LostConjugate said:
So where did I go wrong when I said that fermions were made from bosons..?
[...]
we can get particles from high enough energy photons
(Perhaps my answer below should be in a separate thread, but I put it here for now...)
LostConjugate,
Have you come across the notion of the Wigner method for classification of elementary particles? I suspect the answer is "no", so here's the idea (very briefly):
All elementary particle types are classified according to the so-called "unitary irreducible representations of the Poincare group". Another way of saying this is that every type of elementary particle must correspond to one of the physically distinguishable ways that things can transform under rotations, boosts and translations. It turns out that these "ways" can be classified in terms of 2 invariants: the (relativistic) mass^2 and something known as W^2 -- where W is the Pauli-Lubanski vector, which can be regarded as a relativistic generalization of spin.
So (again cutting a longer story short) we can classify elementary particle types according to their mass, spin (and also their component of spin in an arbitrary direction). This classification is not exhaustive of course, because there's also the other so-called "intrinsic" properties such as electric charge, hypercharge, lepton number, baryon number, etc. The set of all these properties is thought of as the set of "quantum numbers" that make one type of particle different from another.
Additionally, we have ordinary energy, momentum, angular momentum, etc. For all these things to be useful in describing processes, we want their total amounts to be conserved during interactions. E.g., the total charge must be conserved, as must the total energy and momentum, the total lepton number, etc, etc.
So how is all this relevant to \gamma + \gamma \leftrightarrow e^- + e^+ ?
Well, basically the elementary particles are not made "from" anything (else they would not be "elementary"). However, we can describe any given particle instance by the set of quantum numbers outlined above and a few more -- which I'll illustrate by re-writing the equation above with some extra arguments:
<br />
\gamma(E_1, p_1, \sigma_1, \dots) + \gamma(E_2, p_2, \sigma_2, \dots) \leftrightarrow e^-(E_3, p_3, \sigma_3, \dots) + e^+(E_4, p_4, \sigma_4, \dots)<br />
where E means energy, P means momentum, \sigma means spin, and the
"..." means all the other quantum numbers.
For conservation of energy in the reaction, we must have
<br />
E_1 + E_2 = E_3 + E_4<br />
and similarly for the other quantum numbers.
So is total electric charge conserved? Yes, because photons have charge=0 and the
sum of electric charge on the rhs is 1 + -1 = 0.
The only reactions that can occur are those that satisfy these conservation laws for
total quantum numbers.
Can you see where I'm going with all this? Bosons are not "made from" fermions, but we
can find reactions such that a collection of bosons can be
converted into a collection of
fermions, etc, etc.
HTH.