# physical & mathematical fundamentals

104 Pages · 2001 · 1.01 MB · English

developments which contribute to the maturation of physics—to the 11 An edition of those notes was prepared posthumously by several of.

104 Pages · 2001 · 1.01 MB · English

developments which contribute to the maturation of physics—to the 11 An edition of those notes was prepared posthumously by several of.

1
PHYSICAL & MATHEMATICAL
FUNDAMENTALS
Introduction Since “the world is unitary”—with each part connected (however
tenuously) with each other part—it is of some philosophical interest that physics
admits of semiconventional division into semiautonomous “branches” Most
of those branches are concerned with the analysis of fairlygeneral classesof
physical systems (think,for example,of classical mechanics,or of quantum
mechanics,ﬂuid dynamics,thermodynamics),but a few (celestial mechanics,
general relativity,) are concerned with relatively particularized systems It
is useful to note that electrodynamics is,for all of its incredible richness and
variety,a sub ject of the latter sort:al l that fol lows wil l be motivated by a desire
to clarify the structure and dynamical properties of a single physical object—the
electromagnetic ﬁeld
Our ob jective,therefore,is to review progress in a ﬁeld which achieved a
kind of maturity (Maxwell,) just about a century ago,a ﬁeld to which
some of the greatest minds (Einstein,Feynmanand many others) have
contributed,a ﬁeld in which “the last word” has certainlynotbeen written
Much of great value can be learned from close study of the (ongoing)history
of electrodynamicsbut for that I must refer my readers to the relevant
literature A standard source is E T Whittaker’sA History of the Theories
of Aether & Electricity() Since this branch of the history of science
is currently quite active,it would be well to consult recent issues of (say)
History of Science For a good modern account of the “ancient history” of
some of the basic notions see Duane & D H D Roller,“The development
2 Physical & mathematical fundamentals
of the concept of electric charge: electricity from the Greeks to Coulomb” in
J B Conant (editor),Harvard Case Histories in Experimental Science(Volume
II,) You should,of course,take this occasion to become acquainted with
the Victorian founding fathers (Faraday,Maxwell) of our sub ject I urge you
therefore to look intoMichael Faraday: A Biographyby L P Williams (),
James Clerk Maxwel l: Physicist and Natural Philosopherby C W F Everitt
() and/orContributions of Faraday & Maxwel l to Electrical Science()
all of which are informative,yet fun to read Finally,every student of
electrodynamics should peruse the pages of Maxwell’s ownA Treatise on
Electricity & Magnetismthe (posthumous) 3
rd edition () of which was
reissued by Dover in While the history of science is its own reward,the
history of electrodynamics (as of classical mechanics,quantum mechanics)is
also of directly utilitarian value,for it illuminates the processes/circumstances/
developments which contribute to the maturation of physics—to the discovery/
invention ofnewphysics
That electromagnetic phenomenology (and theoretical understanding of
that phenomenology) lies at the base of an elaborate technology—think of
electrical power grids,the electric light,motorized devices,electronic
communication/computation/mealsurement & controlnone of which were
known to the founders of the ﬁeld—is of course not news Less well known to
the general public are the theoretical contributions of classical electrodynamics,
which (directly or indirectly) has stimulated the invention/development of
•special relativity
•quantum mechanics
•the modern theory of gravitation (general relativity)
•elementary particle physics
•many of the methods characteristic of modern applied mathematics
and much else One could perfectly well base a course such as this on the
technological applicationsof our sub ject: such an approach would be considered
standard in schools of engineering,and is reﬂected in the design of many
existing texts I prefer,however,to let (my personal view of ) the theoretical
applications/ramiﬁcations of electrodynamics govern the selection,arrangement
and presentation of the sub ject matter Classical electrodynamics provides a
unique “classical window” through which can be glimpsed many of the principles
which are now recognized to dominate the structure of the micro world (also
the verylarge scale macro worldand much that lies in between) But
to gain access to that window we must pay close and critical attention to
structural issuesand to that end we must from time to time draw upon
mathematical methods which,though of growing importance,have heretofore
not been considered standard to the undergraduate education of physicists The
latter material will be developed in appropriate detail as needed
The “historical approach” (recapitulated psuedo history) which for a long
time dominated instruction in classical and—particularly—quantum mechanics
has never been popular in the electrodynamical classroomand it is certainly
Coulomb?s

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