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Feynman [1]: "Let us show you something interesting that we have recently discovered: All of the laws of physics can be contained in one equation. That equation
by joaorico 12y ago
Feynman [1]: "Let us show you something interesting that we have recently discovered: All
of the laws of physics can be contained in one equation. That equation is
U = 0.
What a simple equation! Of course, it is necessary to know what the symbol means.
U is a physical quantity which we will call the “unworldliness” of the situation.
And we have a formula for it. Here is how you calculate the unworldliness. You
take all of the known physical laws and write them in a special form. For example,
suppose you take the law of mechanics, F = ma , and rewrite it as F − ma = 0.
Then you can call (F − ma) — which should, of course, be zero — the “mismatch”
of mechanics. Next, you take the square of this mismatch and call it U_1 , which
can be called the “unworldliness of mechanical effects.” In other words, you take
U_1 = (F − ma)^2.
[...]
You continue to write U_3 , U_4 , and so on—one for every physical law there is.
Finally you call the total unworldliness U of the world the sum of the various
unworldlinesses U_i from all the subphenomena that are involved; that is, U = SUM (U_i).
Then the great “law of nature” is
U = 0. (25.32)
This “law” means, of course, that the sum of the squares of all the individual
mismatches is zero, and the only way the sum of a lot of squares can be zero is
for each one of the terms to be zero.
So the “beautifully simple” law in Eq. (25.32) is equivalent to the whole
series of equations that you originally wrote down. It is therefore absolutely
obvious that a simple notation that just hides the complexity in the definitions
of symbols is not real simplicity. It is just a trick . The beauty that appears in
Eq. (25.32)—just from the fact that several equations are hidden within it—is
no more than a trick. When you unwrap the whole thing, you get back where
you were before."
[1] Feynman R, Leighton R, and Sands M. The Feynman Lectures on Physics. Volume 2, chapter 25, page 10.
- deleted 12y ago[deleted]
- kam 12y agoThat's why they're all squared. Which is, of course, assuming that none of the equations involve imaginary numbers.
- joaorico 12y ago"Next, you take the square of this mismatch and call it U_1" Each U_i is a square, so it's a sum on non-negative quantities that equals zero so that each U_i = 0 must hold separately. That's the cool trick :)
- pfh 12y agoYes it is, it turns a problem of solving a set of equations into a minimization problem. An algorithm to find the best fit to some data can also be used to find an exact fit if it exists, and is likely to have good numerical stability.
- drdeca 12y agoThat is what the squaring is for, I figure. To make all the terms non-negative. (now, if some of the unreal-ness components were complex, there would be a problem there, but eh)