New paper, may contain a solution to the NuTeV anomaly

Hi,

I took a quick amateur look on your papers:

http://arxiv.org/abs/hep-ph/0509223
http://arxiv.org/abs/hep-ph/0508257

Some quick comments come into my mind when I read those papers
(although my amateur understanding may be not enough about
these matters).

I think these can be best read if one uses computer's
"find command" for "duality" due it is mentioned so numerous
places ?

Mathematics have own duality concept for linear algebra (base elements
are now mappings for dual space and base elements are vectors for
space) and
more complicated tensor formalism (bilinear mappings for tensor product
etc.
which I don't fully understand at the moment).
I don't know has this duality (roughly: electromagnetic field
transformation
E - B and B - -E) nothing to do with these ?

Anyhow you mention "duality vacuum" and you said also
that you have assumed that the vev for duality is same as the Fermi vev
for electroweak theory (v = v_F = 246.220 GeV), and you say also
that "duality vacuum" is same as "Fermi vacuum" (on page 30) so I
assume
that you mean some kind of mathematical dual space which has this
property ?

If so there is perhaps nothing new with your dual formalism due
dual space and space are isomorphic (they have one-to-one and onto
correspondence and preserve also + operation and operation of
multiplying
with constant). This means that they have similar structure ?

You say that local duality symmetry combined with local U(1)_EM
gauge symmetry leads to an SU(2)_D duality gauge group.
I think that if you now use two charges : namely electric and
magnetic then something like this could be expected ?

If SU(2)_D makes sense then should you also have smilarly
than in electroweak theory three massive vector bosons,
now you mention only one ?

I wonder that you say in three places (page 18, 28 and 31) that you
have
used "EDUCATED GUESS" in estimating mass of M^u' (2.554 TeV, in
eq. 5.23) ???

"...educated guess what the mass of M^u' ought to be, especially
because
of the EXACT PARALLEL to ELECTROWEAK THEORY we have seen here.."

"...educated guess of the M^u' mass in equation (5.23)..."

"...educated guess seems to be borne out by a detailed consideration
of symmetry breaking, and we do indeed find a massive vwctor boson M^u'
with a mass upwards of 2 TeV which appears to be responsible for our
inability to observe magnetic monopoles at low energies..."

And in the end I would like to say that magnetism is
considered to be relativistic side-effect of electricity
(I think that this can most easily seen from the Lorentz
transformation equations for electric and magnetic fields in the
Special Theory of relativity)?


Best Regards,

Hannu Poropudas
Vesaisentie 9E
90900 Kiiminki
Finland


Jay R. Yablon wrote:
Hello to all:

I am pleased to announce that my newest paper, "Magnetic Monopoles, Chiral
Symmetries, and the NuTeV Anomaly," has now been published at
http://arxiv.org/abs/hep-ph/0509223.

This paper is a follow up to my earlier publication at
http://arxiv.org/abs/hep-ph/0508257, and takes a closer look at the magnetic
monopoles themselves as fermionic particles. I have reported interim
progress along the way on the sci.+ boards; now you can see the full
picture.

This paper calculates widths and cross sections associated with the
predicted magnetic charge, and determines that there is a very slight
cross-section enhancement at sqrt(s) = M_z ~ 91 GeV due to magnetic
monopoles.

If one were to do experiments and NOT understand the magnetic monopole
origin of this small cross section enhancement, one might instead conclude
that the weak mixing angle had decreased for e/ebar scattering, in relation
to neutino/neutrino-bar scattering, by a small amount. How small? This
paper predicts a reduction of approximately .003, which is right near the
magnitude of the NuTeV anomaly and goes in the right direction as well.

Fundamentally, the NuTeV anomaly is thus seen to be the first experimental
evidence of the existence of the magnetic monopole charges, which have been
a mystery ever since Maxwell's era.

Also, some fundamental connections are drawn between the magnetic / electric
symmetries, and chiral symmetries.

If you want the quick tour, look at equations (9.12) to (9.15) which contain
the final numeric results. Then look at (8.16) through (8.20) which shows
these same results represented in term of the cross section enhancements
from which they were derived.

If you are doing NuTeV experiments, and even if not, look at (7.34) to
(7.44), which show the full and differential cross sections in the most
general form. This should help you with the NuTeV anomaly even if you don't
believe as I do that the magnetic monopole charge at least contributes to
this anomaly. Because these equations tell you how a vector boson (call it
the Z^u' if you wish) with mass M_z would enhance the cross section
generally, whether the origin of that vector boson is from magnetic
monopoles or somewhere else. So, these give you a theoretical framework to
fit the data under a variety of assumptions that you may wish to make.

If you assume two or more massive bosons with mass M_z, then there will be
further cross section terms for each new vector boson, as well as further
cross terms between pairs of vector bosons, the form of which can readily be
understood and deduced from (7.34) to (7.44). My own suspicion is that
there is also an electroweak-based Z^u' in the 1.3 TeV range in addition to
the M^u which mediates the magnetic monopole interaction here. This will
require extending the entire electroweak theory to consider weak and weak
hypercharge magnetic monopoles, and may well be the subject of my next
paper.

Once the cross section enhancement is known under whatever scenario one may
assume, the apparent impact on sin^2 theta_w can be deduced following the
steps shown in section 9. So, there is some good grist here for the NuTeV
folks. And for anyone who is interested in understanding magnetic monopoles
and chiral symmetries.

I also suggest a look at the conclusion.

From there, look at whatever you want.

Happy reading.

Jay.
_____________________________
Jay R. Yablon
Email:

wrote in message
oups.com...
| Hi,
|
| I took a quick amateur look on your papers:

