Non-Symmetric Energy Tensors and Kaluza Klein Experiment
Jay R. Yablon
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
which are based upon the *non-symmetric* energy tensor of trace matter
derived in (11.6). What I have been turning over, is whether I ought to
be comfortable with this result, and my sense runs against it.
However, at the point of original derivation in sections 8-11, I
actually have a choice: I can construct the variation of the Lagrangian
density of matter with respect to g_uv such that a symmetric tensor will
result, or I can choose not to, by creating a symmetric term or not. I
think both paths need to be developed, because they lead to on the one
hand to a symmetric energy tensor, and on the other to a non-symmetric
energy tensor. In either case, the key term distinguishing this energy
tensor from the Maxwell tensor is J^u A^v.
Then, the experiment becomes -- not a test of the torsion tensor -- but
a test as between an energy tensor *with and without torsion*. That is,
the experiment as reformulated, becomes a test of *metric-style versus
Cartan-style* theories of gravitation.
Dealing with the currents J^u is clear. Regarding how to deal with the
potential A^u in doing the experiment, think about a beam of electrons.
They of course will all repel, so the beam will emerge conically from
the electron gun if nothing is done to force them onto a parallel path.
Now, take a circular cross section of electrons from the beam striking
an energy flux detector. One can think of the cross-sectional surface
where the electron stream meets the detector as a "disk," not unlike a
charged, flat, frisbee. I would submit that one can assign a "zero"
potential to the center of the cross section, and a varying non-zero
potential to the periphery. That is, if one were to take a circular
disk and fill it with electric charge, then float some positive charge
nearby, the positive charge -- I believe -- would be attracted toward
and seat itself at the center of the disk, and so that would be a
natural place to define the zero of potential.
A rough analogy with which to think of this: drill a hole through the
center of the earth from the north pole to the south pole (to obviate
rotational effects), or assume a non-rotating earth, and jump in. You
will then start a sinusoidal oscillation through the hole, always
attracted toward the center of the earth. If there is any resistance
along the way, the oscillation will be damped, and the jumper will end
up at the center. The difference is that the earth is a sphere not a
disk, so the potential as a function of radius R will be different, but
aside from that, the earth is analogized to the negative charge and the
jumper to the positive charge, and the analogy roughly works because
both Newton's law and Coulomb's law are 1/R^2 for point charges and
masses. The only other difference, of course, is that the differential
mass elements of the earth are mutually attractive to one another, while
in the electron beam cross section, they repel, but I don't think that
affects the overall analogy because the electron beam assures that
electrons on the disk are constant replenished which maintains a stable
configuration of potential over the disk. (Why do I have a queasy
feeling this thread will turn into a discussion of this analogy rather
than focus on the main points of metric versus torsion and how to
specify the potential?)
Now, gravitational analogy or not, this would also mean that regional
detections of flux toward the fringes of the detector will be different
than toward the center, assuming uniformity of charge distribution,
because the energy created by the potentials among the electrons are
different in different regions. So, there is a way to assign potentials
even applying without an external voltage, though an experimentalist may
want to also apply an external voltage simply to vary the range of
experiments.
Now, to the main point: one should do the experiment with random,
unpolarized electrons, and then again with spins aligned with and
against the direction of propagation, merely to test the symmetric
versus non-symmetric energy tensors one to the other. One will win,
the other not. Metric versus torsion.
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
Daryl McCullough
>
>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).
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.
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.
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.
Putting these objections together with the already known
objection that neutrinos are neutral, but have intrinsic
spin, 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*. 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).
I really think that associating the extra dimension
with intrinsic is barking up the wrong tree.
--
Daryl McCullough
Ithaca, NY
Jay R. Yablon
news:fsbgd...@drn.newsguy.com...
> 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).
> I don't see how that can possibly be correct.
