Question

[Epaminondas]

Dear Vladimir,

It was my pleasure to read your article "REFORMULATION INSTEAD OF
RENORMALIZATIONS" posted on the arxive. I was also interested in
reading discussion of this article on Physics Forums.

As I can see from PF discussion, one of the major arguments of your
opponents there was that your model does not reproduce Maxwell
equations (although you insist that it does. I did not verify that,
but at least I did not see any reference to magnetic field in your
article).

Is there a real problem there? If Maxwell equations are not reproduced
explicitly in your model, do you think that is because Maxwell
equations need to be justified in the case of a particle model, or for
any other reason?

And one more question. If a particle is at rest, with no external
force acting on it, is it necessary that there will be no oscillations
there?

[Vladimir Kalitvianski]

On 27 mar, 14:18, Epaminondas <murod.abdukhaki...@gmail.com> wrote:
> Dear Vladimir,
>
> It was my pleasure to read your article "REFORMULATION INSTEAD OF
> RENORMALIZATIONS" posted on the arxive. I was also interested in
> reading discussion of this article on Physics Forums.
>
> As I can see from PF discussion, one of the major arguments of your
> opponents there was that  your model does not reproduce Maxwell
> equations (although you insist that it does. I did not verify that,
> but at least I did not see any reference to magnetic field in your
> article).

My opponent's argument is too superficial. Not only magnetic field is
absent but also the electric field is absent in one-particle
formulation. These electric and magnetic fields are "attached" to the
particle and are explicitly known if the particle motion is known so
there is no need to write and solve the corresponding equations. The
fields created by a particle have the only meaning - to be put as
external fields into the equations of motion of another charged
particle. As soon as we write equations for one charge, we have no
place to put its fields into, despite we have the field solutions. I
solve only radiated field equations whose field propagates from its
source, and I do it just to show how energy-momentum (work of external
filed) is split between "mechanical" and "wave" subsystems.

> And one more question. If a particle is at rest, with no external
> force acting on it, is it necessary that there will be no oscillations
> there?

If our system (charge+filed) is in its ground state, then no
oscillations (at least classical) should be. But is is very difficult
to prepare such a state because exciting low-energy oscillators is
very easy.

Regards,

Vladimir.

[Epaminondas]

Thanks for your quick response, Vladimir.

Please note that I do not pretend to criticizing your approach. On the
contrary, I admire your explanation of reformulation idea illustrated
by mechanical model.

My questions are very practical and relate to the problem I'm working
on now.

First of all, I'm not sure that there is a need to use the term
"electronium", because an electron has never been detected apart from
its electromagnetic field. It is always a compound system.

As I understand, in your mechanical model "particle 1" can be
associated with fermion field (i.e. the field that relates to smeared
charge and flux distribution), while "particle 2" is associated with
EM field of the electron.

The spring is used to illustrate the following: the dynamics of EM
field is defined by current configuration of fermion field. So,
presumably eqn. (2) in your article can be associated with the
Maxwell equations. That's why I was asking my first question.

Fermion field is also affected by EM field, which is shown by eqn. (1)
(although I'm not quite sure which equation for fermion dynamics can
be associated with your eqn. (1): Dirac, Weyl, some new equation,
etc.?).

When you say that:

> ... Not only magnetic field is

> absent but also the electric field is absent in one-particle
> formulation.

that probably mean that "one-particle formulation" is associated with
the centre of inertia motion. Just like internal motion variables are
not presented in eqn. (9) of your article.

What is not clear is why

> ... These electric and magnetic fields are ... explicitly known if the particle motion is known so

> there is no need to write and solve the corresponding equations.

Do we really know, say, the configuration of electromagnetic fields of
an electron at rest (i.e. with zero centre of inertia motion)? I guess
it is not simply the Coulomb potential.

> If our system (charge+filed) is in its ground state, then no
> oscillations (at least classical) should be. But is is very difficult
> to prepare such a state because exciting low-energy oscillators is
> very easy.

