|
|
Nice diagram, by the way !
Yes, it is, indeed.
As for your further question about the inverse-square law, I don't know enough physics to answer it. But I googled around a bit and found the following explanation by a physicist who calls himself jeff. To find his post, scroll just about half-way down the page and look for the heading
jeff - Photons as the electric field. Question.
jeff's explanation applies to the electromagnetic interaction, but I surmise that there's a similar Lagrangian density for the gravitational interaction (maybe Physicist can help us out on that?). And I should add (as if it weren't obvious) that I'm unable to vouch for the complete accuracy of jeff's response. So it's caveat emptor, as usual.
Anyway, I've edited jeff's explanation in a few places because FR's HTML parser choked on some of the needed HTML tags—my edits are inside the square brackets:
Inverse square laws are a consequence of the structure of tree amplitudes for the exchange of bosons that result from the fact that the lagrangian densities involve two powers of the spacetime derivative. In momentum space, the relevant part of the energy E of interaction between electrically charged particles at x1 and x2 following from these amplitudes is
E = [a constant multiple of the integral of a Lagrangian density over 3-space] = – (1 / (4pir))e – mr
where r [is defined to be] |x1 – x2| [which is the distance between x1 and x2]. Setting the mass m equal to zero for the photon in the case of the electromagnetic interaction and computing [the partial derivative of E with respect to r] yields the familiar inverse square law of coulomb for the electromagnetic force.
If you've had a little calculus, you might recall that the (ordinary) derivative of – (1 / r) with respect to r is 1 / r2, the reciprocal of the square of r, i.e., an inverse square.
You asked a question that isn't completely trivial to answer. And, while it's true that the question has only really been answered for those who fully understand the physics which lies behind jeff's answer, which leaves me out, your question was still a good one.
|
|