Daryl,
Thank you for raising some interesting points. Let me refer you to the
latest material dealing with intrinsic spin, at:
http://jayryablon.files.wordpress.com/2008/03/intrinsic-spin-22.pdf
because a number of the spin issues are more fully developed in this
paper, based on prior comments here and at SPF. That may or may not
affect your comments, but at least we'll be working form the latest
baseline.
> 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.
Look at the development of the spin matrices in the above. Now, I would
agree that even in this latest draft, I have not addressed the
independence of spin from particle / antiparticle. That can only come
from taking the next step to Dirac's equation, because that adds the
extra two-fold degeneracy whereby one can flip the electron spin and
still keep it as an electron. I do not think this to be inconsistent
with the results I have so far.
Just want to be clear: what is G?
>
> 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).
>
> I really think that associating the extra dimension
> with intrinsic is barking up the wrong tree.
>
> --
> Daryl McCullough
> Ithaca, NY
>
This is very helpful. I will give more extended consideration to all of
this, and be back to you.
Thanks again,
Jay.
George Hammond
<jya...@nycap.rr.com> wrote:
>
[Hammond]
Jay, this is a crazy Feynman type of idea... but do you
think it possible that the fundamental mystery of YOUNG'S 2
SLIT EXPERIMENT might be explained by "interference in the
5th dimension".
I mean; what is the separation of the 2 sits in the 4th
spatial KK dimension? Since the 4th spatial dimension
is "cyclical"; is it possible that this is the source of the
mysterious "single particle interference" which is the
sine qua non of this classical experiment? Just a crazy
idea....
Jay R. Yablon
news:2fbju3hfrkgoqi1pl...@4ax.com...
George,
Take a look at two threads below, which I initated about a year ago at
SPF. That reflects my thinking then and now about double slit, but I
will revist this in light of what I now know about Kaluza Klein.
http://groups.google.com/group/sci.physics.foundations/browse_frm/thread/f395f930df5e6771#
http://groups.google.com/group/sci.physics.foundations/browse_frm/thread/482b37431b4005dd#
Jay.
Jay R. Yablon
Oops, here is a third thread I forgot about -- the first in chronology:
http://groups.google.com/group/sci.physics.foundations/browse_frm/thread/5ce4434260b61a17#
Jay.
George Hammond
<jya...@nycap.rr.com> wrote:
>"George Hammond" <Nowh...@notspam.org> wrote in message
>news:2fbju3hfrkgoqi1pl...@4ax.com...
>> On Tue, 25 Mar 2008 10:36:30 -0400, "Jay R. Yablon"
>> <jya...@nycap.rr.com> wrote:
>>
>>>
>> [Hammond]
>> Jay, this is a crazy Feynman type of idea... but do you
>> think it possible that the fundamental mystery of YOUNG'S 2
>> SLIT EXPERIMENT might be explained by "interference in the
>> 5th dimension".
>> I mean; what is the separation of the 2 sits in the 4th
>> spatial KK dimension? Since the 4th spatial dimension
>> is "cyclical"; is it possible that this is the source of the
>> mysterious "single particle interference" which is the
>> sine qua non of this classical experiment? Just a crazy
>> idea....
>
>George,
>
>Take a look at two threads below, which I initated about a year ago at
>SPF. That reflects my thinking then and now about double slit, but I
>will revist this in light of what I now know about Kaluza Klein.
>
>
>http://groups.google.com/group/sci.physics.foundations/browse_frm/thread/5ce4434260b61a17#
>
>http://groups.google.com/group/sci.physics.foundations/browse_frm/thread/f395f930df5e6771#
>
>http://groups.google.com/group/sci.physics.foundations/browse_frm/thread/482b37431b4005dd#
>
>Jay.
>
>
[Hammond]
Vacuum fluctuations are a result of the Heisenberg
Uncertainty Principle. But you have derived the HUP
from spin in the 5th KK dimension. Therefore might we be
talking about the same thing; that actually:
cylical spin interference in the 5th dim. propagates by
Casimir force reconfiguration in 3d?
and accounts for the single particle interference in Young's
2 Slit experiment. Whew....how's that for a handwaving
argument!
