Re: the basis of relativity

Hi Steve
I'll include a bit more detail (word salad).

carlip-nospam@xxxxxxxxxxxxxxxxxxx wrote:
> Ken S. Tucker <dynamics@xxxxxxxxxxxx> wrote:

> > Ok, then define the curvature scalar.
> > Does one exist, and don't trim this question!!!!
>
> R = R^a_{bab}

> Equivalently, let e^i be an orthonormal basis. Then
> R = sum_i K(e^i,e^i)

The above doesn't apply to a g-field, wherein the
basis is nonorthogonal because g_00 =/=g^00 therein,
so I don't get the point of going to an orthonormal
basis as you used it.

> Notice that this is a *sum* of Gaussian curvatures. It is -- I hope
> -- obvious that a sum can be zero even if the individual items being
> added aren't.

No prob, but the relevance in nonorthogonal spacetime
escapes me.

> Ken, you are making elementary mistakes about elementary Riemannian
> geometry.

I understand the classical approach, but a question
arises in studying Weinberg's Eq.(6.10.1) on tidals.
(Yes I understand R^a_bcd is calculated from a single
metric at a point).

Looking at that equation from another PoV, the
geodesics are separated by delta x^gamma, sufficient
to *define* a tidal relation, as Weinberg explains.
It's a place where infinitesmal merges with finites,
for example if the two geodesics, exhibiting g-effects
tidally, are merged into one then the tidal effect
disappears.

The tidal effect also has a relative rotation, as you
can imagine if two circular orbiting satellites have a
slight difference in altitude. The upper satellite will
tend to lag the lower.

Gedanken: Suppose we drop a Hydrogen atom on to a
Neutron-star knowing the geodesic of the p+ and the
e- are tidally different.
Will that change quantum theory in that circumstance?

That's a true astrophysics problem, and Eq.(6.9.1)
tends to simplify it, by using a^u and b^u as the
separate geodesics.

A valid question is whether that H atom emits g-waves
or EM-waves when subject to a differential of the K(a,b)
in Eq.(6.9.1).

That's germaine to LIGO, LISA and other experiments.

> It does not improve your case when you then insult others.

Ha, I just insult BACK better. Someone smacks you
with an undeserved spit-ball, chew up twice as big
a wad and shoot it back twice as hard, otherwise
everybody will thing you're a sissy :-).
Regards
Ken S. Tucker

PS: Dropping a H atom on to the surface on a N-star
which is integrated by the ensemble of all a stars
gas, as it relates to dK(a,b), and the radiation output,
should regarded as a question.

If the dK causes an output of EM-radiation then we
have an answer if g-waves cannot be detected, and
we'll know that EM-radiation can be tidally induced,
and then we consider the relation of K in the QT
and EM.
kxsxt

.