Kaluza-Klein paper unifying electrodynamics and gravitation -- PLEASE REVIEW AND COMMENT
Jay R. Yablon
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.com/2008/02/kaluza-klein-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 believe that this paper fully and
completely unifies gravitation and electrodynamics, and in the scheme of
things, will be as significant in the 21st century, as GTR 1916 was in
the 20th.
Please, see if you can find some time to take a good look. And, keep an
eye on my weblog as well as SPF over the coming days, for final updates
before I take this to the journals.
Any support, help, ideas, etc., would be greatly appreciated at this
time.
Best regards,
Jay.
____________________________
Jay R. Yablon
Email: jya...@nycap.rr.com
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm
Androcles
"Jay R. Yablon" <jya...@nycap.rr.com> wrote in message
news:627gkqF...@mid.individual.net...
| 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.com/2008/02/kaluza-klein-2-22-08.pdf
I found a typographical error.
"The possibility of employing a fifth spacetime dimension to unite
classical gravitation and electrodynamics has intrigued physicists
for almost a century. "
Should read:
"The possibility of employing a fifth spacetime dimension to unite
classical gravitation and electrodynamics has intrigued FUCKHEADS
for almost a century."
Sue...
> 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.com/2008/02/kaluza-klein-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 believe that this paper fully and
> completely unifies gravitation and electrodynamics, and in the scheme of
> things, will be as significant in the 21st century, as GTR 1916 was in
> the 20th.
>
> Please, see if you can find some time to take a good look. And, keep an
> eye on my weblog as well as SPF over the coming days, for final updates
> before I take this to the journals.
>
> Any support, help, ideas, etc., would be greatly appreciated at this
> time.
Your observations ring true: :-)
<< But electrical masses have long presented a dilemma,
because the electrical mass of a material body, say, an
electron, is not equal to its inertial mass, and this
inequivalence is the mainspring of the forces we feel
which clearly, as a physical sensation, differentiate the
acceleration of Newton's a=F/m from that of the
gravitational a=9.8 meters/sec2 near the surface
of the earth. The General Theory of Relativity, in the
end, captured inertial motion and its close
cousin of free-fall motion in a gravitational field,
in the most elegant way, as simple geodesic
motion in a curved Riemannian geometry along
geodesic paths which coincide precisely with the
paths one observes for bodies moving under
gravitational influences. But the electrical motion
of the Lorentz force has long been the "odd man out,"
because it was something distinct from
gravitation: it did not appear to follow a geodesic path,
and it did not "feel" like inertial or
gravitational free fall motions because it created
the sensation of a force which we can measure
when we place a scale between ourselves and the
ground on which we stand or the elevator
which accelerates us upward, because of the collective
electrical repulsion between billions of
electrons in our bodies and billions more in the
surface against which we are pressing.
The key to unlocking this mystery, and ultimately,
to placing gravitation and electromagnetism within the
same framework, is to understand the motion of electrical
masses - as governed by the experimentally-grounded
Lorentz force law - as geodesic motion no less that
that of gravitation, but in a spacetime that is extended
to contain a single additional fifth dimension: the
dimension first proposed long ago by Kaluza and Klein.
By placing electrical masses onto their own geodesics
in a five-dimensional Riemannian geometry which embeds the
spacetime of our daily experience into its seamless
fabric, we find that the long-standing quest to
unite gravitation and electrodynamics may finally
arrive at a safe haven on a firm foundation. >>
--J.R. Yablon
http://jayryablon.files.wordpress.com/2008/02/kaluza-klein-2-22-08.pdf
When should we expect pages 37 through ~75 to formalise
a plausible mechanism along these lines?:
-- C. P. Kouropoulos
http://arxiv.org/abs/physics/0107015
Sue...
>
> Best regards,
>
> Jay.
> ____________________________
> Jay R. Yablon
> Email: jyab...@nycap.rr.com
Jay R. Yablon
news:ce629a5a-3a6c-4dd6...@s37g2000prg.googlegroups.com...
. . .
just with sections 2 and 3 and let me know if you think the premises are
sound.
Jay.
Juan R.
> 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.com/2008/02/kaluza-klein-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 believe that this paper fully and
> completely unifies gravitation and electrodynamics, and in the scheme of
> things, will be as significant in the 21st century, as GTR 1916 was in
> the 20th.
Sorry, but I am rather sure it will be less significant is being claimed.
As a note, it is really interesting i am working now in a paper shows the
deficiencies and limitations of a pure geometric formulation of gravity.
