Re: Many Solutions to Einstein Field Equations in Vacuum

JanPB wrote:

Tom Roberts wrote:

Beware, the nomenclature "dx" can also mean a basis 1-form
for the x coordinate; in the above paragraph I meant "dx" to
to be a small (infinitesimal) real number.

It's probably worth mentioning that in "real" physics or math "dx"
practically always means the 1-form. The "infinitesimal" thingy is not
a well-defined concept (never was) and is used almost exclusively in
popular expositions (much to the confusion of the readers, it seems).

What confuses the heck out of me is to see things which look like my
old friend the infinitesimal differential apparently entering equations
as a finite quantity.

Ed (aside, to differential, dx): don't worry, old chum, you'll always
be Ok in my book. And besides, almost the entire classical development
of thermodynamics is based on your manipulation.

Differential (sniffles): it is?

Ed: Yes -- You are beautiful, no matter what they say. And Pluto is
still a planet.

(they walk off into asymtote, arm in arm)

Physics thrives on the ill-defined.

.

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