Re: Postulates of General Relativity

["John S. Denker" <jsd@MONMOUTH.COM>]

Savinainen Antti wrote:
> I have a question on postulates of the General Relativity (GR). I happened to read from a high school level book (Kerr, Kerr & Ruth 1999, 621) that the postulates of GR are:
>
> 1) Mach's principle -Inertial and gravitational forces are indistinguishable.
> 2) Four dimensional space-time is curved as a result of the presence of mass.
> 3) Objects take the shortest path between two points in space-time.
>
> Are these postulates correctly stated?

The first one is quite messed up.  First of all, the equivalence
only holds pointwise;  over an extended region you can tell the
difference between gravitation and an acceleration.  And even when
correctly stated, it should be called Einstein's principle of
equivalence.  Mach's principle is something else (which is not
very important or useful IMHO).

> Is it really so that GR follows from these three postulates?

Certainly not.  At the very least you would need some sort of
correspondence principle, that says that in the limit of weak
gravitational fields we inherit special relativity and all the
classical laws of physics.

Even then it's not 100% clear the GR follows uniquely.
See the discussion of "PPN" (parameterized post-Newtonian)
models of gravitation in Misner/Thorne/Wheeler.

> I have wondered what is the difference between postulates in
> physics and axioms in mathematics.

According to
  http://mathworld.wolfram.com/Axiom.html
        The word "axiom" is a slightly archaic
        synonym for "postulate".

I agree they are synonymous, although I consider them equally
non-archaic.  I detect no difference in the way mathemeticians
and physicists use the words.  Axiom has the advantage of having
a nice adjective, axiomatic.

This posting is the position of the writer, not that of Goldilocks or
the Three Bears.

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.