🚀 go-pugleaf

thoovler@excite.com (Igor) wrote in message news:<d434b6c6.0402020056.7de6d18b@posting.google.com>...
> selftrans@yandex.ru (Sergey Karavashkin) wrote in message news:<a42650fc.0402011435.6e84feaa@posting.google.com>...
> > Dear Colleagues,
> > 
> > We open the new volume 

[snip]
> > 
> > Please enjoy reading full text:
> > 
> > http://angelfire.lycos.com/la3/selftrans/v4_1/contents4.html#grad
> > 
> > I hope, it will be interesting for many of you, and look forward to
> > hear your opinion.
> > 
> > Sergey.
> 
> There seems to be a mistake on the first page, where you have a scalar
> function dependent on both the radial coordinate and angle theta.  But
> when you take the gradient, you only have a radial component but no
> angular one.  This is why you're concluding that curl grad is not
> zero, when, once you do it properly, it must be.  Curl grad must
> always vanish regardless of the nature of the coordinate system.  It's
> an elementary theorem of vector calculus.  I hope this has been
> helpful.  Good luck.


Dear Igor,

I understand you. You show the most typical reaction to this cycle of
our papers: "Something is wrong! Where is the mistake?" Merely
psychologically, you already do not consider how much logic is the
proof, how much correct is mathematics, you only filter the material,
seeking the trick.

You see the mistake in the formula for potential in the first page of
paper. Let us think, from what are you concluding? That it is
unobvious that the radial component MUST NOT be dependent on other
parameters? Well, this is just unobvious. If you re-read the "New Year
question from Leo" to which we refer, you will see, Leo suggested a
standard problem - radiating element of current. This problem is
axially symmetric, not centrally symmetric. On the other hand, the
radial component can be independent of spherical angles only in case
of central symmetry. You can make sure, reading our paper up to the
problem of pulsing source. In this case the radial component of
gradient of potential does depend only on the distance from source.
But if you read up to the problem of oscillating source, you will see
your prediction failed. In that problem the gradient of scalar
potential already depends on the spherical angle - it means, the
potential depends, too. As I just said, this is due to another
symmetry. So the scalar potential dependent on angle theta in Leo's
problem is correct.

Further, should you attentively read this appendix to the paper on
divergence theorem (just "New Year question from Leo"), you would see,
in this problem the vector and scalar potentials are derived on the
basis of standard formalism, so, when you are saying of mistake, it
would be correct of you to point the incorrectness in the derivation.
You did not point. And as far as I can judge, you will not, as there
is no incorrectness. ;-) All your substantiation is grounded on the
idea of "obvious - unobvious", just as your statement

>This is why you're concluding that curl grad is not
>zero, when, once you do it properly, it must be.  Curl grad must
>always vanish regardless of the nature of the coordinate system.

However this is too little for physics. Just such approach a priori
brings the physics to the obstruction which is so hard-lifted by many
generations of physicists. So I would be very grateful to you if you
admit this simple truth that we have to analyse thoroughly just the
material and to refuse as fully as possible the idea of "obvious -
unobvious" in our judgement. And if speaking of the present problem,
both in the discussed paper and in my respond to Leo you can find the
references, what, where from and how has been taken. As I can see, you
are Russian-speaking and these references are available for you.
Please, take these books and track the solution, then tell me your
result. Of course, if it interests you but is not caused by a trivial
insistence to retain the dogma.

Enjoy analysing,

Sergey