Wow...an amateur look. Us professionals get paid to look.
Androcles


|
| http://arxiv.org/abs/hep-ph/0509223
| http://arxiv.org/abs/hep-ph/0508257
|
| Some quick comments come into my mind when I read those papers
| (although my amateur understanding may be not enough about
| these matters).
|
| I think these can be best read if one uses computer's
| "find command" for "duality" due it is mentioned so numerous
| places ?
|
| Mathematics have own duality concept for linear algebra (base elements
| are now mappings for dual space and base elements are vectors for
| space) and
| more complicated tensor formalism (bilinear mappings for tensor
product
| etc.
| which I don't fully understand at the moment).
| I don't know has this duality (roughly: electromagnetic field
| transformation
| E - B and B - -E) nothing to do with these ?
|
| Anyhow you mention "duality vacuum" and you said also
| that you have assumed that the vev for duality is same as the Fermi
vev
| for electroweak theory (v = v_F = 246.220 GeV), and you say also
| that "duality vacuum" is same as "Fermi vacuum" (on page 30) so I
| assume
| that you mean some kind of mathematical dual space which has this
| property ?
|
| If so there is perhaps nothing new with your dual formalism due
| dual space and space are isomorphic (they have one-to-one and onto
| correspondence and preserve also + operation and operation of
| multiplying
| with constant). This means that they have similar structure ?
|
| You say that local duality symmetry combined with local U(1)_EM
| gauge symmetry leads to an SU(2)_D duality gauge group.
| I think that if you now use two charges : namely electric and
| magnetic then something like this could be expected ?
|
| If SU(2)_D makes sense then should you also have smilarly
| than in electroweak theory three massive vector bosons,
| now you mention only one ?
|
| I wonder that you say in three places (page 18, 28 and 31) that you
| have
| used "EDUCATED GUESS" in estimating mass of M^u' (2.554 TeV, in
| eq. 5.23) ???
|
| "...educated guess what the mass of M^u' ought to be, especially
| because
| of the EXACT PARALLEL to ELECTROWEAK THEORY we have seen here.."
|
| "...educated guess of the M^u' mass in equation (5.23)..."
|
| "...educated guess seems to be borne out by a detailed consideration
| of symmetry breaking, and we do indeed find a massive vwctor boson
M^u'
| with a mass upwards of 2 TeV which appears to be responsible for our
| inability to observe magnetic monopoles at low energies..."
|
| And in the end I would like to say that magnetism is
| considered to be relativistic side-effect of electricity
| (I think that this can most easily seen from the Lorentz
| transformation equations for electric and magnetic fields in the
| Special Theory of relativity)?
|
|
| Best Regards,
|
| Hannu Poropudas
| Vesaisentie 9E
| 90900 Kiiminki
| Finland
|
|
| Jay R. Yablon wrote:
| Hello to all:
|
| I am pleased to announce that my newest paper, "Magnetic Monopoles,
Chiral
| Symmetries, and the NuTeV Anomaly," has now been published at
| http://arxiv.org/abs/hep-ph/0509223.
|
| This paper is a follow up to my earlier publication at
| http://arxiv.org/abs/hep-ph/0508257, and takes a closer look at the
magnetic
| monopoles themselves as fermionic particles. I have reported
interim
| progress along the way on the sci.+ boards; now you can see the full
| picture.
|
| This paper calculates widths and cross sections associated with the
| predicted magnetic charge, and determines that there is a very
slight
| cross-section enhancement at sqrt(s) = M_z ~ 91 GeV due to magnetic
| monopoles.
|
| If one were to do experiments and NOT understand the magnetic
monopole
| origin of this small cross section enhancement, one might instead
conclude
| that the weak mixing angle had decreased for e/ebar scattering, in
relation
| to neutino/neutrino-bar scattering, by a small amount. How small?
This
| paper predicts a reduction of approximately .003, which is right
near the
| magnitude of the NuTeV anomaly and goes in the right direction as
well.
|
| Fundamentally, the NuTeV anomaly is thus seen to be the first
experimental
| evidence of the existence of the magnetic monopole charges, which
have been
| a mystery ever since Maxwell's era.
|
| Also, some fundamental connections are drawn between the magnetic /
electric
| symmetries, and chiral symmetries.
|
| If you want the quick tour, look at equations (9.12) to (9.15) which
contain
| the final numeric results. Then look at (8.16) through (8.20) which
shows
| these same results represented in term of the cross section
enhancements
| from which they were derived.
|
| If you are doing NuTeV experiments, and even if not, look at (7.34)
to
| (7.44), which show the full and differential cross sections in the
most
| general form. This should help you with the NuTeV anomaly even if
you don't
| believe as I do that the magnetic monopole charge at least
contributes to
| this anomaly. Because these equations tell you how a vector boson
(call it
| the Z^u' if you wish) with mass M_z would enhance the cross
section
| generally, whether the origin of that vector boson is from magnetic
| monopoles or somewhere else. So, these give you a theoretical
framework to
| fit the data under a variety of assumptions that you may wish to
make.
|
| If you assume two or more massive bosons with mass M_z, then there
will be
| further cross section terms for each new vector boson, as well as
further
| cross terms between pairs of vector bosons, the form of which can
readily be
| understood and deduced from (7.34) to (7.44). My own suspicion is
that
| there is also an electroweak-based Z^u' in the 1.3 TeV range in
addition to
| the M^u which mediates the magnetic monopole interaction here. This
will
| require extending the entire electroweak theory to consider weak and
weak
| hypercharge magnetic monopoles, and may well be the subject of my
next
| paper.
|
| Once the cross section enhancement is known under whatever scenario
one may
| assume, the apparent impact on sin^2 theta_w can be deduced
following the
| steps shown in section 9. So, there is some good grist here for the
NuTeV
| folks. And for anyone who is interested in understanding magnetic
monopoles
| and chiral symmetries.
|
| I also suggest a look at the conclusion.
|
| From there, look at whatever you want.
|
| Happy reading.
|
| Jay.
| _____________________________
| Jay R. Yablon
| Email:
|

Hello Hannu:

Thank you for your queries, let me see if I can elaborate.


Mathematics have own duality concept for linear algebra (base elements
are now mappings for dual space and base elements are vectors for
space) and
more complicated tensor formalism (bilinear mappings for tensor product
etc.
which I don't fully understand at the moment).
I don't know has this duality (roughly: electromagnetic field
transformation
E - B and B - -E) nothing to do with these ?

Probably the best way to get up to speed on duality as it is used in my
paper is the review the original works by Reinich and Wheeler, or the
treatment of this subject in MTW's "Gravitation" also referenced in the
paper.

In this type of "electric / magnetic duality" which is based on the
Levi-Civita formalism, all of the electric fields in the field strength
tensors are replaced by magnetic fields E -- B, and all of the magnetic
fields are replaced by electric fields B---E as you point out above.

At the first cut, this simply provides a concise formalism, especially for
writing Maxell's magnetic equation as *F^uv_;u = 0 rather than as F^uv;t +
F^vt:u _ F^tu;v = 0 (using Latin indexes for what are Greek with the right
fonts). These two equations in other words, say EXACTLY the same thing once
you plug in the E's and B's into the field strength tensor.

At the second cut, this formalism provides a good way to write the current
for a magnetic monopole -- if such as current were to exist --- as P^v =
*F^uv;u, and to contrast this to the electric current which does exist and
is written as J^v = F^uv_;u. As you correctly note below, "magnetism is
considered to be relativistic side-effect of electricity." In this context,
when J^v is at rest, i.e., J^0 not= 0 and J^k=0 where k=1,2,3, an
electric-field-only emanates outwardly from the charge, and there is no
magnetic field but when one moves relatively to the charge, i.e., J^k not=
0, then there is also a magnetic field. For the magnetic monopole current
P^v = *F^uv;u is exactly reversed. At rest, there emanates only a magnetic
field, but with relative motion, the electric field results. What ties
these together is the fact that an E is an E whether it comes from a J^v at
rest or a P^v in motion, and a B is a B whether it comes from a P^v at rest
or a J^v in motion. Another particle moving in an E or a B field will not
know or care from whence that field came; it will simply behave according to
its usual equation of motion.

At the third cut, we go beyond electric / magnetic duality just as a
formalism, and actually start to use it as a symmetry principle to ask
questions about the physics of observable objects such as currents and
charges. We ask whether the laws of nature are INVARIANT under a
transformation that takes F^uv into *F^uv, to which the answer is NO, at
least not on the surface, otherwise we would observe non-zero P^v just as we
do non-zero J^v. We then ask whether there is SOME circumstance "below the
surface" where the laws of nature ARE invariant under a transformation that
takes F^uv into *F^uv, but which we do not see everyday because this
symmetry has become hidden.

