Tom_McCabe comments on Einstein's Arrogance - Less Wrong

30 Post author: Eliezer_Yudkowsky 25 September 2007 01:29AM

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Comment author: Tom_McCabe 25 September 2007 08:30:56PM 2 points [-]

"Sure, if we don't mind that G and T take a full page to write out in terms of the derivatives of the metric tensor."

The Riemann tensor is a more natural measure of curvature than the metric tensor, and even in that language it's still pretty simple:

8*pi*T = R (tensor) - .5*g*R (scalar)

where R (tensor) (subscript) ab = Riemann tensor (superscript) c (subscript) acb and R (scalar) = g (superscript) ab * R (tensor) (subscript) ab

You can make any theory seem complicated by writing it out in some nonstandard format. Take Maxwell's equations of electromagnetism in tensor form:

dF = 0 d*F = 4*pi*J

Now differential form:

(divergence) E = p (divergence) B = 0 (curl) E = -dB/dt (curl) B = J + dE/dt

Now integral form:

(flux E over closed surface A) = q (flux B over closed surface A) = 0 (line integral of E over closed loop l) = - d (flux of B over surface enclosed by l)/dt (line integral of B over closed loop l) = (current I passing through surface enclosed by l) + d (flux of E over surface enclosed by l)/dt

Now in action-at-a-distance form:

E = (sum q) -q/4/pi * ((r' unit vector from q)/r'/r' + r' * d/dt ((r' unit vector from q)/r'/r') + d^2/dt^2 (r' unit vector from q)) B = (sum q) E x -(r' unit vector from q)