Fwd: notes 128

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Subject: Fwd: notes 128
Date: Sun, 22 Mar 2009 04:01:24 EDT

Agreed, very interesting! Papers such as 97 give a line element for a radiating electron as you know, and it looks as if the mixed index metric ha sa centrally important meaning as you infer. It obeys the new metric compatibility condition

partial sub mu g sup kappa sup nu sub rho = 0

for all mu, nu and rho. This is a powerful result of geometry and physics.

A very interesting result is that the mixed metrig g {sup mu sub nu} can be interpreted as the linear energy-momentum density. Interestingly this is a unit matrix for all diagonal metrics. I had not expected this because spatial variations in a metric should represent a variable energy density. But perhaps this is a hint that there is no background field in Einsteinian theory, therefore the energy density is constant (and probably zero). I will see if I can find a non-constant matrix g {sup mu sub nu} for a non-diagonal metric. This could be added to paper 128.

Horst

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