That is where my paper really starts. We explore the possibility that the
laws of nature are, in fact, invariant under F^uv -- *F^uv as well as
*F^uv -- -F^uv transformations (as well as under continuous global and
local duality transformations based on the complexion angle), but that this
symmetry is "hidden" or "broken" at low energies. And, we explore how this
symmetry breaks so that at low energies, this symmetry is not apparent and
we observe only J^v but not P^v. It turns out that the symmetry breaking
mechanism we explore, if one uses a 246.220 vev, yields a massive vector
boson M^v at about 2.35 TeV which couples P^v in the form g_m P^v M_v, where
g_m is a magnetic charge based on Dirac's Quantization Condition. (In the
paper, these have "primes" after them, because they have been transformed
out of their base states before symmetry is broken.)


Anyhow you mention "duality vacuum" and you said also
that you have assumed that the vev for duality is same as the Fermi vev
for electroweak theory (v = v_F = 246.220 GeV), and you say also
that "duality vacuum" is same as "Fermi vacuum" (on page 30) so I
assume
that you mean some kind of mathematical dual space which has this
property ?

NO, you are reading more into it, but maybe my selection of words can be
refined. I simply mean that just as the Fermi vev = 246.220 GeV sets the
mass scale for the electroweak W+/-^u and Z^u in a well-known way, we assume
that the Fermi vev = 246.220 GeV also sets the mass scale for the M_v in g_m
P^v M_v, but we leave the testing of this assumption to experiment. That
is, we assume v = v_F = 246.220 GeV for development, but leave it to nature
to validate or refute. If the mass scale for the M_v in nature is set by a
vev other than 246.220 GeV, then the ratio v / v_F comes into play, but I
don't think nature will do this to us because that would require a new
coupling constant and I think nature is more economical than that.

One possible experimental test of this is through the NuTeV anomaly, which
gets into the second paper. Using this assumption that v = v_F = 246.220
GeV, we find on strictly theoretical grounds, an anomaly in the weak mixing
angle of .003 at M_Z probe energies. This is promising, but experiments
seem to show that nature gives us .005 as the anomaly at M_Z, so I still
need to nail the other .002 before I can claim complete rather than only
partial experimental backing. One way is to play with the v and not use v =
v_F, but I think that would be the wrong approach. Rather, if we look not
just at magnetic monopoles, but at electroweak magnetic monopoles (four
vector bosons instead of one), then in addition to M^u above, we also get a
Z^u' which mediates interactions of the magnetic monopoles of the particles
mediated by Z^u (neutrinos therefore included). Preliminary calculations
suggest that the Z^u' provides the additional .002, predicting the entire
..005 NuTeV anomaly on the nose, with v = v_F = 246.220 GeV. If my detailed
calculations bear this out, this will for certain be my next paper, probably
later this month or in November.

With this approach, we also get counterparts for the W+/-u, but these are
irrelevant to the NuTeV anomaly, since that is a neutral current phenomenon.
But it could suggest an anomaly in the charged current sector as well -- not
that far in the calculations yet. And I really think -- based on the chiral
development of the second paper, that this will help us find the right
handed weak interaction that many suspect exists at higher energies.


If so there is perhaps nothing new with your dual formalism due
dual space and space are isomorphic (they have one-to-one and onto
correspondence and preserve also + operation and operation of
multiplying
with constant). This means that they have similar structure ?

Again, you are reading more in than needs be read in. But, I do want to say
that there is nothing new with my use of the duality formalism as regards
the "first cut" and "second cut" discussed above, The third cut is what, as
far as I know, is new.


You say that local duality symmetry combined with local U(1)_EM
gauge symmetry leads to an SU(2)_D duality gauge group.
I think that if you now use two charges : namely electric and
magnetic then something like this could be expected ?

That depends on how you proceed to develop the two charges and what
symmetries you postulate. I don't think one can say what to expect in the
abstract.


If SU(2)_D makes sense then should you also have smilarly
than in electroweak theory three massive vector bosons,
now you mention only one ?

NO. I mention three: the photon, the M^u above, and the "dualon" C^u. YES,
I should have three, and I do. NO, you should not assume that they are all
massive, you need to go through the development and see what they are. The
photon is massless, the M^u is massive, and the C^u is probably massive, and
it may be prudent to actually consider SU(2)xU(1) here to get a fourth, but
that is for another paper and another day. I really do think this will lead
us in the end to finally understand, fundamentally, where the Fermion
generations come from. And, since generations are distinguished by mass,
this will put the Fermion masses in the cross-hairs.


I wonder that you say in three places (page 18, 28 and 31) that you
have
used "EDUCATED GUESS" in estimating mass of M^u' (2.554 TeV, in
eq. 5.23) ???

"...educated guess what the mass of M^u' ought to be, especially
because
of the EXACT PARALLEL to ELECTROWEAK THEORY we have seen here.."

"...educated guess of the M^u' mass in equation (5.23)..."

"...educated guess seems to be borne out by a detailed consideration
of symmetry breaking, and we do indeed find a massive vwctor boson M^u'
with a mass upwards of 2 TeV which appears to be responsible for our
inability to observe magnetic monopoles at low energies..."

Yes, I have used the phrase "educated guess" in three places, once where I
introduce that "educated guess," once where I talk about that "educated
guess," and once where I show that the "educated guess" looks to be
confirmed as theoretically correct once we engage in a detailed
consideration of symmetry breaking in a vacuum with some vev, whether
246.220 GeV or something else. SO?

And, in the second paper, I am also starting to show that this "educated
guess" might well have been experimentally confirmed by the NuTeV anomaly.


And in the end I would like to say that magnetism is
considered to be relativistic side-effect of electricity
(I think that this can most easily seen from the Lorentz
transformation equations for electric and magnetic fields in the
Special Theory of relativity)?

That is correct. See the discussion above for how this relates to a
consideration of duality.

Best regards,

Jay.





Best Regards,

Hannu Poropudas
Vesaisentie 9E
90900 Kiiminki
Finland


Jay R. Yablon wrote:
Hello to all:

I am pleased to announce that my newest paper, "Magnetic Monopoles,
Chiral
Symmetries, and the NuTeV Anomaly," has now been published at
http://arxiv.org/abs/hep-ph/0509223.

This paper is a follow up to my earlier publication at
http://arxiv.org/abs/hep-ph/0508257, and takes a closer look at the
magnetic
monopoles themselves as fermionic particles. I have reported interim
progress along the way on the sci.+ boards; now you can see the full
picture.

This paper calculates widths and cross sections associated with the
predicted magnetic charge, and determines that there is a very slight
cross-section enhancement at sqrt(s) = M_z ~ 91 GeV due to magnetic
monopoles.

If one were to do experiments and NOT understand the magnetic monopole
origin of this small cross section enhancement, one might instead
conclude
that the weak mixing angle had decreased for e/ebar scattering, in
relation
to neutino/neutrino-bar scattering, by a small amount. How small? This
paper predicts a reduction of approximately .003, which is right near the
magnitude of the NuTeV anomaly and goes in the right direction as well.

Fundamentally, the NuTeV anomaly is thus seen to be the first
experimental
evidence of the existence of the magnetic monopole charges, which have
been
a mystery ever since Maxwell's era.

