N. 3 - 21 aprile 2001 - Giano Bifronte

MACHIAN THOUGHTS
Relational Mechanics
Andre K.T. Assis
(Apeiron, Montreal, 1999)
The criticism that in his epoch-making history of mechanics Ernst Mach
levelled at the basic concepts of Newtonian mechanics is more or less
familiar to most physicists, thanks to the references to Mach that Albert
Einstein and other relativists interspersed in numberless papers and
books. However, as is typical of the way the historical heritage is
transmitted and absorbed in contemporary scientific education, the main
use that of Machian ideas is usually made is to motivate some of
Einstein's steps in the construction of general relativity (GR), and also,
of course, to give an example of a 'prophecy' seemingly vindicated and
fulfilled by subsequent more rigorous studies. More precisely, it is to
GR that the honour is attributed of having transformed some vague
philosophical intuitions concerning inertia and gravitation into the gem
of a mathematical equation (Einstein's field equation).
However, among specialists in the foundations of mechanics, as
opposed to popularizers, there is much less agreement as to which
extent Einstein implemented Mach's ideas on space and time in his
theory. An amusing indication of the variety of opinions about the
'Machian' quality of general relativity is provided by two opinion polls
made at a conference on the Mach's principle (the proceedings are in the
book Mach's Principle, edited by J. Barbour and H. Pfister, Birkhäuser,
1995). In the entrance poll the question "Is general relativity perfectly
Machian?" got 2 'yes' and 30 'no', while at the exit poll there were 3 'yes'
against 21 'no'. Notice that one of the organizers, Julian Barbour,
contributed a paper entitled "General Relativity as a Perfect Machian
Theory", so there is no mystery as to where he cast his vote. On the
other hand, both his contribution at that conference and the book under
review make it sufficiently clear that Assis shared – rightly, in my
opinion - the majority view.
Relational mechanics is no doubt a less controversial way than GR of
implementing Mach's programme in the foundations of mechanics. To
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