About Special Relativity

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How Much Time to Devote to Relativity?

Modern Physics refers to two "revolutionary" theories that overturned "Classical" or "Newtonian" science. The two theories are RELATIVITY and QUANTUM MECHANICS (or "Quantum Physics" or "Quantum Theory" etc.) The date to remember is 1900. It was in this year that Max Planck first introduced (as a mathematical "trick" - as we will see) the idea that energy comes in "bundles," and also the famous constant ("h") later named for him. Quantum theory is STILL under development, but the non-relativistic version was more-or-less firmly established in 1926-1927 when Schrodinger published his wave theory and Heisenberg his matrix theory - two theories which were later seen to be differing mathematical descriptions of the same basic theory.


Meanwhile, in 1905, Einstein published his paper on Special Relativity. And in 1916 he followed this with General Relativity. Special relativity is "special" because it describes the relation between events viewed from two INERTIAL reference frames. "Inertial" here means that neither is undergoing acceleration. General relativity removes this restriction, and (much to everyone's surprise at the time) shows that this is only possible if one includes gravity in the theory! Thus general relativity is a gravitational theory, and includes such concepts as "warping" of spacetime and other ideas which science fiction has made much of (but without the math).


General relativity will not be part of this course. It turns out that Newtonian gravity and "flat" space are adequate to describe nature everywhere except in really strong gravitational fields, such as those near black holes and/or massive stars. General Relativity is, in a sense, an "unfinished" theory even today: it has been shown that it is inconsistent with Quantum Physics. Thus one of the two (or both) must be modified, or a new theory that incorporates elements of both must be created. A Nobel Prize awaits whomever achieves this.


In contrast to the general theory, Special Relativity has changed little from Einstein's first formulation. Certainly it has been cast in more sophisticated mathematical form, and many implications discovered of which Einstein was unaware, but the basic theory has changed very little. Another difference is that Special relativity is important in the day-to-day understanding of events. In particular, one cannot understand light without it. One cannot understand particle collisions at high energies (which happens trillions of times each second in the upper atmosphere and also in man-made particle accelerators) without it. One cannot understand particle decay without it. It is important in spectroscopy (giving rise to "fine structure") and even in chemistry (electron "spin" is a relativistic phenomenon). It cannot be omitted from the undergraduate physics curriculum.


Where, then, should it be included?


Einstein's original paper was entitled "On the Electrodynamics of Moving Bodies." Thus, electricity (and magnetism) are fundamental to its origin. And, indeed, a fuller treatment of special relativity is included in the second semester of E&M at Eckerd College. This treatment requires about 6 weeks (almost half the semester), and depends on the students' being familiar with Maxwell's Equations for the electric and magnetic fields. Linear algebra and a LITTLE tensor calculus is used in treating the theory. (This later mathematical re-casting of Einstein's theory is due to Minkowski. It does not change the content of the theory, but makes it much more elegant.)


What about special relativity in Modern Physics, then? I have, on some past occasions, simply omitted special relativity when teaching the course. My rationale was that it would be covered in a later course (E&M II), with adequate time devoted to it, and at a higher mathematical level.


Most Modern Physics textbooks (ours is typical) devote one or two chapters to special relativity, and use algebra and some calculus in its treatment. Omitted is the linear algebra/tensor calculus presentation, which displays the beauty of the theory. And tensor calculus is not beyond the grasp of a student in Modern Physics - it just requires time to develop. Without it, relativity looks awkward and algebraically complex - it is "messy" - whereas, in tensor form, it is symmetric and beautiful.


But I CANNOT devote half of Modern Physics to relativity! To do so would mean short-changing the story of the development of Quantum Theory, a MUCH richer and more difficult theory. One can see this simply from the fact that our textbook devotes MANY chapters to the development of quantum theory, and then (beginning around Chapter 10) additional chapters to its application!


So the difficult choice is: (1) do a good job with relativity, using almost half the semester to do this; (2) omit relativity entirely, assuming that physics majors will get it in E&M II; or (3) do a half-assed job with relativity, covering whatever I am able in a couple of weeks.


I am choosing option 3. But I will attempt on occasion to show you GLIMPSES of the beauty of relativity cast in a more advanced form. And I will leave out some of the more interesting problems that arise (e.g., the "twin paradox"). You are welcome to read about these - most can be Googled and many have Wikipedia articles that are not too badly done.


If you have read this far, here is the reason I have asked you to read this: I DO NOT WANT TO TAKE CLASS TIME TO EXPLAIN WHY RELATIVITY IS GIVEN SUCH INADEQUATE TREATMENT IN THE COURSE! It would take almost half a class to say what I am writing here.


Conclusion: I will spend about two weeks (perhaps 5 or at most 6 class days) on special relativity. I will try to give you an idea of why it is needed, what it is good for, and especially to set up the (relatively few, but important) results that we will USE later in the course. I am sure that questions will arise in your mind that I simply do not have time to pursue. I will, on more than one occasion, "apologize" for not giving adequate treatment to a topic. Is this better than omitting relativity entirely? I'm not sure, but it's the (difficult) decision I've made.


Thanks for reading this. I am looking forward to the course.