Scientists stop light

[MrFun]

Originally posted by Rogan Josh

So God didn't say 'Let there be light'. He said 'Let there be a local U(1) symmetry'.

This could be good sig material.

[Japher]

This could be good sig material.

If you were a geek...


The Equivalence of Mass and Energy

I like the wrong way better, it's so much simpilar

[alva]

Are you with me so far?

Uuummhh, nah, lost this thread somewhere in the first few words of the first post.

Although I have absolutely noooooo idea what you guys are talking about (hmm, that's probably why):
unworthy:

[Az]

Now, lets just imagine a quantum mechanics system with only electrons in it. If we had only electrons, and made this transformation, we would find that the physical results do change. It is not a symmetry. But if we include photons in the theory, the transformation on the photons exactly cancels out the transformation on the electrons and we have a symmetry again.

In other words, by insisting that the symmetry transformation be 'local' (ie position dependent), we insist on the existence of light, and in fact the electromagnetic force just drops out too.

In fact, all the forces come this way. Electromagnetism comes from insisting on a U(1) symmetry, the weak nuclear force comes from a local SU(2) symmetry (the symmetry group of a sphere), and the strong nuclear force is local SU(3). It is thought (but not yet proven) that gravity is actually local supersymmetry (supersymmetry is a symmetry between particles with different spins).

Interesting. Now what do you mean by U1 symmetry, or SU2 or SU3? I've never seen this nomenclature.

[Ramo]

Interesting. Now what do you mean by U1 symmetry, or SU2 or SU3? I've never seen this nomenclature.

What a symmetry is, would be to find a change of bases for your system under which the relevant operation (in quantum mechanics, it's looking at the magnitude squared of your wave function) yields the same result. Look at Rogan's example of multiplying by exp(if), for instance.

U(1), SU(2), and SU(3) are all what are called "groups" of transformations, each bringing about some sort of symmetry. Groups are sets of elements such that, under some operation, they're closed under this operation, there's an inverse under this operation for every element, and there exists an identity for this operation.

U(n) is called the unitary group. Any matrix, P, in U(n) where you multiply P by its Hermitian conjugate (basically transpose the matrix and switch the signs of the i's) you get the identity. SU(n) is called the special unitary group, which is the set of unitary matrices whose determinant is 1.

I won't be able to tell you what the unitary group has to do with e&m, or what the special unitary groups have to do with the weak and strong forces.

[Az]

Funny, we use different nomenclature for symmetry groups.

do C3v D6h ring any bells?

[Ramo]

Are those supposed to be two seperate groups? The second one sort of looks like it might be a dihedral group.

[Provost Harrison]

I finally had a research paper published the other day...can't remember the reference though because we are currently moving house and my mother has packed it away

[MrFun]

good ol' mom . . . . . . .

[Rogan Josh]

I had a paper accepted by Nuclear Physics B just today, and sent another one off to Physics Letters B.