Equivalence between the Einsteinian and post-Newtonian theories of gravitation
Introduction
The goal of this reflexion is to highlight the equivalence between
two models, conceptually very different, of the gravitation.
It is necessary to hear the word equivalence in the restricted meaning of predictive equivalence (i.e. any observation or
experimentation which validates one, validates the other and vice versa).
In fact we will show
that they are equivalent in, a priori, a little more strong meaning :
the equations are mathematically locally equivalent. We will finish
obviously by an epistemological consequence known but seldom
taken into account: even if a theory is validated by the observations and
the experimentations, that is not enough to validate the subjacent concepts
of this theory. In the example that we will develop, two theories
of the gravitation, predictive equivalents, validated with an extraordinary
precision, rest on paradoxical definitions of
the concept of space-time. In one of the theories "space-time " is
curved with
a non trivial curvature, in the other "space-time " is flat.
" The rigorous equivalence - and rather paradoxical - between the
simplest Newtonian cosmological model and the model of Friedmann
with space curvarture is evoked... "
J.-M. Souriau
Technical and Epistemological aspects:
and
Here the summary of this second paper:
What can teach us the gravitation on the space-time?
Summary:
In the Twenties, models of universe
were built within the framework of general
relativity. In the Thirties,
one realized that such models could also
be built within the Newtonian framework by taking account of
special relativity.
We expose initially the principles for the construction of these two types
of models and we present their mathematical
equivalence (in the general framework,
without the usual assumption of null pressure).
In one of these theories, the space-time is curved, in the other,
it is flat. This apparent contradiction underlines the difficulty in
drawing from these theories (which are in fact theories for
the movement) conclusions about the nature or properties
of the space-time.
We present also the equivalence of the local
gravitational models built in these two theoretical
frameworks (Einsteinian and Newtonian) and we show why
the use of these two frameworks
is inevitable when one wants to confront general
relativity with the observations, and useful for
the understanding of the committed concepts.
Finally we examine the general problem of
the relation between physical reality and mathematical model
and we recall the positions of
Galileo and Einstein on
the truth of their theories.
Is the Space time Curves And Flat?
" general relativity is a synthesis between the Newtonian
gravitation and special relativity."
J.-p. Luminet