What is the basis of magnetic and electric inductance? In other words,
can the time dependent Maxwell equations be deduced from first
principles? If so, how? I ask this question in the same vein as one
might ask what is the basis of the magnetic field, i.e., we now know
that magnetic fields are Lorentz transforms of electric fields, a la
Special Relativity. (My background is MS Physics)

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Request for Question Clarification by hedgie-ga on 01 Jun 2005 11:00 PDT

dear thverbose-ga

"Can Maxwell equations be deduced from first principles? .."

 I would say  Maxwell equations are one of the first principles,
 particularly when written in the relativistic form.

 So what you want to derive them from ? QED?
 Some electro-weak unified theory?  

 'What is a basis of '  sounds like a  philosophical question

  - some connection to Mach's principle perhaps,
 or an apeal to a more  abstract or more 'fundamental' theory.

Which one are you after?

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Clarification of Question by dearthverbose-ga on 01 Jun 2005 15:16 PDT

My E/M education was via ?Classical Electrodynamics? by Jackson. I
have no knowledge of a relativistic form of Maxwell?s equations. Do
the time dependent equations result from adding special relativity to
electrostatics?

I?m not in a position to set any requirements as to what theory should
form the basis to inductance. If QED or an electro-weak unified theory
allows one to deduce inductance, fine, as long as the answer isn?t
couched in pure math. I?m interested in the physical ideas, not the
mathematical hocus pocus. Besides, I won?t understand the math.

If I asked what is the basis of magnetism, would you also consider
that a philosophical question? I?m willing to accept electrostatics as
a first principle. I simply believe that there must be a physical
basis to inductance just as there is a physical basis to magnetism,
i.e., magnetism is an electrostatic field observed from a moving
reference frame.

I don?t know how to answer your question without simply rewording my
original post, so I don?t think this will help much.

Your clarification was helpful and I will provide references which, 
hopefully, will throw some light on the issue.  These references
are involving some unsolved (or at least 'not fully agreed on') problems.

Just ,please, remember that it is (almost) as dificult to answer this
as it was to ask it. It is a conceptual question about mathematical 
physics. It can be dicussed without math derivations - but people may still
argue what the meaning of 'basis' is, in: 

"I simply believe that there must be a physical
basis to inductance just as there is a physical basis to magnetism"

There is an intriquing correspondence between electrostatics and
magnetostatics, (together with differences - such as 'no magnetic
monopoles')
which is dramaticaly resolved by realization that electric field can
be transformed into magnetic and vice versa. (I believe that is what
you mean by
'basis' -- this realization, implicit in Maxwell equations but fully
formulated by SRT, indeed points to a 'deeper reality' or ' physical
basis').
The 'vice versa' is important however: 
I do not see E to be 'more basic' then H or vice versa. Both are manifestation 
of 4-vector A which is introduced when we formulate Maxwell equations in the
4D space. The Maxwell equations then look like this:
http://relativity.livingreviews.org/Articles/lrr-2004-6/article77x.gif
general reference:
http://relativity.livingreviews.org/open?pubNo=lrr-2004-6&page=articlesu4.html

The Curvature Tensor R is zero on the Minkowski space (=flat space-time). 
The 'square' in that equation is Dalambertian - a 4D form od the 3D
Laplacian - a well known  'triangle' present in  static field
equations.

 This 'manifestly covariant' equation is the 'physical basis' of 
equations for both E and H, of the Maxwell equations, and all empirical laws,
including the Lenz law of induction, as dicussed e.g. in wikipedia:

Elctromagnetic 4-potential A
http://www.nationmaster.com/encyclopedia/Maxwell's-equations

As Simon pointed out in his comment below, there is similar, also intriquing
duality, between electromagnetic field and gravity in which inductance
corresponds to inertia. Actually, we can say inductance IS inertia of
emg field, as suggested e.g. here:

"..electrostatic and magnetostatic fields exhibit inertial properties,
but it is fair to say that there are issues awaiting resolution..."
http://www.mariner.connectfree.co.uk/html/e_m_inertia.html

This intriquing duality (metric tensor of GTR describing gravity, just as
four-potential A describes emg fields) lead Weyl 
http://store.doverpublications.com/0486602672.html

to look for a 'deeper basis' common to both and so (even though he  
miss-interpreted physical meaning of his gauge field
http://www.answers.com/topic/gauge-theory
) spearheaded the whole 'unified field theory' chase , yielding
 some results 
http://hyperphysics.phy-astr.gsu.edu/hbase/forces/unify.html
which show common basis of inductance and inertia.

That, however, does not answer you question, since question 
'what is basis of inertia?' is hard, unsolved, and involving philosophy:

SEARCH TERM: general relativity, electromagnetic field, Mach

brings many articles on 2.4 "Mach's Principle" :

" ..This real point of contact of Mach's influence was clearly
identified only in 1918, when Einstein distinguished what he baptized
as "Mach's Principle" (roughly, that inertial effects stem from an
interaction of bodies) from the principle of general relativity which
he now interpreted as the principle of general covariance. Taken
together with the principle of the equivalence, Einstein asserted that
the three principles, were three "points of view" on which his theory
rested, even if they could not be thought completely independent of
one another. Despite Einstein's intent, there is considerable
disagreement about the extent to which, if at all, general relativity
conforms to "Mach's Principle"...".

http://plato.stanford.edu/entries/genrel-early/


Historically, the similarity between gravity and electrostatic field,
both being described by Laplace equation, was a guiding light for Einstein
in deriving SRT. Basically, he followed Maxwell in adding the 'time term',
and, like Maxwell before him, postulate exixtence of waves - 
this time the gravity waves
http://answers.google.com/answers/main?cmd=threadview&id=172915


So, in conclusion:
Inductance of empty space and inertia have same basis, which is still
shrouded in mystery. There is no conclusion. These are true open
questions, and some of these problems are actively debated (between
that 'happy few' part of the
physics community, which time on there hands, which does not have to
write grant proposals and milesstone reports..:-) by people who have
interest in
foundations of physics and time  to 'ponder the inponderable, in this case the
nature of ponderability. 
http://math.ucr.edu/home/baez/physics/Administrivia/newsgroups.html

Moderated groups are recommended since they save time.
See you there

Hedgie

Inductance is like a train being pushed down the track, inductance=the
mass of the train, voltage=the force applied to the train, amps=the
speed of the train, as you can see it takes time for the Amps/speed of
the train to build up, and when voltage is removed the inductor/train
still has energy in it.
Sorry for talking in baby language, but it is an easy way to learn
about how inductance works.