Special Relativity: Some Notes | Home

I first saw the 1968 movie Planet of the Apes when it was first broadcast on television in 1973, when I was 13 years old. Recall that the ending has Charlton Heston realizing he's been on the Earth the whole time; that having travelled at great speed in his spacecraft for about 18 months, 700 years had passed on Earth upon his return.

That this was due to the time dilation effects of Einstein's special relativity was somehow vaguely known to me; though I don't remember how I knew about this; and of course I had no real understanding of it. But that was probably what first captured my imagination regarding this astonishing phenomenon.

Every few years (or decades) since then, I'd pick up a book on relativity for the layman, hoping to get some inkling, only to put it aside when the mental contortions became too disagreeable. Though it always seemed tantalizingly close to being "simple" enough for a rank amateur to understand, given that the math involved seemed straightforward (indeed, only basic algebra is required for the special theory; the general theory requiring much more advanced math).

In retirement I'm back at it for a bit, and with a bit more success. Enough so that, as a part of the learning process, I wanted to see if I could explain to myself, from scratch, in writing, my still nascent understanding of at least some aspects of special relativity. Thus these notes.

The Crux

As far as I understand it, what's really at the crux of the development and truth of Einstein's special relativity is this:

These are the basic conditions that led Einstein to develop the special theory of relativity (in 1905) with its weird effects of time dilation and length contraction, its undermining of the very notion of what it means for spatially separated events to simultaneous, and its novel concept of a unified spacetime in place of the distinct and absolute time and space assumed by Newton (in 1687). Newton even invoked God: He endures forever, and is everywhere present; and, by existing always and everywhere, He constitutes duration and space.

What's remarkable is that Einstein did this using purely logical reasoning. He didn't draw from physical experiments, or actually mess about with the trains or platforms or clocks or whatnot that he so often imagines in his writing. He just took seriously that the constancy of speed of light, no matter the motion of observers (which was the evidence at the time, but was explained away by various other theories, e.g. the ether), was in fact a fixed law of nature. And using what he called thought experiments (Gedankenexperiment in German), and following rigorous logic, crafted the theories that revolutionized over 200 year of established physics.

By the way, the "special" in special theory of relativity refers to the fact that this theory deals primarily with uniform motion; in other words, constant velocity; meaning, no acceleration (nor non-straight motion); the jargon is inertial reference frame. Einstein later developed the general theory of relativity (in 1915) which deals with accleration (and gravity - which turns out to be effectively equivalent to acceleration), and is substantially more complicated.

My Notes

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