Re: Principle of Equivalence

["JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439" <JLU@hep.anl.gov>]

Hi all-
	A.R. Marlow quotes J.L. Synge as saying:
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"It is to support Minkowski's way of looking at relativity that I find
myself pursuing the hard path of the missionary.  When, in a relativistic
discussion, I try to make things clearer by a spacetime diagram, the 
other participants look at it with polite detachment and, after a pause
of embarrassment as if some childish indecency had been exhibited, 
resume the debate in their own terms.  Perhaps they speak of the 
Principle of Equivalence.  If so, it is my turn to have a blank mind,
for I have never been able to understand this Principle ... Does it mean
that the effects of a gravitational field are indistinguishable from the
effects of an observer's acceleration?  If, so it is false.  In Einstein's
theory, either there is a gravitational field or there is none, according
as the Riemann tensor does not or does vanish.  This is an absolute
property;  it has nothing to do with any observer's worldline. Spacetime
is either flat or curved, and in several places in the book I have been
at considerable pains to separate truly gravitational effects due to 
curvature of spacetime from those due to curvature of the observer's
worldline (in most ordinary cases the latter predominate).  The 
Principle of Equivalence performed the essential office of midwife at
the birth of general relativity, but, as Einstein remarked, the infant
would never have got beyond its long-clothes had it not been for 
Minkiwski's concept.  I suggest that the midwife be now buried with
appropriate honors and the facts of absolute spacetime faced."
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	But I think that the modern view, consistent with the viewpoint
expressed in Weinberg's book on gravitation, is that Synge was begging
the question.
	I think that the principle of equivalence is a statement about
<local> measurements, where <local> means a measurement at a point.
It is true that one cannot distinguish between a gravitational field
and an accelerated reference frame by a purely local measurement.  This
statement expresses my understanding of the principal of equivalence.
The gravitational field is characterized by spacetime curvature (or
tidal forces, if you like), but curvature cannot be determined from
a purely local measurement (tidal forces have non-vanishing derivatives
in at least some directions).
	It is the principle of equivalence that permits one to construct
a local inertial frame at each point of spacetime, even when spacetime
is curved.
	Mathematically, the collection of local inertial frames coincide
with the tangents at each point of the spacetime manifold.
				Regards,
					Jack