"Daryl McCullough" wrote in message
...
Jay R. Yablon says...

Dear friends:

I am just putting the finishing touches on the five-dimensional paper
which I have been working on intensively for the past several weeks,
and
which I have had in mind on and off for several years. I will be
doing
a final proofread tomorrow and posting it to my weblog, then trying to
get it journal-published in the near future. I wanted to give you
all,
and the commentariat at sci.physics.foundations, the first look at
this.

http://jayryablon.files.wordpress.co...in-2-22-08.pdf

It is a long paper, but if you read the introduction, and more
importantly, the conclusion, you should have a pretty good roadmap to
help you navigate through in an efficient way.

I look forward to your comments

I think that the paper is good, except for one small point.
You speculate that the quantity

m d/dtau x_5

represents intrinsic spin. I don't believe that is correct. For
one thing, in your paper, it is already identified with electric
charge. This quantity is nonzero for any charged particle, whether
or not it has intrinsic spin.

It *will* be quantized, because it represents momentum in
the x_5 direction. If the universe is cyclic in that
direction, then that means that any wave function must
be periodic in that direction, which means that the momentum
p_5 is quantized in units proportional to h-bar/(2 pi R)
where 2 pi R is the circumference in the x_5 direction.

--
Daryl McCullough
Ithaca, NY

Hi Daryl:

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.

More generally, I do think the intrinsic spin interpretation is worth
exploring, and I would not dismiss it out of hand. The use of the term
"intrinsic" to describe an inherent quantized angular momentum of
elementary particles, covers up what is actually a deep ignorance of
what this really means. Why? For a material body to have an angular
momentum, one must implicitly consider a radius R with which that body
circles about an origin. At the same time, nobody believes that
intrinsic spin represents an angular momentum about a radius R in the
three usual spatial dimensions. By associating intrinsic spin with
motion through a fourth, compactified, hyper-cylindrical spatial
dimension, one simultaneously makes sense of intrinsic spin and of a
compact fourth spatial dimension. The material body now has a spatial
radius R outside of the usual three spatial dimensions to give meaning
to its "intrinsic" spin, and the compactified fourth dimension now takes
on meaning as something which is physically observed, via the phenomenon
of intrinsic spin, and not merely a fictional idea that gives people
pause about Klauza-Klein theories specifically, and dimensional
compactification in general.

Jay.

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.

--
Daryl McCullough
Ithaca, NY

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.

Edward Green says...

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?

Sure, angular momentum makes sense in any number of dimensions.
It's not a *vector* unless there are exactly 3 spatial dimensions,
but the analogous tensor makes sense no matter what the dimensionality.
The angular momentum tensor L^jk = x^j p^k - x^k p^j makes sense
whenever there is a metric tensor, and it is conserved for central
forces in any number of dimensions. In the particular case of
4D space, there are 6 independent nonzero components of this tensor

L^23, L^31, L^12, L^41, L^42, L^43

The first three are the same as the 3-space angular momentum
components L_x = L^23, L_y = L^31 and L_z = L^12. The last
three are new conserved quantities which, from the 3-D point
of view seem to form a pseudo vector Q with components
Q_x = L^41, Q_y = L^42, Q_z = L^43.

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.

It's recognizable as 3D angular momentum plus another
vector.

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?

The main change that results from rolling up a dimension is that
it tends to make low-energy behavior independent of the curled
up dimension. So physical quantities (scalar, vector and tensor
fields) can depend on x^1, x^2 and x^3, but don't typically depend
on x^4.

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?

Certainly rotations in and out of the extra dimension are
possible. However, if the extent of the curled-up dimension
is very small, it's hard to get any significant torque.

--
Daryl McCullough
Ithaca, NY