The ”Mach’s Principle” has beenconsidered for more than a century as the highest
expression of the philosophical rationality of the western world, but it is possible to
proof that it is built on a unstable ground and with uncomplete assumptions. With a great
intellectual honesty, Ernst Mach showed in his works some awareness of the incompleteness
of his reasoning about inertia. Moreover the Mach Principle is often misinterpreted by
scientific community with an illegitimate extrapolation of the Mach words

Scalera, G.

Earth-prints Repository

pag. 239
G. Scalera, E. Boschi and S. Cwojdzin´ski (eds.), 2012
THE EARTH EXPANSION EVIDENCE – A Challenge for Geology, Geophysics and Astronomy
Selected Contributions to the Interdisciplinary Workshop of the 37th International School of Geophysics
EMFCSC, Erice (4-9 October 2011)
If Space is Material, What Inertia Should Be?
Rediscovering a Dismissed Awareness of Ernst Mach
Giancarlo Scalera
Istituto Nazionale di Geofisica e Vulcanologia – Via Vigna Murata 605, 00143 Roma, Italy
(giancarlo.scalera@ingv.it)
Abstract. The ”Mach’s Principle” has beenconsidered for more than a century as the high-
est expression of the philosophical rationality of the western world, but it is possible to
proof that it is built on a unstable ground and with uncomplete assumptions. With a great
intellectual honesty, Ernst Mach showed in his works some awareness of the incomplete-
ness of his reasoning about inertia. Moreover the Mach Principle is often misinterpreted by
scientific community with an illegitimate extrapolation of the Mach words.
Key words.Mach Principle – Inertia conceptions – Fluid dynamics
Ernst Mach (1838-1916) was person-
ally educated by his father, the ideal-
ist Johann Mach, until he enroll to the
High School on 1853 (Dragoni et al.,
1999). It could be a plausible supposi-
tion that the father’s tuition had a strong
and never completely overcomed influ-
ence on the intellectual pathways of his
son. Ernst Mach became renown (Musil,
1908) with the book Die Mechanik in ihrer
Entwickelung historisch-kritisch danger-
stellt (Mach, 1883) and in particular for the
criticism of the Newtonian concept of iner-
tia founded on the experiment of the water
in a rotating bucket.
Albeit the criticism to the exagerations
of his time in proposing mechanical ad hoc
imaginative interpretations for all physi-
cal phenomena were fully justified, he did
not fully understand that the search for the
causes of the natural phenomena is one
among the main trigger for new progress
in the sciences (Musil, 1908). His argu-
ment of an alleged simmetricity among the
rotation of the bucket with respect to wa-
ter and of the water with respect to the
Fig. 1. Ernst Mach (February 18, 1838, Brno,
Austrian Empire – February 19, 1916, Munich,
German Empire) became Professor of the History
and Theory of Inductive Science at the University
of Vienna.
bucket, with the inertial centrifugal forces
produced only by the motion with respect
to all the distant masses of the universe,
was adopted by scientists and philosophers
as an explanation of the presence of ’iner-
tia’ in the sensible world, and is universally
called ”Mach’s Principle”. It is considered
for more than a century as the highest ex-
240 SCALERA: Inertia for a Material Space
pression of the philosophical rationality of
the western world, but I will try to proof
that, on the contrary, it is built on a unsta-
ble ground and with uncomplete assump-
tions: it is a masterpieces of captious logic
of which the same Ernst Mach had some
awareness.
The Mach’s Principle is very often mis-
interpreted by scientific community with
an illegitimate extrapolation of the Mach
words. I can propose some critics argu-
ments to fix my views:
(1) –Mach’s aim was only to pose a limit, a
boundary, to the possible truthful state-
ments about the experiment of Newton
of the rotating bucket filled with water.
(2) – He did not intend to assign particu-
lar and still unknown properties to the
distant mass of the Universe, but only
and simply to assume them as a suitable
reference frame. Indeed, Mach (1883)
said: No one is competent to say how the
experiment would turn out if the sides
of the vessel increased in thickness and
mass till they were ultimately several
leagues thick. The one experiment only
lies before us, and our business is, to
bring it into accord with the other facts
