First Blog Entry: 1984 paper on "Already Unified Theory"
Jay R. Yablon
I have posted my first substantive Weblog entry, which links to a paper
I wrote in 1984 titled: An Extension of Reinich's Already Unified Theory
to Electromagnetic Sources, In a Simply-Connected Spacetime Topology and
linked at:
http://jayryablon.files.wordpress.com/2007/07/reinich.pdf
This paper still influences the direction of my research today, most
notably as regards my interest in electric/magnetic duality, and my
conviction that baryons will eventually become recognized as third-rank
antisymmetric tensor sources. This original paper, and my blog entry,
shows how these two research interests flow from a common foundation
based on geometrodynamics.
The blog is at:
http://jayryablon.wordpress.com/
I invite discussion both here and there.
Best,
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
Peter
Thank you for providing your ms.
> http://jayryablon.files.wordpress.com/2007/07/reinich.pdf
For me, it contains far-reaching ideas, but is difficult to follow, because
the common sequence of conclusions is changed. - I apologize, if my doubts
are caused by the mediocre quality of my printer.
You state that (5) is tied to "source-free electrodynamics": Is J^u not a
source? How this complies with (9) and (10)?
In view of (8) it seems to me that you deal rather freely with the notion
'Maxwell's equations'. For this, I would like to propose that you start with
the original set, show how to come to (8) and only then discuss the
generalizations and specializations.
In contrast to your text, T thought that (8) stems from (10), what do you
think?
(14a) seems to contradict the original Maxwell equations, for this I stop
here and ask for clarification.
Thank you,
Peter
Jay R. Yablon
news:guest.20070726221720$79...@news.killfile.org...
> Hi Jay,
>
> Thank you for providing your ms.
>
>> http://jayryablon.files.wordpress.com/2007/07/reinich.pdf
Hi Peter:
>
> For me, it contains far-reaching ideas, but is difficult to follow,
> because
> the common sequence of conclusions is changed. - I apologize, if my
> doubts
> are caused by the mediocre quality of my printer.
>
> You state that (5) is tied to "source-free electrodynamics": Is J^u
> not a
> source? How this complies with (9) and (10)?
Actually, as I look at this now, 23 years later, the statement that
F=dA (5)
reduces everything to source-free electrodynamics is wrong. Rather, (5)
is what produces (8).
>
> In view of (8) it seems to me that you deal rather freely with the
> notion
> 'Maxwell's equations'. For this, I would like to propose that you
> start with
> the original set, show how to come to (8) and only then discuss the
> generalizations and specializations.
The best way to look at this is in the linked file below:
http://jayryablon.files.wordpress.com/2007/07/reinich-2007.pdf
> In contrast to your text, T thought that (8) stems from (10), what do
> you
> think?
You are correct.
>
> (14a) seems to contradict the original Maxwell equations, for this I
> stop
> here and ask for clarification.
I agree. See the linked file above.
Jay.
>
> Thank you,
> Peter
>
Jay R. Yablon
I wanted to point out some continuing discussion which Carl Brannan and
I are having over at
http://jayryablon.wordpress.com/2007/07/27/follow-up-discussion-of-lab-note-1-a-2007-update/#comment-4
Best,
Jay.
Jay R. Yablon
news:5gtbkjF...@mid.individual.net...
> "Peter" <end...@dekasges.de> wrote in message
> news:guest.20070726221720$79...@news.killfile.org...
>> Hi Jay,
>>
>> Thank you for providing your ms.
>>
>>> http://jayryablon.files.wordpress.com/2007/07/reinich.pdf
>
> Hi Peter:
>
>>
>> For me, it contains far-reaching ideas, but is difficult to follow,
>> because
>> the common sequence of conclusions is changed. - I apologize, if my
>> doubts
>> are caused by the mediocre quality of my printer.
>>
>> You state that (5) is tied to "source-free electrodynamics": Is J^u
>> not a
>> source? How this complies with (9) and (10)?
>
> Actually, as I look at this now, 23 years later, the statement that
>
> F=dA (5)
>
> reduces everything to source-free electrodynamics is wrong. Rather,
> (5) is what produces (8).
