Re: Principle of Equivalence

["A. R. Marlow" <marlow@beta.loyno.edu>]

In any treatment of the principle of equivalence I think a viewpoint 
expressed 37 years ago by J. L. Synge in his Relativity: The General
Theory (North Holland, 1960) is still worth considering.  At that time
Synge was one of the main proponents of the geometric treatment of 
Relativity, which he points out was mainly Minkowski's contribution to
Einstein's thinking.  He wrote:

"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."

I find myself in great sympathy with Synge's viewpoint.  The view that 
the principle of equivalence somehow implies that every acceleration 
produces a gravitational "force" I class with the similar view that
Coriolis acceleration relative to the noninertial surface of the earth
produces a Coriolis "force," or that centrifugal acceleration relative to
a noninertial rotating platform somehow produces a centrifugal "force."
In all these cases the accelerations are very real but the "forces" are
indetectable, UNLESS you define FORCES as accelerations (and therefore
define dynamics = kinematics) a tendency I have deplored elsewhere.
> From the discussions on this list I have still been unable to discern
whether the tendency has already gone too far to be reversible or not.
Every time I think I have got a trend, the very poster that I thought
had it sorted out will come back with a post that seems to indicate the
opposite!

At the least I think we have to acknowledge that there is a very real
viewpoint of the principle of equivalence as midwife to general
relativity:  It was Einstein's way of weaning his generation (and
himself) from the previous conception of gravitation.  If a uniform
gravitational field is indistinguishable from an acceleration, then it
is indistinguishable from a mere 4-dimensional coordinate transformation,
and hence it cannot be real gravitation which is curvature of spacetime
as expressed in the Riemann tensor, which can never be transformed away.
This goes in the opposite direction from the viewpoint that would have
accelerations producing gravitation (or any other force)  --  it says that
any forces (gravitational or otherwise) produced simply by acceleration
are fictional.  
  
A. R. Marlow                          E-MAIL:  marlow@beta.loyno.edu
Department of Physics, Box 124        PHONE:   (504) 865 3647  (Office)  
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