physical & mathematical fundamentals

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.

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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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