The Logic of Relativity


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"Rest in Peace?! Never!" the now-free spirit cries

as, loosed from matter's inertia, she soars into the skies

to frolic upon an aetherial stage with patient ghostly grace

while waiting for us to follow at our leisurely mortal pace.

It's only temporarily, we know, that we have been bereaved

and we know that soon enough our grief will be relieved.

So we lay up treasure, not of Earth, but of the immortal soul;

for what Death has rent asunder, Death will someday make again whole.

In loving memory of

Gloria Mae Buckles, nee' Stevenson

1927 Oct 25 - 1992 Sep 20 - Ad Aeternitatem


For over thirteen years, from the time that I moved into my apartment on Sawtelle Boulevard (April 1979) to shortly before she died (September 1992), I visited my aunt Gloria almost every Saturday morning. The overt reason for those visits was that of picking up my mail, a "necessity" that I created when I accepted Gloria's offer to use her house as a mailing address rather than have my mail delivered to a too-small apartment mailbox. But, far more often than not, she would invite me to stay for a light breakfast and we would spend a pleasant hour or two discussing whatever was in the news and generally deploring the degenerate state of our culture. In the course of those conversations she made the two comments that, together, inspired me to write this monograph.

On more than one occasion Gloria expressed the wish that she could have confronted Albert Einstein and asked him to explain Relativity to her. It was clear to me that she wanted a full, how-do-we-know explanation that would go far beyond the usual superficial, Sunday-supplement expositions of time dilation and the Lorentz-Fitzgerald contraction and would reveal to her the foundations upon which those effects rest. She wanted the great man to guide her beyond "Gee whiz!" to "Yes, of course!", an order made all the taller by the content of her second comment.

I had gotten myself into the habit of bringing her copies of the articles that I wrote for submission to various magazines. The effort was appreciated but it was also, she told me, mostly futile because I expressed many of my ideas in algebra, a language as incomprehensible to her as Einstein's German would have been. She explained that she had failed the basic algebra course at Beverly High because she could make no sense at all of what the teacher was doing with all those exes, wyes, and other letters of the alphabet.

That difficulty with abstract mathematics seems to run in our family. My mother has told me that she also failed the basic algebra course at Beverly High and for much the same reason that Gloria gave me, only receiving a barely passing grade because she helped the teacher with his attendance records. And I must confess that, in spite of having acquired a Bachelor of Science degree in Physics, I am not nearly as good a mathematician as my training should have made me. Indeed, I have been developing my own simple version of General Relativity since 1987 precisely because I have never been able to master the Riemannian geometry and the tensor calculus that Einstein used in his version.

Nonetheless, I originally learned the theory of Special Relativity through its algebraic expression, which involves considerable manipulation of equations. I knew that I could describe some of the imaginary experiments that Einstein devised to work out the features of Relativity from his basic postulates without the math, but I didn't think that all of them could be so described, at least not coherently. Thus, I was inclined to believe that Gloria's second comment precluded any possibility of her understanding Relativity as she wished. However, my effort to develop my own version of General Relativity has obliged me to reacquaint myself with Special Relativity and gain a degree of understanding that I had never before achieved. At about the same time that I began that project I read the story about Michael Faraday and James Clerk Maxwell that I recount in Appendix V. Those two factors inspired me to think that it might be possible after all (and that it was certainly desirable) to devise a nonalgebraic exposition of Relativity that would nonetheless preserve Einstein's original reasoning or, at least, a reasonable facsimile of it. The fundamentum upon which I worked out that inspiration is the idea that expressing Relativity without algebra is analogous to expressing a song without the music: the lyrics can be read as poetry, and may even be more comprehensible in that way, and the music can be put back into the song at any time.

The consequence of working through that inspiration was a very rough draft of this monograph, a copy of which draft I was able to put into Gloria's hands a week before she exited the matter-mediated stage of her existence. I doubt that she had any opportunity to read it in that last week, though she may have taken a look at it since then. In any case, it was a rushed job and would not have fulfilled her wish as well as I would like it to do, so I have written this refined and completed version in the hope that its pattern will manifest a copy in whatever aetherial library she is using now. And I look forward to the day when I can ask her whether it answered her questions about Relativity.


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