Re: why selfestablished relativists hates partial differential equations?

On Nov 26, 12:08 am, Koobee Wublee <koobee.wub...@xxxxxxxxx> wrote:
On Nov 25, 10:20 pm, JanPB <film...@xxxxxxxxx> wrote:

On Nov 25, 10:01 pm, Koobee Wublee wrote:
The Einstein field equations are merely ordinary partial differential
equations. <shrug>

"Ordinary partial differential equations" - that's a keeper. You are
rapidly descending into white noise.

Hey, you coined the phrase "ODE", ordinary differential equations, did
you not?

No, this is the standard terminology, a very old one, with equivalent
terms used in many languages:

"ordinary differential equation" is an equation with derivatives wrt
to one variable only. If the unknown function depends on other
variables, those other variables are FAPP algebraic parameters as they
do not participate in the differentiation,

"partial differential equation" is an equation with derivatives
involving two or more variables.

Despite this rather arbitrary-looking distinction those two classes of
equations turn out to be vastly different - their properties are like
night and day. For example, any reasonable ordinary diff. eq. has a
solution which is necessarily unique once the initial condition is
specified. This is the classic theorem of Picard-Lindeloef. OTOH with
partial diff. eq. all bets are off in that department - simple
counterexamples exist which show there is no hope for such a nice
existence and uniqueness theorem there.

That's what I meant way back when in that PDF note at
http://www.mastersofcinema.org/jan/sch.pdf where I wrote on p. 6 that
after simplifying the Einstein equation it became an _ordinary_ one -
meaning "involving derivatives with respect to one variable
only" (namely u, as all other derivatives cancelled out). Hence the
standard ODE theory applies to it: existence and uniqueness of the
solution.

--
Jan BIelawski
.

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