Peter,
On a review of the above, I retract my retraction. The statement in my
original 1984 that the Abelian vector potential causes both magnetic AND
electric sources to vanish -- that is, leads directly to source-free
electrodynamics -- is correct. It is just that the proof for the
electric sources is a little bit more complicated, see below . . .
>
>>
>> In view of (8) it seems to me that you deal rather freely with the
>> notion
>> 'Maxwell's equations'. For this, I would like to propose that you
>> start with
>> the original set, show how to come to (8) and only then discuss the
>> generalizations and specializations.
>
> The best way to look at this is in the linked file below:
>
> http://jayryablon.files.wordpress.com/2007/07/reinich-2007.pdf
>
. . . Here is why the Abelian potential zeros out electric as well as
magnetic charge: In the file linked above, equation (9) is wrong. On
the second line, for the term \delta^stlg_tslg&_v, I neglected to flip
the sign between ^st and _ts (^{\sigma\tua and} _{\tau\sigma}). When
you do this, the whole expression in (9) becomes identical to zero.
Then, via 3, the electric current vanishes, F^ts_;t = 0. I knew this 23
years ago, and have recovered this understanding by going back through
the detailed calculations.
This, by the way, is the classical "zero charge" problem I refer to in
my paper at http://arxiv.org/abs/hep-ph/0508257. Much of this paper
explores this "zero charge" problem in depth. The crux of the problem
is that an Abelian potential really does zero away both magnetic AND
electric charge. Short of just postulating a non-Abelian potential
which runs contrary to what we usually employ for U(1) electrodynamics,
the solution to this, shown in section 7 of the above, is to introduce a
LOCAL DUALITY symmetry, and to absorb the gradient of the duality
complexion angle into a new vector boson just as is done in gauge
theory. In fact, in what was quite a surprise to me when I first found
it, an SU(2) symmetry then emerges naturally. So, we do end up with a
Yang-Mills (non-Abelian) potential, but we come by it via local duality
symmetry. Now, the problem becomes that when we return electric charge
to the theory in this way, we also obtain a magnetic charge. The only
way to get rid of the magnetic charge, is to then break the electric /
magnetic symmetry.
In all of this, the potential is a central actor. I am still giving a
lot of thought to the Helmholtz decomposition you suggested. Have you
considered at all, how this relates to non-Abelian potentials?
My latest post, in a brand new thread, is the point from which I'd like
to pick up our discussion.
Best regards,
Jay.
Jay R. Yablon
Actually, on fourth thought, I retract the retraction of my retraction.
The charge does not become zero. Details of why follow below.......
>
>>
>>>
>>> In view of (8) it seems to me that you deal rather freely with the
>>> notion
>>> 'Maxwell's equations'. For this, I would like to propose that you
>>> start with
>>> the original set, show how to come to (8) and only then discuss the
>>> generalizations and specializations.
>>
>> The best way to look at this is in the linked file below:
>>
>> http://jayryablon.files.wordpress.com/2007/07/reinich-2007.pdf
>>
.......Referring again into (9) in the above, one must emply the full,
expanded expressions for:
delta^abc_def = delta^a_d delta^b_e delta^c_f
+ five more terms in antisymmetric combinations.
When those are used, (3) in the above reduces to a trivial identity
which says merely that:
F_vsF^ts_;t = F_vsF^ts_;t
The charge is NOT zeroed. Peter, you were right in your initial
impression.
Jay.
Peter
> >> 'Maxwell's equations'. For this, I would like to propose that you start
> >> with the original set, show how to come to (8) and only then discuss the
> >> generalizations and specializations.
Let me stress this, again. It would be a good idea to start with
Maxwell's 'On physical lines of force', where the complete set is given, and
that _with_ the use of the potentials. What we now call the microscopic
Maxwell, or Maxwell-Lorentz eqs. blurrs the physical roles of the potentials.
Further, I have still not understood the physical motivation for seeking
a 'magnetic charge' within classical electromagnetism.
> This, by the way, is the classical "zero charge" problem I refer to in
> my paper at http://arxiv.org/abs/hep-ph/0508257. Much of this paper
> explores this "zero charge" problem in depth.