Also, some fundamental connections are drawn between the magnetic /
electric
symmetries, and chiral symmetries.

If you want the quick tour, look at equations (9.12) to (9.15) which
contain
the final numeric results. Then look at (8.16) through (8.20) which
shows
these same results represented in term of the cross section enhancements
from which they were derived.

If you are doing NuTeV experiments, and even if not, look at (7.34) to
(7.44), which show the full and differential cross sections in the most
general form. This should help you with the NuTeV anomaly even if you
don't
believe as I do that the magnetic monopole charge at least contributes to
this anomaly. Because these equations tell you how a vector boson (call
it
the Z^u' if you wish) with mass M_z would enhance the cross section
generally, whether the origin of that vector boson is from magnetic
monopoles or somewhere else. So, these give you a theoretical framework
to
fit the data under a variety of assumptions that you may wish to make.

If you assume two or more massive bosons with mass M_z, then there will
be
further cross section terms for each new vector boson, as well as further
cross terms between pairs of vector bosons, the form of which can readily
be
understood and deduced from (7.34) to (7.44). My own suspicion is that
there is also an electroweak-based Z^u' in the 1.3 TeV range in addition
to
the M^u which mediates the magnetic monopole interaction here. This will
require extending the entire electroweak theory to consider weak and weak
hypercharge magnetic monopoles, and may well be the subject of my next
paper.

Once the cross section enhancement is known under whatever scenario one
may
assume, the apparent impact on sin^2 theta_w can be deduced following the
steps shown in section 9. So, there is some good grist here for the
NuTeV
folks. And for anyone who is interested in understanding magnetic
monopoles
and chiral symmetries.

I also suggest a look at the conclusion.

From there, look at whatever you want.

Happy reading.

Jay.
_____________________________
Jay R. Yablon
Email:

$ educated general charge
Magnetic, electric, mass & radiation PRODUCTs of GENERAL CHARGE:
{p1*p2}*Ua = {q1*q2} / Ea = 4*pi*Ga*{M1*m1} = {C2a*C2b} / Ea*c^4
= 4*pi*Gr*G*{M1*m1} = (C2)^2 / Ea*c^4
..note n = mD / m1 - = 4*pi*G*{M1*m1} / (n - 1)
= 4*pi*rA*eG
= 4*pi*[e]^2
..in units of: - kg*m^3 / (sec)^2.
ADDENDUM:
GENERAL GUESS electronvolt ENERGY +eV = -(m1*v1^2 / 2) = + pA*fA.
GENERAL GUESS photon mass [mph] = nA*{mph}*ls / rA = m1 = mD / n.
PARTiCULAR iSS photon mass {mph} = 2*pi*h / tp*c^2 = hbar / ls*c
= hbar / ts*c^2 = h / 2*pi*ls*c.
C2 = SECOND RADiATiON Constant.
{p1*p2} = MAGNETiC pole PRODUCT - (A*m)^2 - {(mol part)*K*sec)}^2
- (A*m*sec)^2 / (sec)^2 - (Debye / sec)^2.
{q1*q2} = ELECTRiCAL CHARGEs PRODUCT = {e}^2 - (A*sec)^2.
{M1*m1} = GRAViTATiONAL mass PRODUCT = (mass)^2 - (Kilogram)^2.
{C2a*C2b} = SECOND RADiATiON PRODUCT = (C2)^2 - ((mol part)*K*m)^2.

The GUESS ambient density is ADDRESSED, with (n - 1), as follows:
G*M1/(n - 1)=G*M1*m1/(mD - m1)=r1*v1^2=r1^2*g=nA*wl*v1^2/ 2*pi*nL
[ ..whe c = wl*f / nL = 2*pi*r1 / nA*tbob = 1 / Uo*Eo*c ].!!

Note v1^2 = rA*g = (vescape)^2 / 2*(n - 1) = G*M1 / (n - 1)*rA
[ m1*c/h=nL/wl=fL/c=pL/h=nA/2*pi*rA=eV/h*fA*rA=pA/h*rA ].!!

Fine Structure VARiABLE (n - 1) = (mD - m1) / m1 = mS / m1;
[ mD is EQUiVALENT ambient DisCHARGE mass, from m1 ].
[ n = mD / m1 ..provides the + or - sign ].

GUESS + is OUTgoing; GUESS - ..iNcoming.!!

Go Google GROUP SEARCH 3-d black hole factor analysis .
Go c PLANCK TEMPERATURE GUESS nomenclature
Go c info itsy-bitsy bytes .

Show "electric / magnetic duality" nomenclature.!!

Physics WAS hard; GUESS simplified ALL that.!!