George Hammond
[Hammond]
Let me clarify the term "cylical spin interference in the
5th dim." To wit: In 3d the 2 slits are only separated in
the x dimension, not in the y or z dimension. My guess is
that they are not separated in the 4th KK dimension either.
This means that the single particle actually DOES pass
through "both slits" in the 4th KK dimension. Might their
be "self spin inerference" in the 4th KK dimension as the
particle passes through both slits at once in the 4th KK
spatial dimension? And then this interference is propagated
through the vacumm in 3d from slit 1 to slit 2 procucing the
classic Young's interference pattern for a single particle
"passing through both slits"?
Jay R. Yablon
Joshua just graduated last year from -- what else -- their engineering
physics department. Comments inline.
"Daryl McCullough" <stevend...@yahoo.com> wrote in message
news:fsbgd...@drn.newsguy.com...
> 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.
Jay R. Yablon
error: but for a "-" sign in front of the Dirac gamma.
change to: but for a "-" sign in front of the spin matrix operator.
Jay.
bz
@mid.individual.net:
> Look at the development of the spin matrices in the above. Now, I would
> agree that even in this latest draft, I have not addressed the
> independence of spin from particle / antiparticle. That can only come
> from taking the next step to Dirac's equation, because that adds the
> extra two-fold degeneracy whereby one can flip the electron spin and
> still keep it as an electron. I do not think this to be inconsistent
> with the results I have so far.
>
The spin of an electron is only apparent through its coupling to a magnetic
field.
Absent an applied magnetic field, electron (and neutron and proton) spins
are aligned in random directions with the exception that when two electrons
occupy the same orbital, their spins are opposite.
Perhaps your 'spin in p5' couples with some OTHER field (like perhaps
gravity, electrostatic, or strong force?) rather than with magnetic?
--
bz
please pardon my infinite ignorance, the set-of-things-I-do-not-know is an
infinite set.
bz+...@ch100-5.chem.lsu.edu remove ch100-5 to avoid spam trap
Daryl McCullough
>
>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.
George Hammond
(Daryl McCullough) wrote:
>>> [McCullough]
>>> 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.
>>
[Hammond]
We're not talking about electrons confined to atomic
orbits here... talk of "orbital" angular momentum is
irrelevant. Orbital ang. mom. is only coupled to intrinsic
spin in the peculiar and unique atomic case, but it has
nothing a priori to do with the orign of intrinsic spin
itself?
>
>>[Yablon]
>>You are continuing the line of thinking from above.
>
>[McCullough]
>Yes, because it is correct. Your p_5 has *nothing* to do
>with angular momentum.
>
[Hammond]
That's an rather impetuous and unsupported statement under
the circumstances.
>
>
>>>[McCullough]
>>> 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.
>>
>>
[Hammond]
Jay has explained this in detail in his paper...the spin
angular momentum vector is de facto orthogonal to p_5 itself
because it must be orthogonal to it's velocity vector along
p_5... but the entire 3d manifold is actually orthogonal to
p_5, ergo the spin angular momentum vector must fall
"somewhere" in 3d space! Ok, say it happens to fall in the
z direction.... then naturally the observer, being totally
unaware of p_5 just assumes (classically) that it must be
some kind of "circular motion in the x-y plane". Of course
it ISN'T it is actually motion along the compactified p_5
dimension which looks circular from 3d! That's a pretty
solid basic argument for p_5 motion causing "spin angular
momentum" in 3d space!
>
>[McCullough]
>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.
>
[Hammond]
Wrong... you're the one who has the preconceived notion
that it can't be caused by circular motion around the rolled
up p_5 dimension. Yablon is not anincompetent idiot you
know!
Jay R. Yablon
> Jay R. Yablon says...
. . .
> 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.
