It is now accepted, virtually without question, that the equations which
govern the electromagnetic fields in vacuuo are those of James Clerk
Maxwell. They take the following extremely elegant and covariant form:
These equations are so familiar to the modern student of physics that they
appear almost timeless in nature. All modern texts on the subject (at least
those published in the last fifty years) quote them, their structure is
almost assumed to be self-evident and they now possess a status similar to
the laws of classical thermodynamics. The question arises as to the way in
which they have attained their current exalted position and the path by
which we have travelled from the myriad of experimental observations of
Faraday and his contemporaries to the current refined state of abstract
understanding. Who were the protagonists and how great did they labour for
our current knowledge? The detailed analysis and understanding of the eighty
or so years of endeavour which led from `Ampere to Einstein' has been the
daunting task that Professor Olivier Darrigol has set himself. I must admit
that I find it very difficult to do justice in a brief review
to this monumental work of scholarship, and for my errors or omission I
apologise at the outset.
Darrigol's monograph is a highly detailed and mathematical account of the
historical development of electromagnetism which, fortunately for the
reader, has been transcribed from the original arcane mathematical
expression into modern vector notation so that one does not have to struggle
with the cumbersome notation of Maxwell or the almost impenetrable notation
of Heaviside to follow the detail of the physical arguments. This in itself
is a great act of generosity to the reader without which this historical
development would be extremely difficult to comprehend. Rather than giving a
blow by blow account of this excellent text I would like to choose a few
areas which have particularly impressed me.
The first is associated with the work of Gauss on magnetism. Gauss was
particularly concerned that the detailed artefacts of particular experiments
should not affect the underlying physics being observed. To this end he
introduced the idea of reducing measurements to absolute units of distance,
force and ponderable mass (pole strength) through an inverse square law of
force. And to ensure that his measurements were independent of the
experimental procedures adopted, he was in the habit of using several
different techniques to measure the same physical quantity. Gauss was an
exceptionally gifted mathematician and practical experimenter and he laid
some very important foundations.
My second area is the incomparable Maxwell. He arrived on the scene when Faraday
had essentially completed his life's work. Maxwell then brought to bear his
formidable mathematical ability to synthesise the complete system of
observations of all the disparate effects of electromagnetism through the
process of mechanically modelling the systems of forces and torques.
Darrigol gives a detailed account of the way in which Maxwell used
complicated mechanical analogues (gears and cogs, frictionless rollers etc.)
to build and translate the jumble of effects into a single mathematical
structure. Without these mechanical analogues it would not have been
possible for Maxwell to construct his system of mathematical equations,
however when the synthesis was complete the mechanical framework could be
allowed to fall away and leave the mathematical structures completely
model-free. Maxwell's set of four equations have thus been raised to the status
enjoyed by the relationships of classical thermodynamics. Darrigol takes
pains to point out that Maxwell had no clear understanding of what for
instance electric current actually was and it is worth re-quoting
Maxwell on this subject:
`It is extremely improbable that when we come to
understand the true nature of electrolysis we shall retain in any form the theory
of molecular charges, for then we shall have obtained a secure basis on which to
form a true theory of electric currents and so become independent of these
provisional theories.'
After Maxwell's great work of synthesis the subject was left with
electromagnetic waves travelling in an aether and a theory which cast
different observations of the same phenomena in frame dependent forms. For
example the theory of the force on a coil moving in a magnetic field
depended upon whether the coil or source of the field were in motion (with
respect to the observer). One also had the difficult problem of the lack of
effect of the motion of the aether upon the velocity of electromagnetic radiation
which was assumed to be its supporting medium. These problems were coped with in
somewhat ad hoc ways and by the turn of the last century they could be
handled reasonably quantitatively, particularly through the far-sighted work
of Lorentz. Darrigol describes in intimate detail the way in which the work
of Poincare, Lorentz and many others foreshadowed the developments made by
Einstein. However, history has rewarded Einstein, somewhat unfairly, for his
contribution to the frame invariant formalism of electromagnetism, for
although his contribution was important it does so many others a
considerable injustice to ignore their own contributions.
In summary I must admit to being somewhat overwhelmed by the depth and
breadth of the study undertaken by Darrigol. However, for anyone who has an
interest in the subject of electromagnetism I would recommend that this book
be put very high on their reading list. When I first started to get to terms
with it, I wondered to whom it was directed. Apart from being a work of quite monumental scholarship, I questioned for whom it was actually written.
It seemed that in order to benefit from studying this text one would need to
have a fair understanding of electromagnetic theory, it would help considerably to be
familiar with special relativity and also to possess a nodding acquaintance
with tensor calculus, although this is not essential. These requirements
would appear to reduce the readership somewhat; however there are lessons to
be learned here for anyone who would make progress in the study of physics.
The fine minds who took part in the noble battle to systematise and
understand electromagnetic theory are some of the greatest scientific thinkers in our
history and although they lived before the internal combustion engine their
approach to problem solving has lessons for us all today. I cannot resist at
this point mentioning a quotation which Darrigol cites from Gauss (p51):
`Nil actum reputans
si quid superesset agendum' (Nothing has been done if something remains to be done).
Gauss lived in an age when
the philosophy, `publish or perish' was not a prerequisite of academic life
and so could complete his work before rushing into print.
History has judged the characters who people Darrigol's study very well:
however one is left to ponder just how well history will judge our present
generations.
