In one of the letters written to the Infeld group in Warsaw Einstein wrote:
"A new manner of thinking is essential if humankind is to survive."

  

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Foundations of General Relativity
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AXIOM OF GR: PRINCIPLE OF EQUIVALENCE
 
Newtonian model applied the term "mass" as
homonym of two distinct concepts: "inertial
mass (IM)" and "gravitational mass (GM)".
Since Galileo's experiment demonstrating that
all objects have equal gravity acceleration
IM was known to be equal to GM, but this was
considered as a coincidence. Several physicists
hoped that more precise measurements may show
some slight difference. In spite of extremely
fine precision, the equality persisted, but
was always considered as accidental.
 
By replacing this equality with equivalence,
by saying that there are no distinct IM and
GM, but only one mass M Einstein created the
General Relativity. One may say that never in 
the history of Science an equally complex 
theory resulted from an equally simple 
assumption.
 
At the first glance it looks incredible.
We have seen that mass is a simple mathematical 
coefficient, devoid as such of any physical 
meaning In Mathematics equality is a special 
case of equivalence relation, so "equal" implies 
necessarily "equivalent" and Principle of 
Equivalence looks like a tautology. 

And it would be a tautology if we forgot the
interrelation of MS and PS. Coefficients GM and
IM correlate respectively Gravity and Inertia
forces in PS. By saying that they are equivalent
we imply that Gravity- and Inertia forces in PS
are equivalent and interchangeable with respect
to their effects on physical phenomena. It means,
back in MS, that the concepts of Gravity- and
Inertia Fields are equivalent and interchangeable.
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QUASI AXIOMATIC RULES AND PRINCIPLES

1.Principle of Relativity extended over 
non-inertial referentials. The importance of this
point cannot be exaggerated. Indeed PS or "universe"
is overwhelmingly, in not entirely non-inertial.
It seems quite reasonable to say that inertial
referentials do not exist at all; that some
non-inertial ones may be approximated as inertial,
in which the laws of SR hold approximately.
SR looks less like a final achievement, than like a
step towards something more universal, but unknown
at the moment of SR creation; a bivouac built
in fog on a steep slope in hope that next etape
will reach over the clouds, into sunshine.
NOTE: Galilean Relativity Principle postulates that 
laws of Mechanics are rigorously identical in all 
Inertial Referentials. 
In SR Einstein extended Galilean Relativity over 
electro-magnetic and optic laws saying that 
Physics is rigorously identical in all Inertial 
Referentials. This Extended Relativity is usually 
referred to as Principle of Relativity.
In GR Einstein extends the Principle of Relativity
over ALL referentials.

2.Local reducibility to SR. Referentials and
parts thereof, where the non-inertial effects
are negligible, may be considered as inertial
with acceptable applicability of laws of SR.

3.Einstein's Covering Principle.
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