Deficiencies and limitations are not noticed in conventional literature:
Carroll, Ivanenko & Sardanashvili, Will, Christian.
It is interesting that set of limitations and deficiencies are not
present in alternative descriptions (e.g. AAAD and scalar-tensor field
theory).
Regarding pure electrodynamics, your description is adding a new set of
geodesical limitations and deficiencies to the well-known limitations and
deficiencies associated to a field approach:
{Chubykalo & Smirnov-Rueda 1996}
Action at a distance as a full-value solution of Maxwell equations: The
basis and application of the separated-potentials method. 1996. Phys.
Rev. E 53, 5373. Chubykalo, Andrew E; Smirnov-Rueda , Roman.
Erratum: Action at a distance as a full-value solution of Maxwell
equations: The basis and application of the separated-potentials method
[Phys. Rev. E 53, 5373 (1996)] . 1997. Phys. Rev. E 55, 3793. Chubykalo,
Andrew E; Smirnov-Rueda , Roman.
> Please, see if you can find some time to take a good look. And, keep an
> eye on my weblog as well as SPF over the coming days, for final updates
> before I take this to the journals.
>
> Any support, help, ideas, etc., would be greatly appreciated at this
> time.
Sorry to say this, but my point is that a more *complete* modelling of
interactions and unification of electrodynamical and gravitational
interactions (which is being done at the Center) is *very* far from the
mathematics and physics on your paper.
In fact, the local time-explicit functions, the metric structure of
spacetime, the geodesic hypotesis and the connection, the past light cone
structure, and even the own structure of spacetime are *approximations*
arise in some well-defined limit of a more fundamental theory is being
developed by me at the Center and by others.
Of course, that does *not* dismiss the achievements on your paper. But
nobody would believe that work is fundamental or will remain a
fundamental piece during 21st...
>
> Best regards,
>
> Jay.
> ____________________________
> Jay R. Yablon
> Email: jya...@nycap.rr.com
> co-moderator: sci.physics.foundations Weblog:
> http://jayryablon.wordpress.com/ Web Site:
> http://home.nycap.rr.com/jry/FermionMass.htm
--
I follow http://canonicalscience.org/en/miscellaneouszone/guidelines.txt
Dono
<j...@canonicalscience.com> wrote:
Karandash
Dono
Karandash
> On Feb 22, 8:23 am, Karandash <D...@trolls.nl> wrote:
>> Troll Dono trolled:
>>
>> http://www.albinoblacksheep.com/flash/youare
>>
>> --http://www.helinium.nl/trolltech.gif
>
> Dono, old fart, go fuck yourself:
>
> http://www.helinium.nl/trolltech.gif
Bryan Olson
> I am just putting the finishing touches on the five-dimensional paper
> I look forward to your comments;
Most journals prefer an informative abstract to a
descriptive abstract. State your primary result in the first
sentence. "We examine" is for the introduction; "first
explored by" is background. An informative abstract is just
your results.
> I believe that this paper fully and
> completely unifies gravitation and electrodynamics,
Then state they are unified, right at the top. From how you
describe what is notable about your paper, the title should
be something like: "Five-dimensional unification of gravity
and electrodynamics"
> and in the scheme of
> things, will be as significant in the 21st century, as GTR 1916 was in
> the 20th.
So cut the weasel-words: "it appears", "may be", "may well be".
It is or it isn't. All "may be" says is that if I read your
paper I still won't know which.
> Please, see if you can find some time to take a good look.
I didn't get beyond the abstract. I'm just a computer programmer.
--
--Bryan
Bill Hobba
Looks fine to me Jay. Good work and thanks for posting it.
The problem with Kaluza Klein is not that it does not unify gravity and EM -
it is the cylinder assumption. This imposes U(1) symmetry which is known to
be the basis of EM. Basically you have assumed EM to start with. But good
work anyway - it is becoming obvious it will probably form part of future
progress eg:
http://astro.uwaterloo.ca/~wesson/
Thanks
Bill
Jay R. Yablon
news:xsFvj.18091$421....@news-server.bigpond.net.au...
>
> "Jay R. Yablon" <jya...@nycap.rr.com> wrote in message
> news:627gkqF...@mid.individual.net...
>> 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.com/2008/02/kaluza-klein-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.
> Looks fine to me Jay. Good work and thanks for posting it.
>
> The problem with Kaluza Klein is not that it does not unify gravity
> and EM - it is the cylinder assumption. This imposes U(1) symmetry
> which is known to be the basis of EM. Basically you have assumed EM
> to start with. But good work anyway - it is becoming obvious it will
> probably form part of future progress eg:
> http://astro.uwaterloo.ca/~wesson/
>
> Thanks
> Bill
Thanks Bill,
Nice to hear something good amidst all the skepticism and cynicism.