Well, if we consider electromagnetic model of electron (charge + EM
field), the ground state is probably a balanced combination of
fermion and EM fields, that is stable in time. I think there might be
only discrete number of such balanced configurations, and for sure
Coulomb potential is not one of them. These balanced configurations
can be found if we correctly define the "spring", i.e. eqns. (1) and
(2) for the model. Do you have any idea what could be the correct form
of eqn. (1)?

Best regards,

Murod

[Vladimir Kalitvianski]

Dear Murod,

I do not mind if you criticize my ideas and results. On the contrary,
your critics is welcome.

I will answer your remarks later, OK?

Regards,

Vladimir.

[Epaminondas]

Ok. Let me know if I'm just bothering you.

[Vladimir Kalitvianski]

No, you do not bother me at all. By the way, there is a blog of mine
in Russian here http://fishers-in-the-snow.blogspot.com/

[Epaminondas]

On Mar 28, 3:15 am, Vladimir Kalitvianski

<vladimir.kalitvian...@wanadoo.fr> wrote:
> No, you do not bother me at all. By the way, there is a blog of mine
> in Russian herehttp://fishers-in-the-snow.blogspot.com/

Very interesting. But LaTeX doesn't work.

[Vladimir Kalitvianski]

> > No, you do not bother me at all. By the way, there is a blog of mine
> > in Russian herehttp://fishers-in-the-snow.blogspot.com/
>
> Very interesting. But LaTeX doesn't work.

Try FireFox to see LaTeX. It is browser-dependent indeed.

[Vladimir Kalitvianski]

On 27 mar, 22:30, Epaminondas <murod.abdukhaki...@gmail.com> wrote:

> First of all, I'm not sure that there is a need to use the term
> "electronium", because an electron has never been detected apart from
> its electromagnetic field. It is always a compound system.

Agree but I have sometimes difficulties in distinguishing the real
electron as a compound system and a charge on which external forces
act.

> As I understand, in your mechanical model "particle 1" can be
> associated with fermion field (i.e. the field that relates to smeared
> charge and flux distribution), while "particle 2" is associated with
> EM field of the electron.

Particle 1 is a charge. I do not mention its statistics because it is
not alone anyway. Spins/statistics describes quasi-particles, in my
opinion.

> The spring is used to illustrate the following: the dynamics of EM
> field is defined by current configuration of fermion field. So,
> presumably eqn. (2) in your article  can be associated with the
> Maxwell equations. That's why I was asking my first question.

The radiated field dynamics is determined with action of an external
force on the charge. So the Maxwell equations are associated with
equation (5), and the half-integer spin system (not obligatory spin
1/2 but 1/2 + n) is associated with (4), speaking roughly and
classically.

> Fermion field is also affected by EM field, which is shown by eqn. (1)
> (although I'm not quite sure which equation for fermion dynamics can
> be associated with your eqn. (1): Dirac, Weyl, some new equation,
> etc.?).

No, a fermion is the whole system, electronium. The external force
acts on the charge which belongs to the system. The charge is strongly
coupled in the system and cannot, in my opinion, have a certain spin.

> When you say that:
>
> > ... Not only magnetic field is
> > absent but also the electric field is absent in one-particle
> > formulation.
>
> that probably mean that "one-particle formulation" is associated with
> the centre of inertia motion. Just like internal motion variables are
> not presented in eqn. (9) of your article.

No. The field equations have an explicit solutions given in many
textbooks. The field of one moving charge can be represented as
electric, magnetic, and radiated. This filed is useful when put in the
mechanical equations of another charge, as external fields. I do not
put these fields into the equations of the sourcing charge (no self-
action is implied). So, when I write dynamics of one real electron (=
electronium), I write dynamics of the CI and relative motion that
depend on the external field. The relative motion dynamics coincides
with the radiated field dynamics of the usual electrodynamics. My goal
was to show that withing this, electronium concept, no self-action is
necessary to radiate. So the electric, magnetic, and radiated fields
are practically the same as in the usual CED.

