On Feb 29, 10:52*am, (Daryl McCullough)
wrote:
Jay R. Yablon says...





Thought more about your point. *As I said in an earlier reply, the
neutrino is the issue. *That is, the neutrino may appear to present a
problem for such an intrinsic spin interpretation, because it does not
have electric charge.

However, the theory I have put forth is a U(1) theory of
electromagnetism and gravitation. *Specifically, the q in the q/m ratio
upon which the intrinsic spin interpretation is based, is a U(1) charge
generator. *Therefore, the only particles one can talk about in this
context are electrons, photons, and gravitons. *Strictly speaking, one
cannot even talk about neutrinos, unless and until the development here
is extended to Yang-Mills theory, and specifically, the SU(2)xU(1)
theory of electroweak interactions. *When SU(2)xU(1) is considered, the
(left-chiral) neutrino, though having q=0, does obtain a non-zero weak
isospin I^3 = 1/2. *This isospin charge, one would suspect, may provide
the basis for understanding the intrinsic spin of the neutrino through a
compactified fifth spatial dimension.

I'm pretty sure that interpreting momentum/velocity in the x_5 direction
as intrinsic spin just doesn't work. Think about a positronium atom,
composed of an electron and a positron in orbit around each other.
The charges cancel, but the intrinsic spins do *not*, necessarily.
They can be aligned, so that the total spin is 1, or they can be
anti-aligned, so that the total spin is 0. Total spin and total
charge are two independent quantities.

Also, the important thing about intrinsic spin, and the reason
it is considered a kind of angular momentum, is because only
Total angular momentum is conserved, not spin or orbital
angular momentum separately.

In contrast, the momentum in the x_5 direction has no connection
with orbital angular momentum.

There are a few things that are not immediately clear, to say the
least. Take a 4 + 1 dimensional world vs. 3 + 1; for now, no "rolled
up" dimensions.

First question: is there an analogue/extension of "angular momentum"
in such a world? It seems to me axial vector only exist in 3
dimensions. Now, that would not mean the posited extension can not
exist, but it might not be very recognizable.

Second question: supposing we have answered the first question, what
happens to this extension of angular momentum when we do roll up the
fifth dimension?

In 3 spatial dimensions each component of angular momentum is
conserved separatedly, but they are in some sense fungible: by
applying an arbitrary torque to a body we can create angular momentum
about axes which previously showed none (creating an opposite
increment in the system supplying the torque). This suggests that the
extra component of angular momentum (assuming this "component"
language makes sense, since the total object may not be represented by
a 4-vector) should be coupled to the other 3 ?

But maybe this just means that paired spins can be simulataneously
created or distroyed.