You FORGOT to dot your j.!!

```Brian


Jay R. Yablon wrote:
In this type of "electric / magnetic duality" which is based on
the Levi-Civita formalism, all of the electric fields in the
field strength tensors are replaced by magnetic fields E - B,--

I wonder that you say in three places (page 18, 28 and 31)
that you have used "EDUCATED GUESS" in estimating mass of
M^u' (2.554 TeV, in eq. 5.23) ???

"...educated guess what the mass of M^u' ought to be,--

"...educated guess of the M^u' mass in equation (5.23)..."

"...educated guess SEEMs to be borne out by a detailed --

Yes, I have used the phrase "educated guess" in three places,
once where I introduce that "educated guess," once where I talk
about that "educated guess," and once where I show that the
"educated guess" LOOKs TO BE confirmed AS THEORETiCALLY CORRECT
ONCE WE engage in a detailed consideration of symmetry breaking
in a vacuum with some vev, whether 246.220 GeV OR SOMEthing ELSE.
SO?

And, in the second paper, I am also STARTiNG TO SHOW that this
"educated guess" MiGHT WELL HAVE BEEN experimentally confirmed
by the NuTeV ANOMALY.

Jay.
_____________________________
Jay R. Yablon
Email:

Jay R. Yablon wrote:
Hello Hannu:

Thank you for your queries, let me see if I can elaborate.


Mathematics have own duality concept for linear algebra (base elements
are now mappings for dual space and base elements are vectors for
space) and
more complicated tensor formalism (bilinear mappings for tensor product
etc.
which I don't fully understand at the moment).
I don't know has this duality (roughly: electromagnetic field
transformation
E - B and B - -E) nothing to do with these ?

Probably the best way to get up to speed on duality as it is used in my
paper is the review the original works by Reinich and Wheeler, or the
treatment of this subject in MTW's "Gravitation" also referenced in the
paper.

In this type of "electric / magnetic duality" which is based on the
Levi-Civita formalism, all of the electric fields in the field strength
tensors are replaced by magnetic fields E -- B, and all of the magnetic
fields are replaced by electric fields B---E as you point out above.


If we take a carefull look to that dual concept.
I found only that Wheeler's book mentioned in your reference list.
Wheeler, J. A., 1962.
Geometrodynamics
Academic Press, New York, U.S.A, 332 pages.

Pages which I found about the subject:

dual and duality, defined for electromagnetic field, 19
dual, defined, 227
dual electromagnetic field tensor, 40
dual form, 31
dual language of electromagnetic fields and metric, convenience of, 24
duality, role of, in formulation of Maxwell's equations, 280-282
dual rotation, compared and contrasted with Lorentz transformation, 240
-defined, 239
-effect of, on a null field, 248-249
-of electromagnetic field and spinor field, compared, 91

And if we take also a carefull look to those (strange to me) complexion

angle and complexion gradient concepts.

complexion, considered as a new aspect of geometry, 23
-as describing lack of uniqueness in square root, 90
complexion, of electromagnetic field, defined, 18, 19, 229, 230, 241
--illustrated, 19
--question of determination from curvaure, 19, 20
-found from integration of its gradient, 20
-gradient integral conditios on, in a multiply connected space, 253-254
-not defined for null field, 23
-question of more geometric rephrasing of, 130

On page 15 there seems to be equation (31, I don't put the
equation below, but only the idea of it) for already unified
(gravity and electromagnetic fields).

Einstein curvature = Geometrized Maxwell tensor

Are you using this equation for curved space-time in your
calculations or something else ?


At the first cut, this simply provides a concise formalism, especially for
writing Maxell's magnetic equation as *F^uv_;u = 0 rather than as F^uv;t +
F^vt:u _ F^tu;v = 0 (using Latin indexes for what are Greek with the right
fonts). These two equations in other words, say EXACTLY the same thing once
you plug in the E's and B's into the field strength tensor.

At the second cut, this formalism provides a good way to write the current
for a magnetic monopole -- if such as current were to exist --- as P^v =
*F^uv;u, and to contrast this to the electric current which does exist and
is written as J^v = F^uv_;u. As you correctly note below, "magnetism is
considered to be relativistic side-effect of electricity." In this context,
when J^v is at rest, i.e., J^0 not= 0 and J^k=0 where k=1,2,3, an
electric-field-only emanates outwardly from the charge, and there is no
magnetic field but when one moves relatively to the charge, i.e., J^k not=
0, then there is also a magnetic field. For the magnetic monopole current
P^v = *F^uv;u is exactly reversed. At rest, there emanates only a magnetic
field, but with relative motion, the electric field results. What ties
these together is the fact that an E is an E whether it comes from a J^v at
rest or a P^v in motion, and a B is a B whether it comes from a P^v at rest
or a J^v in motion. Another particle moving in an E or a B field will not
know or care from whence that field came; it will simply behave according to
its usual equation of motion.

At the third cut, we go beyond electric / magnetic duality just as a
formalism, and actually start to use it as a symmetry principle to ask
questions about the physics of observable objects such as currents and
charges. We ask whether the laws of nature are INVARIANT under a
transformation that takes F^uv into *F^uv, to which the answer is NO, at
least not on the surface, otherwise we would observe non-zero P^v just as we
do non-zero J^v. We then ask whether there is SOME circumstance "below the
surface" where the laws of nature ARE invariant under a transformation that
takes F^uv into *F^uv, but which we do not see everyday because this
symmetry has become hidden.

That is where my paper really starts. We explore the possibility that the
laws of nature are, in fact, invariant under F^uv -- *F^uv as well as
*F^uv -- -F^uv transformations (as well as under continuous global and
local duality transformations based on the complexion angle), but that this
symmetry is "hidden" or "broken" at low energies. And, we explore how this
symmetry breaks so that at low energies, this symmetry is not apparent and
we observe only J^v but not P^v. It turns out that the symmetry breaking
mechanism we explore, if one uses a 246.220 vev, yields a massive vector
boson M^v at about 2.35 TeV which couples P^v in the form g_m P^v M_v, where
g_m is a magnetic charge based on Dirac's Quantization Condition. (In the
paper, these have "primes" after them, because they have been transformed
out of their base states before symmetry is broken.)


Anyhow you mention "duality vacuum" and you said also
that you have assumed that the vev for duality is same as the Fermi vev
for electroweak theory (v = v_F = 246.220 GeV), and you say also
that "duality vacuum" is same as "Fermi vacuum" (on page 30) so I
assume
that you mean some kind of mathematical dual space which has this
property ?

NO, you are reading more into it, but maybe my selection of words can be
refined. I simply mean that just as the Fermi vev = 246.220 GeV sets the
mass scale for the electroweak W+/-^u and Z^u in a well-known way, we assume
that the Fermi vev = 246.220 GeV also sets the mass scale for the M_v in g_m
P^v M_v, but we leave the testing of this assumption to experiment. That
is, we assume v = v_F = 246.220 GeV for development, but leave it to nature
to validate or refute. If the mass scale for the M_v in nature is set by a
vev other than 246.220 GeV, then the ratio v / v_F comes into play, but I
don't think nature will do this to us because that would require a new
coupling constant and I think nature is more economical than that.

One possible experimental test of this is through the NuTeV anomaly, which
gets into the second paper. Using this assumption that v = v_F = 246.220
GeV, we find on strictly theoretical grounds, an anomaly in the weak mixing
angle of .003 at M_Z probe energies. This is promising, but experiments
seem to show that nature gives us .005 as the anomaly at M_Z, so I still
need to nail the other .002 before I can claim complete rather than only
partial experimental backing. One way is to play with the v and not use v =
v_F, but I think that would be the wrong approach. Rather, if we look not
just at magnetic monopoles, but at electroweak magnetic monopoles (four
vector bosons instead of one), then in addition to M^u above, we also get a
