Comments on: What is Your Equation?

By: Sean

Sean — Fri, 19 Oct 2007 19:19:56 +0000

That was really well done, Jim.

By: Jim Clarage

Jim Clarage — Fri, 19 Oct 2007 18:27:40 +0000

Scribbled on a church bulletin to keep me awake one Easter sunday: At risk of a blasphemy towards one or the other, here's a diagrammatic mashup of the BigBang and Genesis.

By: Count Iblis

Count Iblis — Thu, 18 Oct 2007 17:50:07 +0000

Also:

“Amplitudes can then be expressed in terms of the two-dimensional Green function

G (?, ?) = ? d ? I?(?) R(?, ?; ?),

where I = ? J is the Imbessel function, R is the retarded potential, and ? is a dummy variable.”

By: Thomas Larsson

Thomas Larsson — Thu, 18 Oct 2007 11:40:43 +0000

Two more favorites: The Newton-Witten equation: F = ma. The Beatle identity : 1 + 1 + 1 = 3 "We haven't figured out what it has to do with physics yet, but the mathematical relation is so profound there must be some application."

By: Haelfix

Haelfix — Thu, 18 Oct 2007 07:37:13 +0000

The heat kernel equation

By: Stu Savory

Stu Savory — Thu, 18 Oct 2007 03:15:10 +0000

Surprised Maxwell’s Equations not mentioned.

By: Neil B.

Neil B. — Thu, 18 Oct 2007 01:46:08 +0000

OK, here’s my equation:

Delta S = 2 n hbar (A^2 – B^2)

Here, Delta S is the change in the rotational angular momentum (or as transferred by axle etc.) of a half-wave plate through which n photons pass of a given “circularity” (expectation value of angular momentum, derived from the wave function A |R> + B e^(i theta) |L> using newer standard of handness. That is pretty straightforward, since transiting a HWP inverts the rotation of CP light while maintaining “form” (ellipse shape, but axis may change) and has a corresponding effect on photon wave function. (Sometimes circularity is called or confused with ellipticity, but I prefer the former.)

However, there’s another meaning for the equation: Instead of passing n photons through once each, try a return circuit for a single photon. We can re-invert the spin flip with another HWP, and use mirrors to bring the photon back through the first HWP over and over. Indistinguishability says, the plate can’t tell the difference between these two cases. Hence, the plate should build up the same change in AM as shown by the equation, but then n means transits of a photon not “number of photons” (with all due respect for the ambiguity of n for the latter, the uncertainty in n is usually relatively small.)

Well: that would allow finding the circularity of a single photon, which is the projection postulate says we can’t do. Yet the argument (cascading of a known process) seems straightforward. Any thoughts?

By: Sean

Sean — Wed, 17 Oct 2007 20:52:14 +0000

I think the point was not “the best equation ever,” but your equation — either one you have actually come up with, or failing that, the one that you are thinking about most obsessively these days.

By: noname

noname — Wed, 17 Oct 2007 20:36:22 +0000

I’m very surprised that neither

\delta S = 0

nor

\Delta S \geq 0

made it. Those would be my top two choices, for sure.

By: Moshe

Moshe — Wed, 17 Oct 2007 16:48:18 +0000

The beta function equation in string theory, relating spacetime Einstein equation with conformal invariance on the worldsheet. Elementary as it is, still pretty much a mysterious statement for me.