Reply To: Precession of the perihelion of Mercury

[Gyula Szász]

Conservation of Coordinates

Dear Gyula,

Or the invariance of coordinate translations
(or transformations).

I thought I might run this past you to get my
customary slap of your ruler on my wrist.
Maybe even a thread on the Gravitation
forum once it’s cleaned-up.

So, here goes. By demanding the conservation
of “KonserviertMasse”, it also looks like you have
coincidentally or purposefully demanded the
conservation of the Cartesian Coordinate System;
or for that matter, the conservation of ANY
coordinate system that may be chosen; so the
conservation really implies an independence of
the coordinate system chosen; as you suggest.

Under these circumstances, so-called space-time
looks more like a three-dimensional space with
an additional, but imaginary, forth axis. A “stage”
quite independent (it does not warp), of the actors;
if it were not for that minus sign(s) in the invariant.

That minus sign(s) made Einstein think the spacetime
“stage” warps from the weight of the actors and therefore
even partakes in the performance we observe.

I’m considering that it was actually BECAUSE Einstein
was unsure of what so-called “rest mass” is in his
theory, that caused his theory to warp spacetime in
response; and that your treatment conserves
“KonserviertMasse”,and in response demands
KonserviertKoordinaten.

Is this just my mind focusing on trivialities? Or can
we repair my reasoning and discuss this from the
standpoint of physics instead “raw” mathematics?

Sincerely,
Bill Eshleman

Dear Bill,
Minkowski create the correct space-time connection as a 3+1 dimension manifold for the interaction fields which propagate with c. Within this manifold you can define several coordinate systems. The invariants which are given in the Minkowski space, or which you define as invariant, are independent from each coordinate system and invariants under Lorentz transformations: they do not change (are invariant) their values. Such invariant is for instant the distance between two points; the invariant distances connect space and time. Yor can define also an invariant action integral to determine the covariant equations of motions.
Invariant elementary gravitational charges are connected with elementary masses. The elementary masses are conserved. Coordinate are never conserved.
The gravitational masses of bodies, as addition of elementary masses regarding the signs of their elementary gravitational charges, are conserved. Einstein threw away the conserved gravitational masses. Furthermore, Einstein did not understand the “rest masses”, the inertial masses at the impulse p = 0. He could not interpret; he could not calculate the “rest masses”. Einstein thought that the gravitational mass is the same as the inertial mass for each bodies, but this is not true. Einstein did not understand how gravity works.
However, a difficulty arises: you can indeed assign invariants to elementary particles (such invariants are the elementary electric and gravitational charges, thus also elementary masses), but, you cannot assign a discrete point of the Minkowski space, with a precise velocity, to the elementary particles. That is the mean reason from the standpoint of physics.
Please Bill, continue our discussion in the Gravitation forum. It is interesting for other people too.
Sincerely,
Gyula Szász