Z^u' which mediates interactions of the magnetic monopoles of the particles
mediated by Z^u (neutrinos therefore included). Preliminary calculations
suggest that the Z^u' provides the additional .002, predicting the entire
.005 NuTeV anomaly on the nose, with v = v_F = 246.220 GeV. If my detailed
calculations bear this out, this will for certain be my next paper, probably
later this month or in November.

With this approach, we also get counterparts for the W+/-u, but these are
irrelevant to the NuTeV anomaly, since that is a neutral current phenomenon.
But it could suggest an anomaly in the charged current sector as well -- not
that far in the calculations yet. And I really think -- based on the chiral
development of the second paper, that this will help us find the right
handed weak interaction that many suspect exists at higher energies.


If so there is perhaps nothing new with your dual formalism due
dual space and space are isomorphic (they have one-to-one and onto
correspondence and preserve also + operation and operation of
multiplying
with constant). This means that they have similar structure ?


Correct form should be:
"second dual space and space are isomorphic".

Again, you are reading more in than needs be read in. But, I do want to say
that there is nothing new with my use of the duality formalism as regards
the "first cut" and "second cut" discussed above, The third cut is what, as
far as I know, is new.


You say that local duality symmetry combined with local U(1)_EM
gauge symmetry leads to an SU(2)_D duality gauge group.
I think that if you now use two charges : namely electric and
magnetic then something like this could be expected ?

That depends on how you proceed to develop the two charges and what
symmetries you postulate. I don't think one can say what to expect in the
abstract.


If SU(2)_D makes sense then should you also have smilarly
than in electroweak theory three massive vector bosons,
now you mention only one ?

NO. I mention three: the photon, the M^u above, and the "dualon" C^u. YES,
I should have three, and I do. NO, you should not assume that they are all
massive, you need to go through the development and see what they are. The
photon is massless, the M^u is massive, and the C^u is probably massive, and
it may be prudent to actually consider SU(2)xU(1) here to get a fourth, but
that is for another paper and another day. I really do think this will lead
us in the end to finally understand, fundamentally, where the Fermion
generations come from. And, since generations are distinguished by mass,
this will put the Fermion masses in the cross-hairs.


Do you have massive vector bosons (call it X) like W+ and W- but
now corresponding magnetic charges (X -magnetic charge and
X +magnetic charge)?



I wonder that you say in three places (page 18, 28 and 31) that you
have
used "EDUCATED GUESS" in estimating mass of M^u' (2.554 TeV, in
eq. 5.23) ???

"...educated guess what the mass of M^u' ought to be, especially
because
of the EXACT PARALLEL to ELECTROWEAK THEORY we have seen here.."

"...educated guess of the M^u' mass in equation (5.23)..."

"...educated guess seems to be borne out by a detailed consideration
of symmetry breaking, and we do indeed find a massive vwctor boson M^u'
with a mass upwards of 2 TeV which appears to be responsible for our
inability to observe magnetic monopoles at low energies..."

Yes, I have used the phrase "educated guess" in three places, once where I
introduce that "educated guess," once where I talk about that "educated
guess," and once where I show that the "educated guess" looks to be
confirmed as theoretically correct once we engage in a detailed
consideration of symmetry breaking in a vacuum with some vev, whether
246.220 GeV or something else. SO?

And, in the second paper, I am also starting to show that this "educated
guess" might well have been experimentally confirmed by the NuTeV anomaly.


And in the end I would like to say that magnetism is
considered to be relativistic side-effect of electricity
(I think that this can most easily seen from the Lorentz
transformation equations for electric and magnetic fields in the
Special Theory of relativity)?

That is correct. See the discussion above for how this relates to a
consideration of duality.

Best regards,

Jay.





Best Regards,

Hannu Poropudas
Vesaisentie 9E
90900 Kiiminki
Finland


Jay R. Yablon wrote:
Hello to all:

I am pleased to announce that my newest paper, "Magnetic Monopoles,
Chiral
Symmetries, and the NuTeV Anomaly," has now been published at
http://arxiv.org/abs/hep-ph/0509223.

This paper is a follow up to my earlier publication at
http://arxiv.org/abs/hep-ph/0508257, and takes a closer look at the
magnetic
monopoles themselves as fermionic particles. I have reported interim
progress along the way on the sci.+ boards; now you can see the full
picture.

This paper calculates widths and cross sections associated with the
predicted magnetic charge, and determines that there is a very slight
cross-section enhancement at sqrt(s) = M_z ~ 91 GeV due to magnetic
monopoles.

If one were to do experiments and NOT understand the magnetic monopole
origin of this small cross section enhancement, one might instead
conclude
that the weak mixing angle had decreased for e/ebar scattering, in
relation
to neutino/neutrino-bar scattering, by a small amount. How small? This
paper predicts a reduction of approximately .003, which is right near the
magnitude of the NuTeV anomaly and goes in the right direction as well.

Fundamentally, the NuTeV anomaly is thus seen to be the first
experimental
evidence of the existence of the magnetic monopole charges, which have
been
a mystery ever since Maxwell's era.

Also, some fundamental connections are drawn between the magnetic /
electric
symmetries, and chiral symmetries.

If you want the quick tour, look at equations (9.12) to (9.15) which
contain
the final numeric results. Then look at (8.16) through (8.20) which
shows
these same results represented in term of the cross section enhancements
from which they were derived.

If you are doing NuTeV experiments, and even if not, look at (7.34) to
(7.44), which show the full and differential cross sections in the most
general form. This should help you with the NuTeV anomaly even if you
don't
believe as I do that the magnetic monopole charge at least contributes to
this anomaly. Because these equations tell you how a vector boson (call
it
the Z^u' if you wish) with mass M_z would enhance the cross section
generally, whether the origin of that vector boson is from magnetic
monopoles or somewhere else. So, these give you a theoretical framework
to
fit the data under a variety of assumptions that you may wish to make.

If you assume two or more massive bosons with mass M_z, then there will
be
further cross section terms for each new vector boson, as well as further
cross terms between pairs of vector bosons, the form of which can readily
be
understood and deduced from (7.34) to (7.44). My own suspicion is that
there is also an electroweak-based Z^u' in the 1.3 TeV range in addition
to
the M^u which mediates the magnetic monopole interaction here. This will
require extending the entire electroweak theory to consider weak and weak
hypercharge magnetic monopoles, and may well be the subject of my next
paper.

Once the cross section enhancement is known under whatever scenario one
may
assume, the apparent impact on sin^2 theta_w can be deduced following the
steps shown in section 9. So, there is some good grist here for the
NuTeV
folks. And for anyone who is interested in understanding magnetic
monopoles
and chiral symmetries.

I also suggest a look at the conclusion.

From there, look at whatever you want.

Happy reading.

Jay.
_____________________________
Jay R. Yablon
Email:

.. . .

On page 15 there seems to be equation (31, I don't put the
equation below, but only the idea of it) for already unified
(gravity and electromagnetic fields).

Einstein curvature = Geometrized Maxwell tensor

Are you using this equation for curved space-time in your
calculations or something else ?


Hannu, if it is handy, would you mind posting the equation you are asking
about with some context. My copy of this is buried somewhere in my attic.

.. . .

Do you have massive vector bosons (call it X) like W+ and W- but
now corresponding magnetic charges (X -magnetic charge and
X +magnetic charge)?


Not fully developed, but I think the answer will be, YES. But, even the
KNOWN W+ and W- should carry a magnetic charge, since in decaying, say, a
