A fermion is any quantum entity (such as particles or even entire atoms) with total spin angular momentum equal to 1/2 of an odd integer. The Spin-Statistics Theorem shows that all fermions obey the Pauli Exclusion Principle. All fundamental matter particles (fermions and leptons) have spin 1/2. Any quantum entity that is not a fermion is a boson.

Author's Note: this write-up assumes the correctness of standard model quantum theory and quantum electrodynamics. Standard model and QED are most certainly wrong (everything in science is wrong), but they're the best theories we have to date to explain such things. Besides, they're fun.

Ancient alchemists believed it was possible to separate the various qualities of matter. They wanted to distill the "red" from a rose to inject into a pansy, or transfer the "makes you drunk" from wine to eggs, so you can have omelets which make you tipsy. One of the more impressive feats considered was to distill the "substance" or "function" out of something, so you could have scissors without the "able to cut" and "able to cut" without the scissors. With the development of chemistry some of these things were accomplished, but many were found to be laughable under budding chemical theories, especially this last notion. Early chemists were wrong, at least in theory1.

There are two interesting properties of matter:

  1. It takes up space (you can't put other stuff where it is).
  2. It can exert force (you can poke stuff with it).

The first of these is caused by fermions (named after Enrico Fermi), the second of these is caused by boson (named after Satyendra Nath Bose). Everything we call matter is made up of both these basic particles, but they can theoretically be separated.

A pair of scissors sit on your desk (rather then fall through your desk) because both the desk and the scissors are made up of fermions, and two fermions cannot overlap2. A pair of scissors is able to cut paper because the bosons emitted by the edge of the scissors are able to push the molecules of the paper apart. If you could somehow turn all the fermions of a pair of scissors into bosons it would fall into the desk, though they might not pass through the desk cleanly (instead being absorbed or scattered). Likewise, if you could turn all the bosons in a pair of scissors into fermions, the edge would not cut3.

This is somewhat factitious, of course. While getting fermions to behave like bosons is not a problem4, we would probably not be comfortable calling the resultant object a pair of scissors, since it would have little form or structure (you need fermions to provide structure). Likewise, an all fermion pair of scissors would fall apart, since it's the bosons that hold the fermions together (chemical bonds are caused by boson interaction).

This is less of a problem with single particles. The two defining qualities of an electron are: other electrons of the same state cannot coexist with it, and it produces electric and magnetic fields which can exert force on other charged particles. As you can guess by now, the first of these is because the electron itself is a fermion and the second is because the electron is constantly emitting virtual bosons. Separating the fermions from the bosons could give you electrons without fields, and fields without electrons.

This could be done, at least in theory. If we can't do so, then the theory might just be wrong. . ..

1. At least, if certain modern theories are taken to their logical conclusion.
2. Technically, two fermions cannot be in the same state. Location is an important aspect of state, but not the only one. Two fermions can spatially overlap only if they differ in some other aspect of their state (such as spin).
3. You'd have other problems, of course. There'd be infinitely many fermions in the space the scissors used to be, and many of them would undoubtedly be overlapping. If you've been paying attention, you know this can't happen.
4. In theory, getting fermions to behave as bosons is no problem. In practice, it can be tricky. We've done it (such as in the formation of a BEC), but we can't do it in all cases.

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