known to us, and not with the arbitrary
fictions of our imagination. (pag. 232,
English transl., 1919)
(3) – Many followers of Mach, but with a
lower philosophical level, had the unfor-
tunate idea to force the argument toward
the possible existence of an unclear in-
fluence of all the distant masses on the
laboratory test mass. This is somewhat
equivalent to try to restore the concept
of ”action at a distance”, so lowed by
idealism.
(4) – In defining inertia, meditating about
the rotating buckle experiment is not
sucient. It is more important to ob-
serve that a body can be deviate from its
natural rectilinear path only by applying
a force F, and that in the time window
of the action of F ”inertial forces” ap-
pears (e.g. Coriolis forces).
(5) – The preceding point (4) is a funda-
mental clue that cannot be disregarded
about the local and symmetric nature of
what we have to search for.
(6) – A process that fulfills the above re-
quested properties of locality and sym-
metricity is the motion of bodies in a
fluid. Theory of hydrodynamics states
that a solid body can move with con-
stant velocity without friction in a per-
fect fluid. It undergoes resistance only
if accelerates – perceiving only now the
influence of the otherwise undetectable
sourrounding milieu. Symmetrically, a
constant velocity wind of a perfect fluid
is not perceived by a solid body, while
if the wind accelerates, a force is expe-
rienced by the body – perfectly analo-
gous to a gravity force and nothing but
an equivalence principle.
Ernst Mach showed some awareness of
the incompleteness of his reasoning about
inertia by writing (1883) with a great intel-
lectual honesty:
It might be, indeed, that the isolated
bodies A, B, C . . . . play merely a collat-
eral role in the determination of the mo-
tion of the body K, and that this motion
is determined by a medium in which K
exists. In such a case we should have to
substitute this medium for Newton’s ab-
solute space. Newton certainly did not
entertain this idea. Moreover, it is easily
demonstrable that the atmosphere is not
this motion-determinative medium. We
should, therefore, have to picture to our-
selves some other medium, filling, say,
all space, with respect to the constitu-
tion of which and its kinetic relations
to the bodies placed in it we have at
present no adequate knowledge. In it-
self such a state of things would not be-
long to the impossibilities. It is known,
from recent hydrodynamical investiga-
tions, that a rigid body experiences re-
sistance in a frictionless fluid only when
its velocity changes. True, this result is
derived theoretically from the notion of
inertia; but it might, conversely, also
be regarded as the primitive fact from
which we have to start. Although, prac-
tically, and at present, nothing is to
SCALERA: Inertia for a Material Space 241
be accomplished with this conception,
we might still hope to learn more in
the future concerning this hypothetical
medium; and from the point of view of
science it would be in every respect a
more valuable acquisition than the for-
lorn idea of absolute space. (pag. 230-
231, English transl., 1919)
And Musil (1908) considered that:
It is dicult to say whether this
Newtonian hypotheses non fingo should
be taken to signify no more than a
methodological attempt to separate the
secure goals of physico-analytic en-
quiry from the uncertain results of
the philosophico-physical considera-
tions erected on the top of these – such a
boundary would correspond to the level
of knowledge at that time, but could
gradually be changed to incorporate
the ”hypotheses” into what had already
been proven. (pag. 32, English transl.,
1982)
1. Appendix
A synthesis (from text-books of Hydro-
dynamics; e.g. Page, 1958) is shown here
of the hydrodynamical treatment of the
motion of a sphere in a perfect fluid
(incompressible, irrotational, without fric-
tion, infinite extent, at rest at infinity, no
gravity or body forces acting on it). The
well known equation of continuity
@
@t
=  r  (v)
with incompressible fluids ( = const) re-
duces to: r  v = 0 ; or, if the fluid is irro-
tational:
r  r = 0;
(1)
namely the Laplacian of the scalar field ,
from which the velocities components can
be derived:
vx =
@
@x
; vy =
@
@y
; vz =
@
@z
:
It is straightforward to show that, trans-
forming to polar coordinates, equation (1)
can be written:
@
@r
 
