What Is the Best Way to Teach Special Relativity?

[silagadze]

Here is an article I submitted to ArXiv some time ago:
http://uk.arxiv.org/abs/0708.0929 (Relativity without tears).
It is about Special Relativity (in fact a sort of review of it) and contains nothing unorthodox at all (I hope), although the angle of view might be somewhat unusual. The reason why I'm posting about it at IR is that it is not yet published (although submitted to a journal). I hope your comments can help avoid typos and make the presentation more clear, if necessary, for alleged publication. Especially I'm interested in important references about topics considered which I could overlook.

The abstract of the paper
Special relativity is no longer a new revolutionary theory but a firmly established cornerstone of modern physics. The teaching of special relativity, however, still follows its presentation as it unfolded historically, trying to convince the audience of this teaching that Newtonian physics is natural but incorrect and special relativity is its paradoxical but correct amendment. I argue in this article in favor of logical instead of historical trend in teaching of relativity and that special relativity is neither paradoxical nor correct (in the absolute sense of the nineteenth century) but the most natural and expected description of the real space-time around us valid for all practical purposes. This last circumstance constitutes a profound mystery of modern physics better known as the cosmological constant problem.

and its list of contents
1. Introduction (a one-postulate derivation of SR goes back to von Ignatowsky's 1910 paper)
2. Relativity without light (a variant of such a derivation combining ideas of several authors)
3. Relativistic energy and momentum (a modification of Davidon's derivation of relativistic energy and momentum stressing not the radical break but continuity with concepts already acquired by students)
4. Relativity without reference frames (the existence of inertial frames in general space-times is neither obvious nor guaranteed)
5. What is geometry? (Felix Klein's Erlangen program -- basic principle of Galois theory applied to geometry)
6. Projective metrics (projective geometry is a good starting point to study different kinds of linear and angular measures)
7. Nine Cayley-Klein geometries (and the 2-dimensional Minkowski geometry is one of them)
8. Possible kinematics (there are only eleven relativity theories of Bacry and Levy-Leblond)
9. Group contractions (and all of them are related to each other via Inonu-Wigner group contractions)
10. Once more about mass (in Galilei invariant theory mass has a cohomological origin and acts as a Schwinger term as opposed to the relativistic case)
11. The return of æther? (vacuum in modern physics is more like Lorentz invariant æther than empty space. Condense matter analogy suggests some intriguing reasons to restore the word 'æther' in the physics vocabulary)
12. Concluding remarks (Cartan geometry underlines modern physics and unifies Riemannian and Kleinian trends in geometry)
13. References (153 references, some ot them very nice)

With best regards, Zurab Silagadze.

 

[Dale]

I don’t feel that this particularly simplifies relativity in a pedagogical sense. You do minimize the irritating “thought experiments” that plagued my textbook, but other than that it is not particularly improved in my opinion. Also, the pro-aether stance negatively impacts the credibility of the entire work. I, for one, don’t buy the claim that the vacuum in modern quantum theory is closer to the aether.