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.
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.