Maddenation

The Meaning of Relativity

I’ve been rereading Einstein’s The Meaning of Relativity for the purpose of really understanding it this time. I haven’t quite given up yet, but, lemmetellamon, it’s hard. Parts of it are easy, of course—some of the simple math he starts with, some of the concepts, some of the figures. But then he (and here I resist the temptation to capitalize “he”) takes off for no apparent reason into the lala land of transformations, and then says that what he’s done is the famous “Lorentz transformation.” For reasons that are more apparent, I go into a cold sweat just reading about the Lorentz transformation (and become apoplectic upon the mere mention of “Laplace transformations”). Now here’s the thing, I’m still kind of following him at this point, but then he does a “special Lorentz transformation,” describing it as “…a rotation, through an imaginary angle, of the four-dimensional system of co-ordinates.” I’m still following him, but can’t for the life of me understand why anyone would want to do this.

And speaking of dimensions, along the way, weird Al plays fast and loose with the dimensions of time and space. For example, after defining v as the velocity of the moving frame of reference and l as “light-time” (equal to ct, where c is the velocity of light and t is regular, garden-variety time), he says x1 = vl. Hello! D = rt. So l is really not a time, but the distance light travels in a unit time. The term x1 is a distance, so it most certainly cannot be equal to a velocity times a distance. Al covers himself later (I think he knew what he was doing all along) by saying, “If we introduce the ordinary time t … then we must replace l by ct and v by v/c.” OK, Al, now I’m with you.

Al goes on, through more transformations and introduction of imaginary variables (his parents attest that Einstein had many imaginary friends as a child) to point out that normal Euclidean geometry and Newtonian physics can’t hold in interstellar space because light speed is always the same, no matter what (well, he says something about different frames of reference, but he means “no matter what”). He cites Michelson and Morley’s experiments with the interferometer as proof of this conjecture. So nothing goes faster than light and time has to slow down and things have to get shorter when they move. This is so a moving observer will always measure the same speed of light, even if he’s travelling alongside the light ray at half the speed of light!

So that’s weird enough, right? Well what Al does next is even more amazing. Working with geometry and the equations of motion (Newton’s laws, which Einstein only assumes are correct over infinitesimal distances) and momentum and energy, he derives the equation E = mc2! Amazing! In other words (well, my words) the fact that light speed is everywhere the same leads irrefutably to the conclusion that E = mc2. Wow. That something so “mechanical” as motion and geometry could lead to such a deep conclusion about nuclear chemistry is at once mind-boggling and beautiful. And next year will mark 100 years since this discovery was first published.

DadConnections/Ideas/Observations/Reviews04/07/04 0 comments

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