I am certainly foursquare in tune with the Space-Time-Matter STM crowd
that is looking at Kaluza-Klein to unify EM and GR and at the same time,
give rise to matter out of the fifth dimension. What has been a bit of
a surprise to me, it the vehemence with which some people are dead set
against this approach.
Best,
Jay.
xxein
>
> I am just putting the finishing touches on the five-dimensional paper
> which I have been working on intensively for the past several weeks,
xxein: Weeks! It must then contain all thruths to be known.
Jay R. Yablon
news:179c0c06-bdd8-464e...@q33g2000hsh.googlegroups.com...
Sure does! ;-) Jay.
Daryl McCullough
>
>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.com/2008/02/kaluza-klein-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
Jay R. Yablon
--
_____________________________
PRIVILEGED AND CONFIDENTIAL
Law Office of Jay R. Yablon
910 Northumberland Drive
Schenectady, New York 12309-2814
Phone / Fax: 518-377-6737
Email: jya...@nycap.rr.com
"Daryl McCullough" <stevend...@yahoo.com> wrote in message
news:fpo4n...@drn.newsguy.com...
> 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.com/2008/02/kaluza-klein-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.
Hi Daryl,
You are correct on this. If the electric charge q or a particle is
non-zero, then my (4.3) says that particle must have intrinsic spin.
Conversely, if a particle has no intrinsic spin, it must be neutral in
charge.
The question then turns experimental. Is there any charged particle
without intrinsic spin, i.e., a charged scalar? I don't think so, and,
for example, when SU(2) is broken in electroweak theory, the Higgs comes
out neutral. There are no charged scalars theorized or observed that I
am aware of (except for composites like scalar mesons but that is a
different story because you are canceling two intrinsic spins against
one another).
Your point actually cuts the opposite way: the biggest pain-in-the-butt
particle we know of -- the neutrino -- is neutral. But it has intrinsic
spin. That would seem to contradict my interpretation of (4.3). Need
to think on that. This also means that the neutrino is stationary in
x_5. That damned neutrino always screws up everything. ;-)
>
> 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.
Agreed, and an excellent observation.
This is a good example of how these internet groups can be used for
serious collaboration, and not just a forum for people to take out their
frustrations on each other. (I resisted more colorful language.)
What you doing in Ithaca? My son Joshua just graduated from Cornell
last year with a degree in -- what else -- engineering physics.
Jay.
>
> --
> Daryl McCullough
> Ithaca, NY
>
Thanks Daryl,
You reply is an example of how great the internet is for scientific
collaboration, if we can get past the people who use these forums to
simply throw mud at each other.
I agree that m d/dtau x_5 is i
Ken S. Tucker
> "Bill Hobba" <rubb...@junk.com> wrote in message
>
> news:xsFvj.18091$421....@news-server.bigpond.net.au...
>
>
>
> > "Jay R. Yablon" <jyab...@nycap.rr.com> wrote in message
To Jay, Charles and all.
(I posted this to SPF as well).
On Feb 22, 3:07 pm, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spake Jay R. Yablon <jyab...@nycap.rr.com>
> >To my physics 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
> >the first look at this, and am taking the liberty of directly emailing
> >to some folks as well as posting to SPF.
>
> >http://jayryablon.files.wordpress.com/2008/02/kaluza-klein-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 believe that this paper fully and
> >completely unifies gravitation and electrodynamics, and in the scheme of
> >things, will be as significant in the 21st century, as GTR 1916 was in
> >the 20th.
> Just how do you propose to describe Dirac particles, or any of qed in
> five dimensions.
To emphasis Charle's point...
I studied 5D in the 70's for about 3 years, but could
not quite coordinate with physical reality that ultimately
requires descriptions in 4D. I learned a lot of hard math
doing that but I also learned to prefer to use mathematics
to follow hard physics, here's an interesting article,
http://www.artfact.com/catalog/viewLot.cfm?lotCode=0WYUY4JM
(I ended up burning over 2000 pg's of notes on 5D,
my Old Boy almost freaked, but I explained that was
a finished mathematical exercize, obviously Jay has
far more mathematical talent than I'll possess, so my
experience may not be relevent).
I found the mathematics of 5D to be quite beautiful,
and mesmerizing, so much so, I went on to study
tensors allowing the indices to be variables, without
fixing the specific dimensionality.