r2
@
@r
!
+
1
sin 
@
@
 
sin 
@
r@
!
= 0;
that should be solved adopting the two
boundary conditions: 
@
@r
!
r=a
= V cos ; and
 
@
@r
!
r=1
= 0;
with V the velocity of the sphere along the
X axis, and a the radius of the sphere.
With few algebra it is easy to show that
a solution is
 = Ar  cos  +

B=r2

 cos :
From the boundary conditions, it is possi-
ble to infer the two constants A and B:
A = 0; and B =
1
2
Va3;
and finally
 =
Va3
2r2
 cos :
Now we have all the elements to derive
the kinetic energy Ek of the fluid:
vr =  
r
=
Va3
r3
cos ;
v =   r =
Va3
2r3
sin ;
v2 = v2r + v
2
 =
 
Va3
r3
!2

 
cos2  +
1
4
sin2 
!
;
Ek =
Z 1
a
Z 
0
1
2
v2  2r2  sin   ddr =
= V2a6

Z 1
a
dr
r4
Z 
0
(cos2  +
1
4
sin2 ) sin d =
=
1
3
a3V2 =
1
4
M0V2:
242 SCALERA: Inertia for a Material Space
The constant quantity M0 is the mass of
the fluid displaced by the sphere and 12M
0
is the apparent mass of a massless sphere.
This mass produce an inertial eect, what-
soever was the mass of the sphere, a fact
that points towards the uselessness of the
concept of mass of the bodies. Both mass
and inertia could well be attributes coming
from a pervading medium.
The astonishing and wonderful thing in
this simple derivation of the inertial ef-
fect is that we can imagine the sphere as
a simple massless geometrical entity. This
means that a meditation deserves the role
of geometry in this conception. Could the
distorsions of the space be redefined in
a more local manner? Are waiting pure
shapes and extents for a deeper role in fun-
damental physics?
References
Aiton E.J. (1969). Newton’s ether Stream
Hypothesis and the inverse Square Law of
gravitation. Annals of Science, 25, 255-260.
Blinov V.F. (2011). Geophysical Advances in
Earth’s Evolution – Kinetic Gravity and
Expanding Earth. This volume.
Cahill R.T. (2009). Dynamical 3-Space: A Review.
In M.C. Duy and J.L. Levy (eds.) Ether Space-
time and Cosmology: New Insights into a Key
Physical Medium. Apeiron, 135-200.
Dragoni G., Bergia S., Gottardi G. (eds.) (1999).
Ernst Mach. In: Dizionario Biografico degli
Scienziati e Tecnologi, Zanichelli, Bologna,
1600 pp.
Edwards M.R. (ed.) (2002). Pushing Gravity: New
Perspectives on Le Sage’s Theory of Gravitation.
Roy Key Inc., Montreal.
Hilgenberg O.C. (1976). The formation and de-
velopment of the Earth: contraction or expan-
sion? (Fragments from the last unpublished
manuscript. Translation of Dorotea Nicosia, re-
vision of Karl Luckert). In: Scalera G. & Jacob
K.-H. (eds.) Why expanding Earth? A book in
honour of O.C. Hilgenberg. INGV, Rome, 53-64.
Huygens C. (1690). Discours de la cause de la pe-
santeur (Discourse on the Cause of Gravity).
Mach E. (1883). Die Mechanik in ihrer
Entwickelung historisch-kritisch dangerstellt.
English translation by Thomas J. McCormack
(1919, fourth edition) The science of Mechanics
– A critical and historical account of its de-
velopment. The Open Court Publishing Co.,
Chicago-London.
Musil R. (1908). Beitrag zur Beurteilung der
Lehren Machs. Doctoral Thesis Dissertation on
14 March 1908 at the University of Berlin.
English translation by K. Mulligan (1982) On
Mach’s theories. Catholic University of Am.
Press, Mu¨nchen-Wien, 97 pp.
Page L. (1958). Introduction to Theoretical Physics.
Van Nostrand Company, 701 pp.
Scalera G., Jacob K.-H. (eds.). Why expanding
Earth? – A book in honour of O.C. Hilgenberg.
INGV, Rome, 465 pp.
Van Lunteren F. (2002). Nicolas Fatio de Duillier on
the mechanical cause of gravitation. In: Edwards
M.R. (ed.) Pushing Gravity: New Perspectives
on Le Sage’s Theory of Gravitation. Roy Key
Inc., Montreal, 41-59.
Yarkovsky I.O. (1888). Hypothe`se cine´tique de la
gravitation universelle en connexion avec la for-
mation des e´le´ments chimiques. Published by the
author in Moscow.
Author’s Biographical Notes: Giancarlo Scalera
was born in Barletta, Italy, on 4 April 1949. He get
the University degree in Physics at the University of
Bari (1975) discussing a Doctoral Thesis on foun-
dation of Physics. Immediately after, he proposed a
mechanical and local model that is able to violate
the Bell’s inequality. On 1976 Scalera was Assistant
lecturer at the Geodesy Institute of the University
of Bari and he collaborated to the maintenance of
the seismic network of the University of Calabria.
On 1979 he was at work in the INGV in Rome.
The map of the Maximum Intensity Felt in Italy
was drawn by Scalera and co-authors and he
found correlations between the Felt Intensities
and a number of geological and geophysical
characteristics of the Italian region. Research was
made in global tectonics, paleogeography and
geodynamics, adopting the expanding Earth model.
He performed historical researches about shape
and movements of the Earth, and biographical
researches on scientists involved in the expanding
Earth. Presently is proposer of a new mechanism
of muntain building based on isostasy. Giancarlo
married on 1980 and has a doughter. He loves
painting and sculpturing, and – ever more rarely –
use the bicycle for excursions.


If Space is Material, What Inertia Should Be? - Rediscovering a Dismissed Awareness of Ernst Mach

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If Space is Material, What Inertia Should Be? - Rediscovering a Dismissed Awareness of Ernst Mach

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