From: "Michael Weiss" Subject: Elementary, my dear Oz Date: Tue, 16 May 2000 18:45:56 -0400 Newsgroups: sci.physics.research Summary: [missing] Dear Oz, I think it was Wigner who first said that an elementary particle *is* an irreducible representation of the Poincare group. This post won't give the whole story --- for that, you'll have to wait for the mini-series. Instead I'll just chat about a classical analogy. Let's say we have a classical point-particle. Being hard-working physicists goofing off on s.p.r., we want to *describe* the state of the particle ---- five foot two, eyes of blue....No, of course we don't describle particles that way. To keep things simple, let's just describe the position. So we give three numbers, (x,y,z). These depend on our coordinate system, naturally. So we give rules for converting *this* batch of three numbers for one coordinate system into *another* three numbers for any other coordinate system. What if we have *two* point particles, forming a composite (i.e., non-elementary) particle? We will need *six* numbers, naturally, to describe the state of the composite particle. And when we switch coordinate systems, we have to transform the coordinates. Let us suppose that Sherlock Holmes is looking over our shoulder as we transform the coordinates. He doesn't know what the numbers represent --- they could represent the lengths of the cat's toe-nails, for all he can tell. But he does notice that the six numbers behave a certain way when they are transformed. Namely, they can be divided into two groups of three, with the property that the two groups transform independently --- to transform the first group of three numbers, you don't need to know any of the values in the second group. And vice versa. This isn't true for the three numbers describing a *single* point-particle. You need all three numbers to transform any one of them (except for especially simple coordinate changes). Just from the way we transform coordinates, Sherlock can deduce that the six numbers represent something composite, and the three numbers represent something elementary. In roughly the same way, by studying how the *description* of a quantum particle changes as you change your viewpoint, you (or Sherlock) can decide if the particle is elementary or composite. Of course, this depends on having the right description in the first place.