What is an electron?

[numan]

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An electron does not exist as a real particle -- at any time -- if by particle we mean an object similar to those we see around us.

If "particle" is a useful notion, it is something which has a tenuous hold on position in time and space. An electron can be localized only if its momentum is high. Low momentum mean a particle with no definite position in space -- or time.

Moreover, the notion of "an" electron is severely compromised -- like the Buddha, they have no "self-nature," they have absolutely no individuality, even in principle, for that would contradict clear scientific evidence.

Electrons are mutually indistinguishable; if they were distinguishable, they would obey Boltzmann statistics. In fact, they obey Fermi-Dirac statistics---statistics of indistinguishable entities which cannot share states; as opposed to indistinguishable entities, like photons, which can share states, and thus obey Bose-Einstein statistics.
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[numan]

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When counting states in statistical mechanics, to assert that electron A is in state 1 and electron B is in state 2, and then repeat the statement with the letters A and B interchanged, is not to describe two separate arrangements but only one.

An analogy would be to try exchanging two exactly equal bank balances between the two individuals to whom they are credited.

It is important to understand that the exactly equal bank balances represent the two particles, and the two people represent the two states!

This is somewhat counter-intuitive because the two states are distinguishable -- like the people. The two equal bank balances are not distinguishable -- like the electrons.

In those situations where an electron appears to have a continuous individual existence (as, for example, when the track of a trajectory appears on a photographic plate), the illusion is caused because the states which the electron occupy do have distinguishable individuality, even though electrons do not. When a series of contiguous states are occupied one at a time, and others nearby are not simultaneously occupied, then we have the case of a particle track or trajectory.

By the way, the space which the states occupy is not our ordinary space, but infinite-dimensional, complex Hilbert Space. If you do not have some knowledge of mathematics, you have no idea how much it differs from ordinary, four-dimensional Minkowski space-time!
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[numan]

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Erwin Schrödinger was so provoked by the slovenly concepts of matter that most people have that, in 1950, he condescended to write an article that could be understood by mere ordinary people, "What Is an Elementary Particle?" In it, he described three different ways of existing, which represent the statistics of physics: classical statistics (which describe objects which can be distinguished), and the statistics of two classes of indistinguishable objects: Bose-Einstein statistics (for particles with integer spin, like photons of light), and Fermi-Dirac statistics (for particles with half-integer spins, like electrons, protons, and neutrons).
My paraphrase follows :

Three schoolboys, Tom, Dick, and Harry, deserve a reward. The teacher has two rewards, to distribute to them (the rewards represent two particles).

1. The two rewards are two memorial medals with portraits of Newton and Shakespeare, respectively. Two boys get a medal, the third does not. Thus, there are three times three, that is nine, ways of distributing them: nine distributions. (classical statistics)

2. The rewards are two indistinguishable quarter-coins. Two boys can get a quarter, the third going without, just as in classical statistics -- but, in addition, one boy may get both quarters, the other two boys going without. Thus, there are three plus three, that is, six possible distributions. Remember, because the coins are indistinguishable you have fewer possibilities than in the classical statistics, and are left with only Tom and Dick; Dick and Harry; or Tom and Harry -- plus Tom, Dick, or Harry each getting two coins. (Bose-Einstein statistics)

3. The two rewards are two memberships in a country club. Two of the boys get a membership, the third does not. There are three, and only three, ways of distributing the memberships. [you cannot give two memberships to a single boy: memberships do not add when given to a single recipient] (Fermi-Dirac statistics)

Do not forget that the rewards represent the particles -- the boys represent the states which the particles [the rewards] may be in. Thus, "Newton is given to Dick" means : the particle "Newton" is in the state Dick.

The ways of counting are determined by the different natures of the particles : distinguishable medals, indistinguishable quarters, and memberships [both indistinguishable and incapable of being added together] .

The quarters are identical, but there can be different numbers of them in a specific state. There is no point in two boys exchanging their quarters, as there might be in the case of the memorial medals. Each boy can have different numbers of coins, though.

That possibility does not exist in the case of the club memberships. You cannot be a member of a club twice over --- you either are a member, or you are not.
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[numan]

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"The example may seem odd and inverted. One might think, "Why cannot the people be the electrons and various clubs their states? That would be so much more natural."

"The physicist regrets, but he cannot oblige. And this is just the salient point : the actual statistical behaviour of electrons cannnot be illustrated by any simile that represents them as identifiable things. Their actual physical and statistical behaviour clearly shows that they are not identifiable things."
----Erwin Schrödinger, key founder of quantum physics

Again, let us be absolutely clear : electrons [and other fundamental particles] are not THINGS ! --- not in the way that we are used to things being things !

Bosons are particles subject to Bose-Einstein statistics. They are indistinguishable entities of which any number can occupy the same quantum state -- fundamental to the existence of lasers, the strange behavior of liquid helium, super-conductivity, Bose-Einstein condensates, and many other physical phenomena.

Fermions are indistinguishable particles subject to Fermi-Dirac statistics. No two fermions can occupy the same quantum state. This fact explains the way electrons flow through wires as electricity -- and why all stars do not instantly collapse into black holes.

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