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Tuesday, 27 August 2019

An Ontology of an Electron

The electron “has the properties” mass, charge and spin. That trick of grammar makes it seem like this:

i) Firstly, we have an electron,
ii) and then we have its properties.

Perhaps it's more accurate to say that an electron equals its properties. Thus:

electron = charge (−1) + mass (9.109389 × 10 −31 kg) + spin

This is the position known as the “bundle theory” and it's usually applied to macro-sized objects. In fact it seems that the bundle theory is more applicable to electrons that it is to, say, trees or persons.

We also have the position of Gottfried Wilhelm (von) Leibniz, who argued that all the properties of an object are essential to that object. There are, of course, arguments against this position. However, surely this claim is truer of an electron than it is of, say, a tree or a person. After all:

i) If an electron were not to have mass, charge and spin,
ii) then it wouldn't be an electron.

Or to say the same thing with more detail:

i) If an electron didn't have a charge of -1, a mass of 9.109389 × 10 −31 kg and spin,
ii) then it wouldn't be an electron.

After all, these three properties are equally essential to a electron being an electron. If it lost just one property (say spin) then it would no longer be an electron.

The problem with Leibniz's position is that it's only applicable to what philosophers call “individuals”. This is how Leibniz expressed his position:

The nature of an individual substance or of a complete being is to have a notion so complete that it is sufficient to contain and to allow us to deduce from it all the predicates of the subject to which this notion is attributed.”

That is to say that each “individual substance” has a complete “individual concept”. That complete individual concept contains all the properties of that subject. Or, in a more up-to-date jargon, all the “predicates” which are true of are also essential to x.

The problem here is that electrons are not individuals. That is, every electron is identical to every other electron - save for its spatial and locational properties. So, on a Leibnizean reading, every electron has the same essence. Therefore every electron can't be an individual. Boris Johnson, on the other hand, is an individual. That's because he doesn't share all his properties with every other person. That is, Boris Johnson's “individual essence” is not identical to, say, Swiss Tony's individual essence.

There is another Leibnizean issue here. According to the Principle of the Identity of Indiscernibles (PII), no two “substances” can be qualitatively identical yet still be (numerically) different objects. As you can see, this doesn't work for electrons. And that's one reason why they can't be classed as “individuals”. That's unless, as already mentioned, relational properties are included. Now, clearly, no two electrons can have the same relational/extrinsic properties. So, on a Leibnizean reading, how are we to treat the properties of location, etc. when it comes to electrons? Are they properties which can simply be ignored? Leibniz himself believed that spatial and temporal properties are properties of the individual itself. They were genuine properties.

Finally, it's mainly because most laypersons (as well as a few physicists) still see electrons as not being equal/identical to their charge, mass, spin, etc. that they see them as being Newtonian "hard" particles instead.

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