| I took a quick amateur look on your papers:
Wow...an amateur look. Us [sic] professionals get paid to look.

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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:

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: