're investigating at the time.

This is how I still envision fields.

The difference between this and fundamental fields is that there's no substrate for the quantum field. There is no aether serving the role of the electromagnetic field that has some property that we excite electromagnetic waves in, and whose interactions with electrons are particulate photons. There is just the electromagnetic field. The same is true of the gluon field and weak fields. However just as water waves give you an analogy for water waves, the atoms in a material give you an idea about how a field works.

And it's more than a simple analogy. Many of the big "verifications" of high energy theorists that we've seen in recent years, Dirac and Majorana fermions, for example, are coming out of materials and metamaterials research in condensed matter. Experimentalists can construct systems with the correct symmetries to realize the particles. It's like creating universes on demand, universes that contain the thins you want to find.

In material, it's even easy to see something that becomes difficult to envision: how do these (at least) 25 fundamental fields of the standard model superpose over the entire universe? In our crystal lattice, quasiparticle fields correspond to different properties of the atomic and material structure. Lattice vibrations become phonons. Magnetic exicitations are magnons. And there are many others, but they all have this character of being related to properties of the collective properties of the material.

You can view string theory in a similar way: there is this fundamental structure of the string, and the 25 fields are all different manifestations of the properties of the string. Is it open or closed? How does it vibrate? In string theory there is just one kind of thing, the string, and since the different manifestations of this kind of string are all conceptualized as excitations in universal fields. So, there may be only a single, universal field.

Both of these interpretations, every particle is a string or every particle is an excitation in the stringy field, would count as Aristotle's "one principle."* String theory is a monist theory, the kind that Aristotle tries to disprove here. I don't think that the arguments he propounded in Physics I.2 really refute string theory, partly because many of them are arguments against specific philosophers and partly because many of them have mistaken logic of Greek mathematics.

For example, if I change a line in Physics I.2 to read "if there is a continuous fundamental field, then immediately it must be many fields because anything continuous must be divisible," then we have string theory exactly as I described it. But, string theory is logically consistent. It is also logically coherent. There is no obvious logical problem with string theory as mathematics. It's only possible problem is correspondence: even though it's currently the best guess at a unified theory of the world, it may never be shown to actually predict anything. But although string theory might not be correct, and there may even be no theory of everything,(*3) the field theoretic structure has both the continuity (say, the electromagnetic field) and the divisibility (say, the photon) built in. In some way. And in some way, it is a counterexample to Aristotle's assertions against monism in Physics I.2.

So, it seems to me, string theory refutes these assertions by Aristotle.

Monism is at least possible.

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* In the translation the, Aristotle is arguing against the idea that there is only one "principle," whether that principle is "a substance, a quantity, or a quality." Democritus has an "infinite number of principles," because his atomic theory had atoms of "all shapes" -- and there are no limits on the number of shapes there could be (If I recall, Epicurus would have a limited number in the form of regular polygons, when he finally got around to being born, if I recall). Heraclitus, apparently, had zero principles. So the wording here made life difficult for me: I wanted a principle to be something like Newton's Law, rather than a substance like water or air.

** I think. There probably should be a quantum mechanical description of transverse mechanical waves on strings, although I don't know what its use would be, or how you'd do an experiment to detect it.

This would be like building up the vibration of a guitar string by adding transverse vibrations to individual atoms, one at a time. That would probably make them phonons.

(*3) Although I should go through these arguments on the TOE page for Wikipedia before I say that.

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