That is exactly my point. The circular motion through x_5, is
orthogonal to all of x,y,z. But circular motion has a vector which
always projects orthogonally. So the x_5 motion creates a vector which
points with equal (squared) magnitude isotropically into all of x,y,z.
That is *already* non-classical, because classically, vectors have a
definite direction and here the vector can and does point every which
way. Then, when we take the square root of this, and treat it as an
operator, we pop out the spin matrices, and their non-classical
two-valuedness. But the foundation is laid geometrically, in the x^5
dimension, and not just superimposed by brute force onto four dimensions
which is that state of affairs in physics at the present day.
Jay.
Daryl McCullough
> We're not talking about electrons confined to atomic
>orbits here... talk of "orbital" angular momentum is
>irrelevant. Orbital ang. mom. is only coupled to intrinsic
>spin in the peculiar and unique atomic case, but it has
>nothing a priori to do with the orign of intrinsic spin
>itself?
That's just wrong. It doesn't matter whether an electron
is inside an atom or not---spin is not conserved in an
electron, and angular momentum is not conserved, but the
sum is.
>>>>[McCullough]
>>>> 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.
>>>
>>>
>[Hammond]
> Jay has explained this in detail in his paper...the spin
>angular momentum vector is de facto orthogonal to p_5 itself
>because it must be orthogonal to it's velocity vector along
>p_5... but the entire 3d manifold is actually orthogonal to
>p_5, ergo the spin angular momentum vector must fall
>"somewhere" in 3d space!
That doesn't make any sense. The momentum p_5 is orthogonal
to the 3 usual spatial dimensions, which means that it does
*not* fall anywhere in 3d space.
The idea of p_5 as intrinsic spin just does not make any sense.
Daryl McCullough
>
>"Daryl McCullough" <stevend...@yahoo.com> wrote in message
>news:fsdja...@drn.newsguy.com...
>> Jay R. Yablon says...
>. . .
>
>> 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.
>
>That is exactly my point. The circular motion through x_5, is
>orthogonal to all of x,y,z.
Then it doesn't make any sense for that motion to have a projection
in the z-direction.
>But circular motion has a vector which always projects orthogonally.
No, it doesn't. If an object is moving in a circle in the x-y plane,
then its angular momentum is in the x-y plane, not orthogonal to it.
Angular momentum in any number of dimensions can be defined as follows:
L^ij = x^i p^j - x^j p^i
Angular momentum component L^ij represents motion in the ij plane.
Angular momentum is natural a bivector, *not* a vector.
It's only a peculiarity of 3d space that allows us to associate
the components of angular momentum with vectors. We call the components
L_x, L_y and L_z but they really should be called L_yz, L_zx and L_xy.
The number of components of angular momentum in D dimensions is
D(D-1)/2. So in 2-D, there is only one component of angular momentum.
In 3-D, there is 3 components, in 4-D there are 6 components, and
in 5-D there are 10 components of angular momentum.
It's just a coincidence of 3D that there are 3 components of
angular momentum and 3 spatial directions, so we can associate
each angular momentum component with a spatial direction.
>So the x_5 motion creates a vector which
>points with equal (squared) magnitude isotropically into all of x,y,z.
Which is unlike intrinsic spin. The intrinsic spin of a particle
does *not* point equally in all directions.
George Hammond
(Daryl McCullough) wrote:
>Jay R. Yablon says...
>>
>>"Daryl McCullough" <stevend...@yahoo.com> wrote in message
>>news:fsdja...@drn.newsguy.com...
>>> Jay R. Yablon says...
>>. . .
>>
>>> 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.
>>
[Hammond]
I accidently typed "p_5" when I meant "x_5"; a
typographical error. And excuse my noziness; in case you
haven't already realized it, unlike you and Yablon I
actually am a (concerned) but incompetent physics idiot!
(my expertise lies in a distantly related field).
>
>>That is exactly my point. The circular motion through x_5, is
>>orthogonal to all of x,y,z.
