INTRODUCTION
In 1976, just before he died, Werner
Heisenberg, one of the founders of the modern theory of quantum mechanics, the
physics of the atom, made a remarkable statement. He said that he had two
questions that he wanted to ask God: Why Relativity? and Why turbulence? He then
went on to declare his confidence that God would have an answer to the first of
those questions. Dr. Heisenberg's intent in making that statement may have been
facetious. Though he is better known for discovering the matrix formulation of
quantum mechanics and for drawing from it his famous indeterminacy principle, he
actually expended some effort in his youth toward gaining an understanding of
turbulence, the chaotic motions that arise spontaneously in moving fluids. His
deathbed statement may have been no more than a tongue-in-cheek expression of
vexation over the fact that physicists had gained no significant understanding
of turbulence in his lifetime. The idea that God would answer the first question
readily and the second perhaps not at all plays on the popular idea that
Relativity itself has no rationale behind it, that it stands before us as a
mystery forever inaccessible to human reason.
As Heisenberg's quantum theory does,
this theory of Einstein's defies our intuitive understanding of Reality, appears
so contrary to our experience of the world, that we expect to discover that
Nature laid its foundations in patterns that we mere mortals can have no hope of
ever comprehending. This implied irrationality of Nature has added its bleak
color to Twentieth-Century thinking about Science to such an extent that we are
properly astonished by the idea that the relationship between space and time is
relativistic for a perfectly comprehensible reason, that reason being that we
live in a universe of finite extent. Even more astonishing, we can demonstrate
that idea in a straightforwardly rational way.
I shall begin this series of essays
with that demonstration. Beginning with the simplest possible axioms, I shall
deduce Einstein's two postulates of Relativity. To the best of my knowledge, no
one has ever done such a thing before, so this part constitutes my own
contribution to Special Relativity.
Then I shall lay out, much as Einstein
did, the derivation of the rules (in place of the equations) of the Lorentz
Transformation. That set of rules contains within it the relatively familiar
phenomena of time dilation (that is, the phenomenon of some moving clocks
running slow relative to stationary clocks) and the Lorentz-Fitzgerald
contraction, which shortens moving objects. Again following Einstein's lead, I
shall work out those rules through the use of certain caricatures of familiar
situations to aid your imagination: in particular, I shall ask you to imagine
the operations of a railroad in a world in which the speed of light is merely
one hundred miles per hour. As improbable as it seems, such fantasies do,
indeed, yield valid results.
Finally I shall apply the rules of the
Lorentz Transformation to the dynamics of bodies. I shall focus your attention
onto the relativistic effects of motion on mass, momentum, and energy, aiming
your thoughts at deducing, as Einstein did, and explaining the most famous
equation in the world. Thus, you shall have a full explanation of the theory of
Special Relativity.
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