(I posted on the "Calculus Field" to show the basis
of that, and that fits very well with GR).
I noted that Jay's Eq.(9.7) is equivalent to AE's
GR1916 Eq.(66) and the one following it, (66+).
The equation (66+) depends upon the vanishing of
the Lorentz Force, however Jay bases his reasoning
on his Eq.(2.6), that implies to me a non-vanishing
Lorentz Force, which is a contradiction in my mind.
> Regards
> Charles Francis
> http://www.teleconnection.info/rqg/MainIndex
Regards
Ken S. Tucker
Eric Gisse
>
> (I ended up burning over 2000 pg's of notes on 5D,
> my Old Boy almost freaked, but I explained that was
> a finished mathematical exercize, obviously Jay has
> far more mathematical talent than I'll possess, so my
> experience may not be relevent).
>
> I found the mathematics of 5D to be quite beautiful,
> and mesmerizing, so much so, I went on to study
> tensors allowing the indices to be variables, without
> fixing the specific dimensionality.
> (I posted on the "Calculus Field" to show the basis
> of that, and that fits very well with GR).
What's a metric signature, Ken?
Yua...@gmail.com
> What's a metric signature, Ken?
>
> Now you have to explain why the masses of the planets as determined
> through Kepler's 3rd law is wrong,...
Doesn't the Equivalence Principle imply that a satellite's orbit isn't
a function of its mass?
Where am I going wrong?
Love,
Jenny
Eric Gisse
> On Feb 23, 7:17 pm, Eric Gisse <jowr...@gmail.com> wrote:
>
> > What's a metric signature, Ken?
>
> > Now you have to explain why the masses of the planets as determined
> > through Kepler's 3rd law is wrong,...
I didn't say that in this thread.
Yua...@gmail.com
> On Feb 23, 4:44 pm, Yuan...@gmail.com wrote:
>
> > On Feb 23, 7:17 pm, Eric Gisse <jowr...@gmail.com> wrote:
>
> > > What's a metric signature, Ken?
>
> > > Now you have to explain why the masses of the planets as determined
> > > through Kepler's 3rd law is wrong,...
>
> I didn't say that in this thread.
>
>
chance. Now you have a third chance.
Love,
Jenny
Yua...@gmail.com
Fourth chance!
Jay R. Yablon
<Yua...@gmail.com> wrote in message
news:17f16449-6551-4204...@n77g2000hse.googlegroups.com...
> On Feb 23, 7:17 pm, Eric Gisse <jowr...@gmail.com> wrote:
>
>> What's a metric signature, Ken?
>>
>> Now you have to explain why the masses of the planets as determined
>> through Kepler's 3rd law is wrong,...
>
> Doesn't the Equivalence Principle imply that a satellite's orbit isn't
> a function of its mass?
Yes! Jay.
Juan R.
In my own experience they (Carlip, Roberts, dlz, Eric, Bill...) often do
not answer queries.
I have a set of questions i have explicitly asked people here, such as
Tom Roberts, during years and i am still waiting reply.
Juan R.
Well i am still from him to compute the linear limit of a geodesics.
apart from some lies i have not received reply in last 2 years!
Juan R.
> <Yua...@gmail.com> wrote in message
> news:17f16449-6551-4204-b9fe-
b69bbe...@n77g2000hse.googlegroups.com...
>> On Feb 23, 7:17 pm, Eric Gisse <jowr...@gmail.com> wrote:
>>
>>> What's a metric signature, Ken?
>>>
>>> Now you have to explain why the masses of the planets as determined
>>> through Kepler's 3rd law is wrong,...
>>
>> Doesn't the Equivalence Principle imply that a satellite's orbit isn't
>> a function of its mass?
>
> Yes! Jay.
Explains that to Eric then.
Dono
You can stop trolling now :
http://en.wikipedia.org/wiki/Orbital_period#Two_bodies_orbiting_each_other
Dono
<j...@canonicalscience.com> wrote:
>
> Explains that to Eric then.
>
> --
> I followhttp://canonicalscience.org/en/miscellaneouszone/guidelines.txt
You too, can stop trolling now, old ignorant fart:
http://en.wikipedia.org/wiki/Orbital_period#Two_bodies_orbiting_each_other
Lady Chacha
You can stop trolling now, old ignorant fart:
http://www.helinium.nl/trolltech.gif
--
Dono is concubine Lady Chacha
Lady Chacha
Jay R. Yablon
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.
Daryl McCullough
>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.
Edward Green
wrote:
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.
Daryl McCullough
>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.