>
>Then it doesn't make any sense for that motion to have a projection
>in the z-direction.
>
[Hammond]
z was only a hypothetical example, in that the vector has
to fall somewhere in 3-d space, to be measured.
>
>>But circular motion has a vector which always projects orthogonally.
>
>No, it doesn't. If an object is moving in a circle in the x-y plane,
>then its angular momentum is in the x-y plane, not orthogonal to it.
>
[Hammond]
Not so in 3-d space as you note below. In 3-d the
bivector can be represented by its dual which is an axial
vector.
>
>Angular momentum in any number of dimensions can be defined as follows:
>L^ij = x^i p^j - x^j p^i
>Angular momentum component L^ij represents motion in the ij plane.
>Angular momentum is natural a bivector, *not* a vector.
>It's only a peculiarity of 3d space that allows us to associate
>the components of angular momentum with vectors. We call the components
>L_x, L_y and L_z but they really should be called L_yz, L_zx and L_xy.
>The number of components of angular momentum in D dimensions is
>D(D-1)/2. So in 2-D, there is only one component of angular momentum.
>In 3-D, there is 3 components, in 4-D there are 6 components, and
>in 5-D there are 10 components of angular momentum.
>It's just a coincidence of 3D that there are 3 components of
>angular momentum and 3 spatial directions, so we can associate
>each angular momentum component with a spatial direction.
>
>
>
[Hammond]
A bivector can't exist in one dimension! The electron is
ONLY moving in the 4th KK dimension and not in any other
dimension.
The conjecture is however that this dimension is rolled
up (tightly curved) so that this motion "appears" to be
originating as submicroscopic circular motion somewhere in
3d-xyz space since it manifests itself as as a readily
detectable 3d axial vector known ad hoc as "electron spin".
Ken S. Tucker
On Mar 26, 9:43 am, stevendaryl3...@yahoo.com (Daryl McCullough)
wrote:
> Jay R. Yablon says...
>
>
>
> >"Daryl McCullough" <stevendaryl3...@yahoo.com> wrote in message
Here's a ref about "volume tensors",
http://relativity.livingreviews.org/open?pubNo=lrr-2007-1&page=articlese19.html
Best text book ref I've found is in Pauli's
"Theory of Relativity" Eq.(55), that looks
something like,
X*^a = (1/sqrt(g)) X_bcd.
I'll paraphrase what is developed in that chp.
The X*^a is a vector perpendicular to all of
the lengths enclosing volume X_bcd, proportional
to that volume. A permutation may be used like,
X_cbd = -X_bcd, to produce
Y*^a = - X*^a.
Just as we have the relativity of a + and -
end of a number line, we also have + and -
volumes.
Essentially, X*^a is a 4th dimensional spatial
vector. By unitizing (quantizing) the volume
X_bcd, one achieves 2 spatial magnitudes
perpendicular to the 3D as the 4th using
X*^a and -X*^a.
6 *area* equations follow from that,
X12, X23, X31 and X14, X24, X34.
IMO the first 3 maybe regarded as spins, with
a magnetic component projected into 3D, and
the last 3 electric field components.
Looks ok to me.
Regards
Ken S. Tucker
Ken S. Tucker
> Here's a ref about "volume tensors",http://relativity.livingreviews.org/open?pubNo=lrr-2007-1&page=ar...
>
> Best text book ref I've found is in Pauli's
> "Theory of Relativity" Eq.(55), that looks
> something like,
>
> X*^a = (1/sqrt(g)) X_bcd.
>
> I'll paraphrase what is developed in that chp.
>
> The X*^a is a vector perpendicular to all of
> the lengths enclosing volume X_bcd, proportional
> to that volume. A permutation may be used like,
> X_cbd = -X_bcd, to produce
> Y*^a = - X*^a.
>
> Just as we have the relativity of a + and -
> end of a number line, we also have + and -
> volumes.
