vktamhane12@rediffmail.com (V.K.Tamhane) wrote in message news:<9d62a326.0408152216.7082ef2d@posting.google.com>...
> selftrans@yandex.ru (Sergey Karavashkin) wrote in message news:<a42650fc.0408140220.2005f522@posting.google.com>...
> >      You have taken great efforts to prove the basic and fundamental
> > > mechanisms and certainly differentiated between the two actions
> > > responsible for the magnetic field based electromotive force.
> > 
> > Dear Mr Tamhane, how exactly you noted the connection between the
> > mathematical and physical formalism in comprehension of deep
> > underpinning of processes in nature. I from my side can only add that
> > the mathematical formalism can be true even with some incorrect
> > phenomenology. We see many examples in today physics based on the
> > principle properly formulated by Feynman: "Philosophers try to tell of
> > the nature without mathematics. I try to describe the nature
> > mathematically".
> 
>       How can nature be described mathematiclly when by nature we mean
> physical phenomena? This is something impossible. Concepts cannot be
> outcome derived from mathematical equations. Maxwell did predict EM
> wave but his mathematical treatment was based on solid foundation of
> aether. When aether goes so also the wave. What you said is true that
> without mathematical equations physics is incomplete. However
> mechanism of the physical phenomenon is of primary importance and I
> must say very difficult to come by.
>            By calling those indulging in verbose logic philosophoers
> and not physicists, Feynman is degrading improtance of concepts. No!
> Excellent work can be done without mathematics. Faraday is an immortal
> example.
> 
>          Rest of what you said, I snip because I fully agree with it.
> Give me some time to get acquainted with your work. Thanks.


Dear Mr Tamhane,

I fully agree with you, and first of all that Faraday is really
perfect, immortal example of checked phenomenology and searching mind.
In addition, I would like to recall Faraday's letter which he
bequeathed to open in 100 years after his death and in which he was
first who understood that the speed of light is finite. This does not
disparage a least the merits of Maxwell and Hertz either of Eichenwald
experiments, but it speaks of Faraday genius.
I would like to mark that Maxwell, if we follow just Maxwell, also
understood the versatile and complicated processes in EM field much
deeper than is proposed now as a marc. The system of four equations is
not Maxwellian. Different sources tell, Maxwell had 12 or 14
equations. Four equations are just like "Saga of Foresights" in the
last page of newspaper. And this is Hertz' or Heaviside's, but not
Maxwell's. I am far from mind to belittle these scientists, but having
shortened the general phenomenology, they shortened the meaning,
pursuing the simplicity like in Newtonian equations. It worsened the
situation that Maxwell, Hertz and Heaviside had available only
conservation laws for stationary fields and had not any experience,
how to work with delayed potentials. Should they have our conservation
theorems for dynamic fields to which I referred you, Maxwell would not
need to foresee the magnetoelectric induction law which completes the
general systems of equations. He would simply derive this law as a
corollary from the dynamic conservation theorem of circulation of
vector. But the fact that he predicted, even without all other what
Maxwell had done during his short life, makes him immortal. At the
same time, prediction cannot fully solve the problems of
phenomenology. The phenomenology is created as a symbiosis of physical
and mathematical formalism. If we ground only on philosophy, it is too
easy to slip into sophistry and philosophical fabrication. Operating
with mere mathematics, it is impossible to catch the nut of effect and
the way to improve the mathematical formalism. It is too easy to pass
to manipulations with mathematical symbols and to vary the statement
of problem, passing, just as in the first case, to a self-confident
abstraction. But without mathematics we cannot build a harmonious
conception. And just the fact that Maxwell had not a complete set of
initial data to formulate the integral phenomenology has caused the
complicacy and, finally, incompleteness of his conception. This was
not his guilt, it was a circumstance that experimental physics and
mathematical formalism of that time were not ready for solutions of
such level. And pity that many generations of scientists clearly saw
the problems of this system of equations and obeyed Maxwell authority
whose name this system bears, but they did not dare to enter this
labyrinth. I met also here in the newsgroups the colleagues who lost
the ability to think independently when approaching to the entrance to
this labyrinth.
This is the trouble of today physics that Relativity by Einstein and
his followers has brought to physics not so much new conception (all
their works are a patch-work quilt  of separate unfinished works by
classical physicists) as the methodology to manipulate with
mathematics. Not in vain Feynman whom I cited in his following
lectures is surprised that, despite all bricks seem to be present, the
result does not tally. Their so-called discoveries are such for one
day, they fail after next experiments. And the problem is just that
mathematical formalism has to strongly follow the phenomenology stated
in the problem. If we have well studied phenomenology, the
mathematical formalism enables us to improve many aspects of
phenomenology and to operate with the help of tables, plots and
numerical predictions. But the mathematical formalism is not able to
exceed the limits of phenomenology, and if someone forced it, there
comes to force a known rule of extrapolation: the farther from
reliably checked results the lower reliability of prediction. To
develop, we have to improve the phenomenology which would
automatically improve the modelling equations and will allow us to
find the solutions exceeding the limits of today phenomenology. This
is the way as I see it - the only way of development which brings a
real and long-lasting success.
As an example I would mention Newton's equations. If we work with
small velocities, these equations give a complete and exact pattern of
processes. In my discussions with colleagues I multiply encountered
the attempts, so to say, to re-formulate or doubt Newtonian system in
the domain where it is true. Vain attempts. It remains impeccable and
closed as the mathematical formalism. But if we pass to high
velocities, the action and counter-action become inequal - the basic
principle on which the Newton's formalism is grounded is broken. This
naturally changes the modelling equations and solutions. Lorentz
understood it well, but due to definite circumstances he could not
finally formulate it. While Einstein simply primitivised Lorentz
equations and made so a bad service to physics. Some time we need to
sort these things out. The more that the issues of magnetic field 
nature and of gravitation lay in these heaps. We tend this direction,
as possible.
On the other hand, as I already said, the phenomenological conception
without mathematics is doomed. We can recall Descartes. He formulated
all laws of dynamics "on his fingers", before Newton! But he had not a
trifle - he did not know the infinitesimals, though we cannot think
him mathematically ignorant, can we? ;-) And Newton would not succeed
to write his Principia, if not the conception of infinitesimals which
he had due to his teacher. The matter is, the outcome to some new
phenomenology is always caused by the developed new class of modelled
equations. Having these equations unsolved, it is difficult, or rather
impossible to correct our penetration into the unknown area. See,
Faraday with all his genius carried out his experiments with unipolar
motor - one step to a generator! - but he has not this step done,
because all his work was "on fingers". Mathematics did not follow his
phenomenology, and he was unable to make an advanced prediction. And
when Maxwell developed his mathematics, though complicated and
imperfect but allowing to calculate, it started the time of great
technological discoveries. And we can illustrate this connection
between the phenomenology and mathematical formalism by many facts
from the history of physics. So I am saying namely of symbiosis, and
in no case of chaotic turns of physics and mathematics. Such
"sequence" can create only monsters. The phenomenology and first basic
corroborating experiments have to precede. Then mathematical modelling
and new experiments have to be done, which with numerical
characteristics will corroborate this model correct and in this way
open the way for further development of phenomenology. Such is the way
which we see and our experience says it is successful.

I would be interesting to hear your opinion.

All the best,

Sergey