Yes. From it, I have understood that
*F_uv = M_u;v - M_v;u
leads to wrong results. Hence, either '*' is not the magnetic<->electrical
duality operation, or there is no M_u such, that
*(A_u;v - A_v;u) =/= M_u;v - M_v;u
BTW, do the operations '*' and ';' commute?
> The crux of the problem
> is that an Abelian potential really does zero away both magnetic AND
> electric charge. Short of just postulating a non-Abelian potential
> which runs contrary to what we usually employ for U(1) electrodynamics,
> the solution to this, shown in section 7 of the above, is to introduce a
> LOCAL DUALITY symmetry, and to absorb the gradient of the duality
> complexion angle into a new vector boson just as is done in gauge
> theory. In fact, in what was quite a surprise to me when I first found
> it, an SU(2) symmetry then emerges naturally. So, we do end up with a
> Yang-Mills (non-Abelian) potential, but we come by it via local duality
> symmetry. Now, the problem becomes that when we return electric charge
> to the theory in this way, we also obtain a magnetic charge. The only
> way to get rid of the magnetic charge, is to then break the electric /
> magnetic symmetry.
This sound rather artificial, doesn't it? This suggest first to find a
physical need for the magnetic charge, then it will become much easier to
find the maths :-)
> In all of this, the potential is a central actor. I am still giving a
> lot of thought to the Helmholtz decomposition you suggested. Have you
> considered at all, how this relates to non-Abelian potentials?
No, since the Helmholtz decomposition is a property of 3D vector fields.
Best wishes,
Peter
Jay R. Yablon
>> >> In view of (8) it seems to me that you deal rather freely with the
>> >> notion
>> >> 'Maxwell's equations'. For this, I would like to propose that you
>> >> start
>> >> with the original set, show how to come to (8) and only then
>> >> discuss the
>> >> generalizations and specializations.
>
> Let me stress this, again. It would be a good idea to start with
> Maxwell's 'On physical lines of force', where the complete set is
> given, and
> that _with_ the use of the potentials. What we now call the
> microscopic
> Maxwell, or Maxwell-Lorentz eqs. blurrs the physical roles of the
> potentials.
Peter, I just figured out how to formulate Helholtz decomposition
covariantly (which does require, however, that we add a &A/$t term),
will write up and post.
>
> Further, I have still not understood the physical motivation for
> seeking
> a 'magnetic charge' within classical electromagnetism.
>
>> This, by the way, is the classical "zero charge" problem I refer to
>> in
>> my paper at http://arxiv.org/abs/hep-ph/0508257. Much of this paper
>> explores this "zero charge" problem in depth.
>
> Yes. From it, I have understood that
>
> *F_uv = M_u;v - M_v;u
>
> leads to wrong results. Hence, either '*' is not the
> magnetic<->electrical
> duality operation, or there is no M_u such, that
>
> *(A_u;v - A_v;u) =/= M_u;v - M_v;u
>
> BTW, do the operations '*' and ';' commute?
No, because the dual of a second rank antisymmetric tensor is not the
samed as the dual of a third rank antisymmetirc tensor or a vector. See
http://arxiv.org/pdf/hep-ph/0508257 starting at eqaution (4.1) for a
discussion of first / third rank duality in relation to second/second
rank duality.
Perhaps.
>
>> In all of this, the potential is a central actor. I am still giving
>> a
>> lot of thought to the Helmholtz decomposition you suggested. Have
>> you
>> considered at all, how this relates to non-Abelian potentials?
>
> No, since the Helmholtz decomposition is a property of 3D vector
> fields.
Will soon post on Helmholtz.
Jay
>
> Best wishes,
> Peter
>
Peter
> >> >> In view of (8) it seems to me that you deal rather freely with the
> >> >> notion
> >> >> 'Maxwell's equations'. For this, I would like to propose that you
> >> >> start with the original set, show how to come to (8) and only then
> >> >> discuss the generalizations and specializations.
Still waiting for the result :-)
The discretization of electrical charge is most seducing. However, why no
effects have ever been observed?
Furthermore, Jackson's formulae suggest magnetic charge, g->0 as h->0. On the
other hand, he modifies Maxwell's eqs. for introducing g, but these have
nothing to do with h at all :-o
Please advise!
Best wishes,
Peter