>
> Essentially, X*^a is a 4th dimensional spatial
> vector. By unitizing (quantizing) the volume
> X_bcd, one achieves 2 spatial magnitudes
> perpendicular to the 3D as the 4th using
> X*^a and -X*^a.
>
> 6 *area* equations follow from that,
> X12, X23, X31 and X14, X24, X34.
Those 6 equations are antisymmetrical,
X12 = -X21 etc.
Jay R. Yablon
>>>But circular motion has a vector which always projects orthogonally.
>>
>>No, it doesn't. If an object is moving in a circle in the x-y plane,
>>then its angular momentum is in the x-y plane, not orthogonal to it.
>>
> [Hammond]
> Not so in 3-d space as you note below. In 3-d the
> bivector can be represented by its dual which is an axial
> vector.
>>
>>Angular momentum in any number of dimensions can be defined as
>>follows:
>>L^ij = x^i p^j - x^j p^i
>>Angular momentum component L^ij represents motion in the ij plane.
>>Angular momentum is natural a bivector, *not* a vector.
>>It's only a peculiarity of 3d space that allows us to associate
>>the components of angular momentum with vectors. We call the
>>components
>>L_x, L_y and L_z but they really should be called L_yz, L_zx and L_xy.
>>The number of components of angular momentum in D dimensions is
>>D(D-1)/2. So in 2-D, there is only one component of angular momentum.
>>In 3-D, there is 3 components, in 4-D there are 6 components, and
>>in 5-D there are 10 components of angular momentum.
>>It's just a coincidence of 3D that there are 3 components of
>>angular momentum and 3 spatial directions, so we can associate
>>each angular momentum component with a spatial direction.
[Yablon]
Daryl,
George is absolutely correct, and I also understand now, one place where
you and I are disconnecting.
Any L^ij can always be represented by its dual defined via the Livi
Civita tensor, with a rank suitable to the dimension of the space.
Thus, for N *linear* (not compact) dimensions, we can specify the
C(N,N-1) planes. Those planes can be represented by a bi-vector to
specify the parallel plane as you say, and also, via the dual, by an N-2
vector, to specify the orthogonal N-2 dimensional surface. In a 3-D
space, that dual is a 1-vector, and is the usual vector "direction" of
angular momentum.
Where I think we are having one disconnect, is in the fact that x^5 is
curled up, not linear. Therefore, x^5 all by itself defines a "plane"
using only one coordinate, not two, though the "plane" is restricted
because motion can only occur on the "loop," (I stay away from the more
loaded term "string.") (This is presuming that we are employing a
"Bohr-atom-model" in considering where the electron can and cannot
traverse in KK, or to put it differently, the probability amplitude
always has to be somewhere in x^5 and cannot wander into the plane of
x^5 because that would be a sixth dimension and by definition we do not
have in 5-D KK.)
So, here, when x^5 is compact, the "dual" angular momentum is a
three-vector that gets projected out from orthogonally to the x^5
plane -- although that "plane" is restricted such that the "interior"
and "exterior" of the loop is outside of the manifold, i.e., the
probability for any event to be there is zero because it lies in a
dimension that we do not have.
Jay.
Jay
Jay R. Yablon
> Jay R. Yablon says...
. . .
>>points with equal (squared) magnitude isotropically into all of x,y,z.
>
> Which is unlike intrinsic spin. The intrinsic spin of a particle
> does *not* point equally in all directions.
>
sigma_z^2=(1/4)hbar^2. The Pauli matrices are one solution to this, and
happen to be the one nature chooses.
Jay.
Jay R. Yablon
. . .
If you check out my newest thread at sci.physics.relativity, you will
see that I have revamped my paper, and have incorporated much of what
you laid out here, with credit and thanks. The link to the updated
paper is below:
http://jayryablon.wordpress.com/files/2008/03/intrinsic-spin-30.pdf
The "orthogonal" stuff is behind me. I am now arguing the case from
spatial "isotropy." Looking forward to continuing our discussion.
Best,
Jay.