Re: Non-Symmetric Energy Tensors and Kaluza Klein Experiment

Daryl, before I forget, are you at Cornell over in Ithaca? My son
Joshua just graduated last year from -- what else -- their engineering
physics department. Comments inline.

"Daryl McCullough" <stevendaryl3016@xxxxxxxxx> wrote in message
news:fsbgdu01lk1@xxxxxxxxxxxxxxxxxx
Jay R. Yablon says...

After reviewing some very helpful discussion in prior threads
regarding
non-symmetric energy tensors and a Kaluza-Klein experiment, and am
starting to shift my viewpoint to be in opposition to the idea of
using
a non-symmetric (Cartan / Tortion) energy tensor because of the
adverse
impact this has on formulating a metric theory of gravitation.

There is a *non-symmetric* energy tensor in equations (15.11) to
(15.13)
of:

http://jayryablon.files.wordpress.com/2008/03/kaluza-klein-theory-and-lorentz-force-geodesics-60.pdf

It's a nice paper, but I just don't think that the section on
intrinsic
spin is correct. You speculate that intrinsic spin is "velocity" in
the
extra, rolled-up dimension (actually, it's momentum in the extra
dimension,
p_5, since you have to multiply by mass to get a constant).

It is both. You do not have a momentum without mass and velocity.

I don't see how that can possibly be correct.

Kaluza-Klein already associated p_5 with
electric charge, and we know that charge is unrelated to intrinsic
spin.
Note that an electron's spin can be in two states: spin-up and
spin-down.
If spin is associated with charge, then that would imply that flipping
the spin would flip the charge, changing an electron into a positron.
That is not observed.

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. 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. These then combine to give gamma^1,2,3 in the Weyl
representation, and the gamma^5 emerges from the SU(2)xU(1) symmetry of
the space dimensions. The gamma^0 for time then arises from principles
of general covariance.

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? 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. This is not like monogamy -- p_5 is
already married with charge and can't also fool around with spin (though
living right near the State Capitol of New York and watching our
governors this past week, I probably should stay away from those sorts
of jokes ;-). 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. This is how x^5 motion "projects" itself into to
observable universe, and this is all *direct* evidence of the a fifth
dimension which has been heretofore dismissed for want of direct
evidence. These a-e are not mutually exclusive, and in a proper
unification that is exactly the sort of thing one should be keeping an
eye out for. To take your approach would be like Maxwell saying "Gauss
says the electric charge generates the electric field, so how can it be
responsible for magnetic fields also?" Thinking in such a way is much
too restrictive.

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. I will say, first,
I believe both orbital and spin angular momentum will eventually be
shown to arise from p_5. Second, I am thus far only looking at spin,
and can readily overcome the objection raised by considering an l=0 m=0
s=1/2 electron. Ground state. Then, all we are dealing with is spin.
Just explaining spin -- divorced from angular momentum (just like our
former governor will proably be ;-) -- on a geometric foundation is
something that to my knowledge, nobody has succeeded at before.


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. You are back to forcing p_5 to
be monogamous.


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. It takes SU(2)_W x U(1)_Y to get to the neutrino.
But, once we go that route, I am confident that this will be solidly
resolved.

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 2 pi R is the distance
*around* the fifth dimension, then an electron's wavelength
lambda will necessarily be such that an integral number
of wavelengths fit in 2 pi R. So this leads to the
quantization condition

lambda = 2 pi R/n

or in terms of p_5,

p_5 = 2 pi h-bar/lambda = n h-bar/R

Since p_5 is proportional to Q/square-root(G),
this gives

Q = constant * n * h-bar * square-root(G)/R

If we set n=1 and Q=the charge on an electron,
this again gives R around a Planck length
(to within a factor of 10 or so).

These are very good calculations to work from -- and I realize that G is
the gravitational constant -- sorry, my mind earlier was on G_uv. These
will be helpful in trying to get a handle on rest mass, which is also in
my queue for this project.


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.

Jay.


--
Daryl McCullough
Ithaca, NY



.

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