neutrino into an electron, the W+ must -- based on my earlier results --
also carry away one unit of magnetic charge in addition to one unit of
electric charge. So, the X+ and X- will have the same internal symmetries
as the W+ and W-, but a) will be more massive because of the larger charge
arrived at through a weak version of the Dirac Quantization Condition and b)
very importantly, will couple only RIGHT-HANDED chiral states, thus leading
to a SU(2)L x SU(2)R weak interaction. If you look at my Volovik citation,
you will see that is an important step on the road to unifying the particle
phenomenology of quarks and leptons and the gauge generators of weak and
strong interactions to arrive at electromagnetic interaction sitting across
the weak and strong interactions thus unifying all three, which is where I
am ultimately driving. I think B-L using SU(4) is the ultra-high energy
symmetry of QCD, and when you combine this with SU(2)L x SU(2)R, you get
leptoquark unification, again, see Volovik. The one "inelegant" feature of
Volovik which needs to be cleaned up is the "spinon / holon" fudge to deal
with spin 1/2. It turns out that the magnetic monopoles add degrees of
freedom that will overcome this fudge and yield an even cleaner result where
what are now the spinons and the holons each have spin 1/2, and yet the
fermions they combine to form also have spin 1/2 due to a beautiful
conspiracy between the mathematics of chirality and the mathematics of
magnetic monopoles and the internal symmetries of isospin and leptoquark
QCD. I hope to demonstrate all of this in a future paper. (Problem is, I
have at least ten papers in the queue which will dramatically add to our
understanding of HEP. First priority is to fully nail NuTeV at .005, so
people will see that this stuff really is right and experimentally
confirmed, and not just wheel spinning, and some of the big shots will start
to pay attention.)

It is the third member of the triplet, call it X^0 corresponding to the Z,
(I called it Z' in my last post) which a preliminary calculation suggests
may pick up the extra .002 in the weak mixing angle to go from the .003
NuTeV anomaly I have theoretically arrived at so far to the total .005
anomaly observed experimentally.

Jay.

Jay R. Yablon wrote:
. . .

On page 15 there seems to be equation (31, I don't put the
equation below, but only the idea of it) for already unified
(gravity and electromagnetic fields).

Einstein curvature = Geometrized Maxwell tensor

Are you using this equation for curved space-time in your
calculations or something else ?


Hannu, if it is handy, would you mind posting the equation you are asking
about with some context. My copy of this is buried somewhere in my attic.


I copy from the book some lines below:

R^v_u - (1/2)d^_v R = 2 f^a_u f^v_a - (1/2)d^v_u f^t_s f^s_t (31)

This is a little different form on page 227 (I put some equations
of allready unified fields (gravity and electromagnetism) below):

(1) (3!)^-1 [abcd] (Df_bc / Dx^d) = 0 (half of Maxwell's equations),

(2) (-g)^(-1/2) (D/Dx^b) (-g)^(1/2) f^ab = 0 (the other half),

(3) R - (1/2)g_ab R = 2 f_ab f^d_b - (1/2)g f_st f^st)

(curvature of metric by Maxwell stress-momentum-energy density).

(D = ordinary partial derivation mark, a, b, c, d, s, t should be
really Greek labels, but I don't have them available here at
the moment)

Where g_uv are as source of metric fields, exclusively electromagnetic
fields,

F_ab = (c^2 / G^(1/2)) f_ab ,

and electromagnetic fields that are themselves free of all sources.




. . .

Do you have massive vector bosons (call it X) like W+ and W- but
now corresponding magnetic charges (X -magnetic charge and
X +magnetic charge)?


Not fully developed, but I think the answer will be, YES. But, even the
KNOWN W+ and W- should carry a magnetic charge, since in decaying, say, a
neutrino into an electron, the W+ must -- based on my earlier results --
also carry away one unit of magnetic charge in addition to one unit of
electric charge. So, the X+ and X- will have the same internal symmetries
as the W+ and W-, but a) will be more massive because of the larger charge
arrived at through a weak version of the Dirac Quantization Condition and b)
very importantly, will couple only RIGHT-HANDED chiral states, thus leading
to a SU(2)L x SU(2)R weak interaction. If you look at my Volovik citation,


If you take SU(2)L x SU(2)R as a basis in your first try I think
that you should now have those six particles (massive vector bosons ?)
which mediates interactions between magnetic monopoles

(this could perhaps be compatible what I suggested you earlier with
H-M's particle drawings, eight color electricity colored magnetic
monopoles [four right- and four wrong- types of
neutrinos, right-types are not observable in expanding part of
the Universe] and six color electricity colored particles
which mediates their interactions [perhaps three {massive or
not massive vector bosons?} for both sides]?

I must admit that I have not very clear picture about
those H-M's drawings, so this above is my understanding
them at the moment. H-M's mass definition is also different
than what our physics has, this is why I have not put
any mass estimations here.

One problem could still exist, namely what follows if it
turns out later times that our famliar massive vector bosons
W+, W- and Z^0 have substructures as was pointed also
in H-M's drawings ?

I must read that Wheeler's book more closely in order
that I could get better understanding of the mathematics
he has used.

you will see that is an important step on the road to unifying the particle
phenomenology of quarks and leptons and the gauge generators of weak and
strong interactions to arrive at electromagnetic interaction sitting across
the weak and strong interactions thus unifying all three, which is where I
am ultimately driving. I think B-L using SU(4) is the ultra-high energy
symmetry of QCD, and when you combine this with SU(2)L x SU(2)R, you get
leptoquark unification, again, see Volovik. The one "inelegant" feature of
Volovik which needs to be cleaned up is the "spinon / holon" fudge to deal
with spin 1/2. It turns out that the magnetic monopoles add degrees of
freedom that will overcome this fudge and yield an even cleaner result where
what are now the spinons and the holons each have spin 1/2, and yet the
fermions they combine to form also have spin 1/2 due to a beautiful
conspiracy between the mathematics of chirality and the mathematics of
magnetic monopoles and the internal symmetries of isospin and leptoquark
QCD. I hope to demonstrate all of this in a future paper. (Problem is, I
have at least ten papers in the queue which will dramatically add to our
understanding of HEP. First priority is to fully nail NuTeV at .005, so
people will see that this stuff really is right and experimentally
confirmed, and not just wheel spinning, and some of the big shots will start
to pay attention.)

It is the third member of the triplet, call it X^0 corresponding to the Z,
(I called it Z' in my last post) which a preliminary calculation suggests
may pick up the extra .002 in the weak mixing angle to go from the .003
NuTeV anomaly I have theoretically arrived at so far to the total .005
anomaly observed experimentally.

Jay.

wrote:
Jay R. Yablon wrote:
. . .

On page 15 there seems to be equation (31, I don't put the
equation below, but only the idea of it) for already unified
(gravity and electromagnetic fields).

Einstein curvature = Geometrized Maxwell tensor

Are you using this equation for curved space-time in your
calculations or something else ?


Hannu, if it is handy, would you mind posting the equation you are asking
about with some context. My copy of this is buried somewhere in my attic.


I copy from the book some lines below:

R^v_u - (1/2)d^_v R = 2 f^a_u f^v_a - (1/2)d^v_u f^t_s f^s_t (31)

http://en.wikipedia.org/wiki/Electrovacuum_solution

Might help here. No more to add, just lurking.
Ken

OK, this is what I thought you were referring to.

Please take a look at an unpublished paper I have posted at:

http://home.nycap.rr.com/jry/Papers/...0Draft%204.pdf pages 1
through 8, equation 14. Also note in the foregoing how equation 4, the
identity used in the first Eprint at http://arxiv.org/abs/hep-ph/0508257,
operates like the Bianchi identity to replace the contracted derivative of
the Maxwell tensor and ensure energy conservation.

This was first found in another unpublished paper I prepared registered in
the US Copyright office in 1984, which is also at the same web site, at
