Re: Non-Symmetric Energy Tensors and Kaluza Klein Experiment

Jay R. Yablon says...

Daryl, before I forget, are you at Cornell over in Ithaca?

No, I'm a "townie", unconnected with Cornell.

The draft at
http://jayryablon.files.wordpress.com/2008/03/intrinsic-spin-22.pdf goes
part way there. I will be adding a new section in the near future to
show the ground-up derivation of Dirac's equation out of the compact
dimension. This will take care of particles and antiparticles on top of
spins. In brief, what I will show is that 5th-D rotation in *one*
direction yields particles with two-valued spin, as I have already
shown.

It's not just that spin is two-valued. It is two valued *relative*
to an axis. That is, given a direction D in 3-space, an electron
is measured either to have spin +1/2 relative to that direction,
or -1/2 relative to that direction. The spin can be +1/2 relative
to one axis and -1/2 relative to another. I don't see how that
can possibly work with the momentum p_5.

The 5th-D rotation *oppositely* produces antiparticles with two
valued spin by the exact same development, but for a "-" sign in front
of the Dirac gamma.

But the problem is that charge is *independent* of spin state.
You can have a spin-up electron, a spin-down electron, a spin-up
positron, a spin-down positron. The sign of p_5 can account for
the difference between an electron and a positron, but it cannot
*also* account for the difference between a spin-up electron and
a spin-down electron. A point particle in the lowest energy state
in Kaluza-Klein space has 2 possible states: p_5 positive and
p_5 negative. You need 4 states to account for spin and charge.

I would like for a moment to pick apart your statement "Kaluza-Klein
already associated p_5 with electric charge, and we know that charge is
unrelated to intrinsic spin," because I see several flaws. "We know
that charge is unrelated to intrinsic spin" is no more than an
assertion. How do we know?

Because there are neutral particles with spin, and because
there are positively charged particles with spin-up and
positively charged particles with spin-down and there are
negatively charged particles with spin-up and negatively
charged particles with spin-down. And because charge is
conserved in all interactions, but spin orientation is
not.

When you say "Kaluza-Klein already
associated p_5 with electric charge," yes, I agree, but your implication
is that the p_5 is "already spoken for" and since charge already has it,
the spin can't have it too.

That's exactly the case. For a particle in lowest energy state,
there are two possible p_5 states: p_5 can be positive, or it
can be negative. But you need at least 4 states to account for
positive charge/spin-up, positive charge/spin-down,
negative charge/spin-up, negative charge/spin-down.

Unification of theories is all about finding *confluence
of phenomena.* The more phenomena which can be shown to emerge from a
common foundation, the better. In my view, the x^5 motion is
responsible for a) charge, b) intrinsic spin c) orbital angular momentum
(though I have not developed that yet) d) the particle mass and e)
uncertainty.

Yes, that's your view, but it seems to me that it is certainly
false.

We also know that an electron's spin state is *not* a constant.
Total angular momentum (the sum of spin angular momentum and
orbital angular momentum) is conserved, but spin by itself is
not. So there is a coupling between spin and ordinary, orbital
angular momentum. There is no such coupling between orbital
angular momentum and p_5.

You are continuing the line of thinking from above.

Yes, because it is correct. Your p_5 has *nothing* to do
with angular momentum.

Also, intrinsic spin has a *direction* in ordinary 3-space. A
particle has spin-up or spin-down relative to a particular
direction in 3-space. In contrast, p_5 has no relationship to
the other 3-space directions.

Same thinking. Lots of preconception.

It seems to me that you have a preconception that
spin has something to do with p_5, in spite of the
fact that there is zero reason to believe that, and
many reasons for believing the opposite.

Putting these objections together with the already known
objection that neutrinos are neutral, but have intrinsic
spin,

I would agree that I cannot explain the neutrino spin from what I have
developed so far, because this is a U(1) theory of gravitation and
electrodynamics.

Sure. So it explains the electrodynamics of charged, zero-spin
particles.

it would seem to me that there is no reason at all
for believing that p_5 has anything to do with intrinsic
spin. The fact that it is quantized is not evidence that
p_5 has to do with spin, it is evidence that p_5 is momentum
in a dimension that is *circular*.

It is evidence of both. What motion do we know of, which is circular,
which does not have an associated angular momentum magnitude with
orthogonal orientation?

If you want to call p_5 an "angular momentum", you can. The
point is that it *isn't* L_x, L_y, or L_z. The angular momentum
L_x represents angular motion in the y-z plane. L_y represents
angular motion in the x-z plane. L_z represents angular motion
in the x-y plane. p_5 has *nothing* to do with the x-y plane
or x-z plane or y-z plane. It's orthogonal to all of those.

I really think that associating the extra dimension
with intrinsic is barking up the wrong tree.

Only time will tell what is up that tree. I will keep barking, because
I nose is telling me that this tree ain't empty, ;-)

Thanks again Daryl -- very constructive and helpful comments.

Okay, good luck, but I don't see it as very promising.

--
Daryl McCullough
Ithaca, NY

.

Relevant Pages