> Do we really know, say, the configuration of electromagnetic fields of
> an electron at rest (i.e. with zero centre of inertia motion)? I guess
> it is not simply the Coulomb potential.

Experimentally we often observe an inclusive picture where many
inelastic low-energy processes are occurring. An inclusive picture
resembles a point-like charge, at least at large distances.

>
> Well, if we consider electromagnetic model of electron (charge + EM
> field), the ground state is probably a  balanced combination of
> fermion and EM fields, that is stable in time. I think there might be
> only discrete number of such balanced configurations, and for sure
> Coulomb potential is not one of them.

I think there may be many smeared charge configurations, like in
atoms. Only the ground state is stable; the others are not. Their
"decay" time depends strongly on the external fields and boundaries.

> These balanced configurations
> can be found if we correctly define the "spring", i.e. eqns. (1) and
> (2) for the model. Do you have any idea what could be the correct form
> of eqn. (1)?

No. For the low-energy electrodynamics it is mostly elastic forces
(photon creation and absorption) but starting from some energy
threshold the may be pair creation channels. I have not tried to
describe this yet. It is inexhaustible matter.

My electronium construction is mathematically and physically similar
to the atom description. An atom has an infinite number of excited
states. An atom next to another atom has different spectrum of excited
states. So the quasi-particles are different. I do not think we will
be able to encompass all possible quasi-particles.

Regards,

Vladimir.

[Epaminondas]

Dear Vladimir,

I guess I understand your point now.

I've also read a lecture by F. Rohrlich (referenced in your article)
that explains the overall picture (which, by the way, did not change
significantly in almost 50 years).

Of course, re-forlmulation makes sense, at least it helps avoiding
meaningless "renormalization" procedure in solving every single
physical problem. But even in this context re-formulation of the
modern QED has not been completed yet (correct me if I'm wrong).

What I'm concerned about is that re-formulation does not help much (or
at all) in resolving major problem of the theory, i.e. developing the
correct particle model.

I'm sure that only one thing is missing but needed to complete the
model. That is something that would replace the "Lorentz force", i.e.
appropriate equation for the charge.

It has to be an assumption independent of Maxwell's equations, but
reduced to them in the case of the "free particle", i.e. particle at
rest.

In modern ED the Dirac equation is used to determine charge dynamics.
But Dirac himself said that Dirac equation is wrong, and it is only
because it leads to divergences.

If the correct equation will be found, we would be able to derive the
value of electron mass from the theory. (By the way, this is probably
the only kind of argument that would be admitted by the "mainstream
physicists".) On the other hand, this would enable us to identify the
explicit particle structure, i.e. remove dependence of the whole
theory on the need to define the structure on ad hoc basis. Hence,
there will be no need to consider particle as point-like (in order to
get rid of structure dependence), and no divergences will appear in
the theory.

This is actually something I'm working on now. I've derived the
appropriate equation for the charge dynamics, and it looks very
similar to Dirac equation (which is not surprising I guess). This
discussion helped me very much to sort out all the things. Many thanks
for your time and cooperation.

Yours,

M.

[Vladimir Kalitvianski]

On 31 mar, 19:13, Epaminondas <murod.abdukhaki...@gmail.com> wrote:

> Of course, re-formulation makes sense, at least it helps avoiding

> meaningless "renormalization" procedure in solving every single
> physical problem. But even in this context re-formulation of the
> modern QED has not been completed yet (correct me if I'm wrong).

No, the reformulation has not been completed yet. My efforts are just
a very modest try.

> This is actually something I'm working on now. I've derived the
> appropriate equation for the charge dynamics, and it looks very
> similar to Dirac equation (which is not surprising I guess). This
> discussion helped me very much to sort out all the things. Many thanks
> for your time and cooperation.

You are welcome anytime!

Vladimir.