Does a Particle have a Personality?

(I once heard of somebody who named their two cats Article and Particle. But I digress...)

Among the many things I'm currently in the middle of reading is Lisa Randall's Warped Passages. It's a good way for a layman to learn a bit about many recent developments in theoretical physics. Even if some of her stories are a bit hokey and her name-dropping a bit grating.

I was led to the following thought:

Generally a mathematical abstraction is just that, an abstraction of certain aspects of objects (or situations or experiences or whatever). They gather together what entities have in common, explicitly leaving aside what makes them individuals, unique. Uniquenesses do not mathematical relations make.

When statisticians count "households" in a demographic, there's no concern for who is arguing with whom under any particular roof. We count nine planets (wait...eight...damn you Neil DeGrasse Tyson...) without in counting distinguishing that Saturn has rings and Mercury does not.

But particles are represented differently, as nothing beyond pure abstraction. There is nothing that makes them individuals. A photon is a photon is a photon. Same with electrons, etc. Any can be replaced with another of its own kind, and this replacement makes not the slightest bit of difference.

But...can this be right? Does a particle's individual history not matter at all, not serve to distinguish it from others of its kind? Does photon #17483 have no individual quirks and eccentricities that serve to distinguish it from photon #334981?

For nothing at scales above simple molecules is this true. Unicellular organisms are (barely) distinguishable individuals. Galaxies and galactic clusters are unique. Potentially, so are universes, with separate sets of physical laws (or at least separate constants and parameters of those laws) and different, quite complex histories.

Is there a scale of sizes of things such that, when we get small enough, we suddenly (or is it gradually) transition from the incorrigibly unique to the thoroughly interchangeable?

Nietzsche's Individualism

When a traveler who had seen many lands and national and several continents was asked what characteristic he discovered to be common to all of humanity, he replied: "They have a tendency toward laziness." To many it will seem that his reply would have been more accurate and valid if he had said: "They are all fearful. They hide behind customs and opinions." At bottom, every human being knows perfectly well that he lives in the world just once, as a unicum, and that no coincidence, regardless how strange, will ever for a second time concoct out of this amazingly variegated diversity the unity that he is. He knows this, but he conceals it like a bad conscience. Why? Out of fear of his neighbor who demands convention and who cloaks himself with it. But what is it that forces the individual to fear his neighbor, to think and act like a part of a herd instead of taking pleasure in being himself? Modesty, perhaps, in a few rare instances. In most instances it is convenience, indolence--in short, that tendency toward laziness of which the traveler spoke. He is right: human beings are lazier than they are fearful, and what they fear most are those hardships that unconditional honesty and nakedness would foist upon them. Artists alone despise this lethargic promenading draped in borrowed manners and appropriated opinions, and they expose the hidden secret, everyone's bad conscience, the principle that every human being is a one-of-a-kind miracle. They dare to show us how every human being, down to each movement of his muscles, is himself and himself alone; moreover, they show us that in the strict consistency of his uniqueness he is beautiful and worthy of contemplation, as novel and incredible as every work of nature, and anything but boring. When the great thinker disdains human beings, it is their laziness he disdains, for it is laziness that makes them appear to be mass-produced commodities, to be indifferent, unworthy of human interchange and instruction. The human being who does not want to be a part of the masses need only to cease to go easy on himself; let him follow his conscience, which cries out to him: "Be yourself! You are none of those things that you now do, think, and desire."

(from "Schopenhauer as Educator" in Unfashionable Observations, p. 171-172)

Or in contemporary slang: do you.