http://home.nycap.rr.com/jry/Papers/Reinich.pdf.

The upshot is that one has duality invariance, even with sources, if and
only if spacetime is a vacuum, T^uv=0. When one breaks duality symmetry,
one inherently breaks the vacuum.

So, the duality-invariant equations of electrodynamics, with and without
sources, are those of the vacuum. And, by breaking duality symmetry as in
the first paper at http://arxiv.org/abs/hep-ph/0508257, we inherently bring
about matter. I hope to find the exact mechanism for this, i.e., onc that
can account for why the masses are as they are, and have made some recent
preliminary progress in that direction.

Jay.

_____________________________
Jay R. Yablon
Email:
wrote in message
ups.com...

Jay R. Yablon wrote:
. . .

On page 15 there seems to be equation (31, I don't put the
equation below, but only the idea of it) for already unified
(gravity and electromagnetic fields).

Einstein curvature = Geometrized Maxwell tensor

Are you using this equation for curved space-time in your
calculations or something else ?


Hannu, if it is handy, would you mind posting the equation you are asking
about with some context. My copy of this is buried somewhere in my
attic.


I copy from the book some lines below:

R^v_u - (1/2)d^_v R = 2 f^a_u f^v_a - (1/2)d^v_u f^t_s f^s_t (31)

This is a little different form on page 227 (I put some equations
of allready unified fields (gravity and electromagnetism) below):

(1) (3!)^-1 [abcd] (Df_bc / Dx^d) = 0 (half of Maxwell's equations),

(2) (-g)^(-1/2) (D/Dx^b) (-g)^(1/2) f^ab = 0 (the other half),

(3) R - (1/2)g_ab R = 2 f_ab f^d_b - (1/2)g f_st f^st)

(curvature of metric by Maxwell stress-momentum-energy density).

(D = ordinary partial derivation mark, a, b, c, d, s, t should be
really Greek labels, but I don't have them available here at
the moment)

Where g_uv are as source of metric fields, exclusively electromagnetic
fields,

F_ab = (c^2 / G^(1/2)) f_ab ,

and electromagnetic fields that are themselves free of all sources.




. . .

Do you have massive vector bosons (call it X) like W+ and W- but
now corresponding magnetic charges (X -magnetic charge and
X +magnetic charge)?


Not fully developed, but I think the answer will be, YES. But, even the
KNOWN W+ and W- should carry a magnetic charge, since in decaying, say, a
neutrino into an electron, the W+ must -- based on my earlier results --
also carry away one unit of magnetic charge in addition to one unit of
electric charge. So, the X+ and X- will have the same internal
symmetries
as the W+ and W-, but a) will be more massive because of the larger
charge
arrived at through a weak version of the Dirac Quantization Condition and
b)
very importantly, will couple only RIGHT-HANDED chiral states, thus
leading
to a SU(2)L x SU(2)R weak interaction. If you look at my Volovik
citation,


If you take SU(2)L x SU(2)R as a basis in your first try I think
that you should now have those six particles (massive vector bosons ?)
which mediates interactions between magnetic monopoles

(this could perhaps be compatible what I suggested you earlier with
H-M's particle drawings, eight color electricity colored magnetic
monopoles [four right- and four wrong- types of
neutrinos, right-types are not observable in expanding part of
the Universe] and six color electricity colored particles
which mediates their interactions [perhaps three {massive or
not massive vector bosons?} for both sides]?

I must admit that I have not very clear picture about
those H-M's drawings, so this above is my understanding
them at the moment. H-M's mass definition is also different
than what our physics has, this is why I have not put
any mass estimations here.

One problem could still exist, namely what follows if it
turns out later times that our famliar massive vector bosons
W+, W- and Z^0 have substructures as was pointed also
in H-M's drawings ?

I must read that Wheeler's book more closely in order
that I could get better understanding of the mathematics
he has used.

you will see that is an important step on the road to unifying the
particle
phenomenology of quarks and leptons and the gauge generators of weak and
strong interactions to arrive at electromagnetic interaction sitting
across
the weak and strong interactions thus unifying all three, which is where
I
am ultimately driving. I think B-L using SU(4) is the ultra-high energy
symmetry of QCD, and when you combine this with SU(2)L x SU(2)R, you get
leptoquark unification, again, see Volovik. The one "inelegant" feature
of
Volovik which needs to be cleaned up is the "spinon / holon" fudge to
deal
with spin 1/2. It turns out that the magnetic monopoles add degrees of
freedom that will overcome this fudge and yield an even cleaner result
where
what are now the spinons and the holons each have spin 1/2, and yet the
fermions they combine to form also have spin 1/2 due to a beautiful
conspiracy between the mathematics of chirality and the mathematics of
magnetic monopoles and the internal symmetries of isospin and leptoquark
QCD. I hope to demonstrate all of this in a future paper. (Problem is,
I
have at least ten papers in the queue which will dramatically add to our
understanding of HEP. First priority is to fully nail NuTeV at .005, so
people will see that this stuff really is right and experimentally
confirmed, and not just wheel spinning, and some of the big shots will
start
to pay attention.)

It is the third member of the triplet, call it X^0 corresponding to the
Z,
(I called it Z' in my last post) which a preliminary calculation suggests
may pick up the extra .002 in the weak mixing angle to go from the .003
NuTeV anomaly I have theoretically arrived at so far to the total .005
anomaly observed experimentally.

Jay.

Jay R. Yablon wrote:
OK, this is what I thought you were referring to.

Please take a look at an unpublished paper I have posted at:

http://home.nycap.rr.com/jry/Papers/...0Draft%204.pdf pages 1
through 8, equation 14. Also note in the foregoing how equation 4, the
identity used in the first Eprint at http://arxiv.org/abs/hep-ph/0508257,
operates like the Bianchi identity to replace the contracted derivative of
the Maxwell tensor and ensure energy conservation.

This was first found in another unpublished paper I prepared registered in
the US Copyright office in 1984, which is also at the same web site, at
http://home.nycap.rr.com/jry/Papers/Reinich.pdf.

The upshot is that one has duality invariance, even with sources, if and
only if spacetime is a vacuum, T^uv=0. When one breaks duality symmetry,
one inherently breaks the vacuum.

So, the duality-invariant equations of electrodynamics, with and without
sources, are those of the vacuum. And, by breaking duality symmetry as in
the first paper at http://arxiv.org/abs/hep-ph/0508257, we inherently bring
about matter. I hope to find the exact mechanism for this, i.e., onc that
can account for why the masses are as they are, and have made some recent
preliminary progress in that direction.

Jay.

Absolutely excellent Jay!
Let g=|g_uv|, Fred remember we discussed how fundamental
"g" can be, I think Jay has exposed an important part.

Let me try to demo, a bit short on math and longer on
intuition.

I'll ref to (the archaic) Pauli's "Theory of Relativity"
Eq. (54b), for an exposition of dual tensors, and find,
(I'll renotatize for convenience),

F*_14 = sqrt(g) F^23 .

which I'll call

E(x) = sqrt(g) B(x)

where E and B are Electric and Magnetic fields.

For a freely propagating wave c=1 and g=0
corresponding to the Euclidian metric, in 0,1...

g = 1 -V
-V 1

That means if E^x is real, B_x vanishes in a
Euclidian space for a light wave because the
EM wave E-field is perpendicular to the B-field.

When the wave encounters a density like,

g = 1-2phi -V+2phi
-V+2phi 1+2phi

the "g" is not zero, E is NOT perpendicular
to B, so the light will deflect, and therefore
indicate the existance of gravity and matter,
and may be regarded as a definition of matter.

What I see is Jay converting his "complexion
angle" to GR's "g" at a nuclear level.

The "magnetic monopole" term stands in for an
E-field modified by the high densities encountered
in the neighbourhood of the nucleus, as opposed
to the conventional relativistic modification of
the E-field by relative velocity.

Since the density of the nucleus is ~2.3*10^17
kg/m^3, and in view of AE's Guv = k*Tuv we should
expect a variation at the nuclear scale just as
we have found Newtons predictions to be modified
to prediction the orbit of Mercury.

Regards
Ken S. Tucker