From: meron@cars3.uchicago.edu
Subject: Re: Do physicists really use real numbers?
Date: Thu, 14 Sep 2000 04:30:57 GMT
Newsgroups: sci.math,sci.physics
Summary: [missing]

In article <39c06aea.49706541@news-server>, jpolasek@cfl.rr.com (John C. Polasek) writes:
>On Thu, 14 Sep 2000 02:35:48 GMT, meron@cars3.uchicago.edu wrote:
>
>>In article <39c04fb1.42736426@news-server>, jpolasek@cfl.rr.com (John C. Polasek) writes:
>>>On Wed, 13 Sep 2000 23:56:53 GMT, meron@cars3.uchicago.edu wrote:
>>>Big Snip
>>>
>>>> In vector analysis language you assume div(E) = rho 
>NOT
>>>>(i.e. charge density)
>Thanks for the explanation
>>>> and rot(E) = 0.
>>>
>>>No, Div D = rho
>>>
>>>>  This assumptions are 
>>>>mathematically equivalent to stating that E is proportional to 1/r^2.
>
>I'd be interested to have you show me how this follows; I can't do it.
>>>
There is a known theorem (by Helmholz, I think) that any continuous 
field decreasing to zero at infinity is *uniquely* defined by its div 
and rot.  Uniquely means that if you know div(E) and rot(E) over the 
whole space, then there is only one E that fills the bill.  Thus, if 
you've found a solution, that's the only solution.  In the case I 
outlined we have a solution, i.e. constant/r^2 and by the theorem 
that's the only one.  This is the story in a nutshell.  If you want a 
full proof with all the epsilons and deltas, any good book of 
classical field theory should've it.
>
>>This is included in the above.  Should be quite 
>>obvious.
>
>What is included in the above? I may need help herer.
>
The case of div(E) = 0 is simply a special case of div(E) = rho.

>You're doing it again.  You said Div E = rho, and that's wrong.
> Div D = 0 and Rot E = 0

D is a macroscopic description where we sweep all the microscopic 
effects of polarization under the rug of dielectric function.  
Microscopically there is only E.

 and youre trying to say I deduced the inverse
>square law from it. 

I'm saying that That it is equivalent, yes.
>>
>>It may interest you that in CGS the units of charge are 
>>cm^(3/2)*gr^(1/2)/sec.  Enjoy:-)

>Your erudition continues to amaze. But I already pointed out that
>simple rational exponents are common in my reply above (9/13 2:26PM).
>You will never see a number like 1.9999999999.>
>
Frankly, I don't especially expect to see one.  But there is no law of 
nature saying that this is impossible.

Mati Meron                      | "When you argue with a fool,
meron@cars.uchicago.edu         |  chances are he is doing just the same"