The cornerstone of Newtonian mechanics is the inertial frame of reference. With this frame we can understand the difference between real and fictitious or pseudo forces and the importance of these two types of forces in Newton’s analysis of his rotating bucket. This analysis was the basis of his belief in absolute space. Mach, who believed strongly in an empiricist view of science, showed that the existence of inertial forces leads to a refutation of absolute space. He replaced absolute space with a frame of reference at rest with respect to the distant fixed stars considered as a rigid system. His principle, which was not expressed explicitly by him, is that the inertia of a body is a consequence of its interaction with all other bodies in the universe. Mach’s refutation of absolute space made Einstein’s general theory of relativity possible. Einstein later abandoned Mach’s principle and found the source of inertia in the nonzero curvature of the space-time metric, a fact that does not diminish the importance of Mach in Einstein’s early thinking.

1.
A.
Sommerfeld
,
Mechanics
(
Academic
, New York,
1952
), pp.
59
62
.
2.
H.
Goldstein
,
Classical Mechanics
(
Addison-Wesley
, Cambridge, MA,
1951
), pp.
14
18
.
3.
I.
Newton
,
The Principia
, translated by
I. B.
Cohen
and
A.
Whitman
(
Univ. of California
, Berkeley,
1999
), pp.
412
413
.
4.
Reference 3, p.
413
.
5.
Reference 1, p.
9
.
6.
R. S.
Cohen
, “
Ernst Mach: Physics, perception, and the philosophy of science
,” in
Ernst Mach Physicist and Philosopher
, edited by
R. S.
Cohen
and
R. J.
Seeger
, Boston Studies in the Philosophy of Science (
Reidel
, Dordrecht,
1970
), Vol.
VI
, pp.
126
164
.
7.
P.
Frank
, “
The Importance of Ernst Mach’s philosophy of science for our times
,” in
Ernst Mach Physicist and Philosopher
, edited by
R. S.
Cohen
and
R. J.
Seeger
, Boston Studies in the Philosophy of Science (
Reidel
, Dordrecht,
1970
), Vol.
VI
, pp.
219
234
.
8.
R.
von Mises
, “
Mach and the empiricist conception of science
,” in
Ernst Mach Physicist and Philosopher
, edited by
R. S.
Cohen
and
R. J.
Seeger
, Boston Studies in the Philosophy of Science (
Reidel
, Dordrecht,
1970
), Vol.
VI
, pp.
245
270
.
9.
A.
Einstein
, “
Ernst Mach
,”
Naturwiss.
17
,
101
104
(
1916
).
10.
G. J.
Holton
, “
Mach, Einstein, and the search for reality
,” in
Ernt Mach Physicist and Philosopher
, edited by
R. S.
Cohen
and
R. J.
Seeger
, Boston Studies in the Philosophy of Science (
Reidel
, Dordrecht,
1970
), Vol.
VI
, p.
166
.
11.
E.
Mach
,
The Science of Mechanics
, 9th ed., translated by
T. J.
McCormack
(
Open Court
, La Salle, IL,
1960
), p.
284
.
12.
Reference 11, p.
xxviii
.
13.
F.
Pirani
, “
On the definition of inertial systems in general relativity
,”
Helv. Phys. Acta, Suppl. IV
,
198
203
(
1956
).
14.
A.
Pais
,
Subtle Is the Lord
… (
Oxford U. P.
, Oxford,
1982
), pp.
282
288
.
15.
C.
Will
, “
The renaissance of general relativity
,” in
The New Physics
, edited by
P.
Davies
(
Cambridge U. P.
, Cambridge,
1989
), pp.
8
9
.
16.
D.
Sciama
,
The Physical Foundations of General Relativity
(
Doubleday
, New York,
1969
), especially Chaps. 2 and 9.
17.
Reference 11; pp.
252
254
.
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