Relational
Mechanics(paperback, 285 pages; ISBN 0-9683689-2-1)
Relational
Mechanics
(paperback, 285 pages; ISBN 0-9683689-2-1)
Andre
K.T. Assis
Relational
Mechanics is a new mechanics that replaces Einstein's theories of relativity. It
implements Mach's principle quantitatively based on Weber's relational law and
the principle of dynamical equilibrium. It explains Newton's bucket experiment
as due to gravitational interaction between the water and the distant universe
when in relative rotation. The book is intended for physicists, engineers,
mathematicians, historians, philosophers of science and students.
From
the Author's Preface
This book
presents Relational Mechanics, a new mechanics which implements the ideas of
Leibniz, Berkeley, Mach and many others. Relational mechanics is based only on
relative quantities, such as the distance between material bodies, their
relative radial velocity and relative radial acceleration.
In this new
mechanics the absolute concepts of space, time and motion do not appear. The
same can be said of inertia, inertial mass and inertial frames of reference.
When we compare relational mechanics with Newtonian mechanics, we will gain a
new and clear understanding of these old concepts. Relational mechanics is a
quantitative implementation of Mach's ideas utilizing a Weber's force law for
gravitation. Many people have contributed to its development, including Erwin
Schrödinger.
This is the
first time such a book has been written, bringing together all the features and
characteristics of this new world view. This allows it to be seen in its proper
light, and a comparison with old worldviews is easily accomplished.
Considerable
emphasis is placed on Galileo's free fall experiment and on Newton's bucket
experiment. These are some of the simplest experiments ever performed in
physics. Despite this fact, no other experiment has had such far-reaching
consequences for the foundations of classical mechanics. An explanation of these
two experiments without utilizing the concepts of absolute space and inertia is
one of the major accomplishments of relational mechanics.
In order to
show all the power of relational mechanics and put it in perspective, we first
present Newtonian mechanics and Einstein's theories of relativity. We address
the criticisms of Newton's theory made by Leibniz, Berkeley and Mach. Then we
present relational mechanics and show how it solves all these problems
quantitatively with a clarity and simplicity unsurpassed by any other model. We
also discuss the history of relational mechanics in detail, emphasizing the
achievements and limitations of all major works along these lines. In addition,
we present several notions which are beyond the scope of Newtonian theory, such
as the precession of the perihelion of the planets, the anisotropy of an
effective inertial mass, the adequate mechanics for high velocity particles,
etc. Experimental tests of relational mechanics are also outlined.
This book is
intended for physicists, mathematicians, engineers, historians and philosophers
of science. It is also addressed to teachers of physics at university or high
school levels and to their students. After all, those who have taught and
learned Newtonian mechanics know the difficulties and subtleties of its basic
concepts (inertial frame of reference, fictitious centrifugal force, inertial
and gravitational masses, etc.) Above all, it is intended for young unprejudiced
people who have an interest in the fundamental questions of mechanics: Is there
an absolute motion of any body relative to space or only relative motion between
material bodies? Can we prove experimentally that a body is accelerated relative
to space or only relative to other bodies? What is the meaning of inertia? Why
do two bodies of different weight, form and chemical compositions fall with the
same acceleration in vacuum on the earth's surface? When Newton rotated the
bucket and saw the water rising towards the sides of the bucket, what was
responsible for this effect? Was it due to the rotation of the water relative to
some material body? What flattens the earth at the poles in its diurnal
rotation? Is it the rotation of the earth relative to something? Is the earth
really rotating and translating? We show that the answer to these questions with
relational mechanics is much simpler and more philosophically sound and
appealing than in Einstein's theories of relativity.
Nowadays the
majority of physicists accept Einstein's theories as correct. We show this is
untenable and present an alternative theory which is much clearer and more
reasonable than the previous ones. We know that these are strong statements, but
we are sure that anyone with a basic understanding of physics will accept this
fact after reading this book with impartiality and without prejudice. With an
understanding of relational mechanics, we enter a new world, viewing the same
phenomena with different eyes and from a new perspective. It is a change of
paradigm. This new formulation will help put physics on new rational
foundations, moving it away from the mystifications of this century.
We hope
physicists, engineers, mathematicians and philosophers will adopt this book in
their courses of mechanics, mathematical methods of physics and history of
science, recommending it to their students. We believe the better way to create
critical minds and to motivate the students is to present to them different
approaches for the solution of the same problems, how the concepts have been
growing and changing throughout history and how great scientists viewed
equivalent subjects from different perspectives.
A Portuguese
version of this book was published under the title Mecânica Relacional.
Preface
Chapter 1
Newtonian Mechanics
Chapter 2
Applications of Newtonian Mechanics
Chapter 3
Non-inertial Frames of Reference
Chapter 4
Gravitational Paradox
Chapter 5
Leibniz and Berkeley
Chapter 6
Mach and Newton's Mechanics
Chapter 7
Einstein's Theories of Relativity
Chapter 8
Relational Mechanics
Chapter 9
Applications of Relational Mechanics
Chapter 10
Beyond Newton
Chapter 11
History of Relational Mechanics
Chapter 12
Conclusion
Index
About
the Author
Andre K.T.
Assis, born in 1962, is Professor of Physics at the State University of Campinas,
Brazil. He held a post-doctoral position at Culham Laboratory, UKAEA, England,
during 1988, and was a visiting scholar at the Center for Electromagnetics
Research, Northeastern University, Boston, USA, from 1991 to 1992. He has
published dozens of papers on relational mechanics and Mach's principle, Weber's
electrodynamics and Ampere's force between current elements, Hubble's law of
redshifts, the cosmic background radiation and cosmology. He is the author of
Weber's Electrodynamics (Kluwer, 1994) and five other books in Portuguese on
related subjects.