Some of my readership may be familiar with Plato’s Theory of Forms. The short version is that there are the circles, squares, trees, palaces, and goodnesses of the world we live in. And there is the ideal/perfect circle, square, tree, palace, and goodness in some other World of Forms. Because our world is constantly changing, it’s unreliable. It must be this static world filled with these ideal Forms that is the source of true knowledge and that is the true reality. As a metaphysics, this is clearly untenable.

Still, the notion of a perfect circle or square doesn’t offend us. No one feels cheated that our worldly squares deviate from equal sides when we measure precisely enough. So maybe Plato should have just stopped at geometry.

Well, maybe one step further. Listen to physicists sometime. “We’ve split the atom.” “We’ve measured the mass of the positron.” “We’ve found the Higgs boson.” As if there were only one of these particles. Curious, isn’t it?

In the standard model of particle physics1, there are six quarks, six leptons, and a few bosons.2 These are understood as classifications where the universe contains vast numbers of each. We have no problems allowing that each electron is exactly the same as every other electron. Here, we can grant, no, we must grant, that there is an ideal Form of an electron with a particular mass, charge, magnetic moment, lepton number, etc. that every incarnation must possess. In this case, the realized Form is as perfect as the ideal. Remarkable, isn’t it?

I’m not suggesting the belief is poorly-founded. Far from it. We’ve performed all manner of experiments that continually justify the equivalence of particles of a kind in every meaningful way. We can even observe that matter across the universe behaves the same as matter here, and so must also be identical. And since looking further away means looking further into the past, matter earlier in the universe is identical to matter now. Remarkable, isn’t it?

A classmate once told me about a theory he claimed checks out mathematically that maybe there’s only one electron (and presumably likewise for the other particles). It just zips around forwards and backwards through time (observed as positrons when going backwards) occasionally interacting, and thereby filling space-time with itself. This would explain why every electron has the same measurements: it’s always the same electron. Seductive, isn’t it?

I find this hard to believe given the imbalance between matter and antimatter, the problem of accounting around interactions, and it seems to require a fully pre-determined universe. Still, I find every interpretation of quantum mechanics hard to believe. If this model accords well with observations and makes good predictions, well, we’d have to consider it.

What a privilege for physics to be able to have such well-behaved objects of study. You can’t get more pure than pure Forms.

  1. The standard model looks clean and elegant as a table, but the equation that expresses this is anything but. We also know it’s wrong. But it sure makes really good predictions. That’s kind of a problem. 

  2. Six. Why six? I reject any spiritual or numerological appeals, but I’m going to come back to this number soon.