The book “Relational Mechanics and Implementation of Mach’s Principle with Weber’s Gravitational Force” (2014) is by Andre Koch Torres Assis. A bound copy is available through Amazon and a pdf is online at http://www.ifi.unicamp.br/~assis/Relational-Mechanics-Mach-Weber.pdf. Recall “Mach’s Principle”: Newton’s concepts of absolute space and time were not accepted by all scientists and the call for a reformulation of mechanics in terms of purely relational quantities never stopped. Although Mach was not the first who insisted on such a reformulation, he was the most influential one and his critique of the Newtonian concepts of absolute space and time published in his “Mechanics” was later loosely termed “Mach’s principle” by Einstein. However, since Mach made only tentative proposals, there are various interpretations and formulations of this principle.
After a thorough review of classical and relativistic mechanics and their problems, the author introduces relational mechanics based on his formulation of Mach’s Principle. He says in the Preface: Relational mechanics is a quantitative implementation of the ideas of Leibniz, Berkeley and Mach utilizing Weber’s force for gravitation. It is based only on relational concepts such as the distance between material bodies, the relative radial velocity between them and the relative radial acceleration between them. Several scientists took part in its development, including Wilhelm Weber himself and Erwin Schrödinger. The goal of this book is to present the properties and characteristics of this new physics, together with the main aspects related to its historical development after Newton. In this way relational mechanics can be seen in a broad perspective. A great emphasis is given to Newton’s bucket experiment. When a bucket partially filled with water remains stationary in the ground, the water surface is observed to remain horizontal. When the bucket and the water rotate together relative to the ground around the bucket’s axis with a constant angular velocity, the surface of the water is observed to become concave, higher at the sides of the bucket than along the its axis. This is one of the simplest experiments ever performed in physics. Despite this fact no other experiment had so deep and influential consequences upon the foundations of mechanics. We place it at the same level Galileo’s experimental discovery that all bodies fall freely towards the ground with a constant acceleration, no matter their weights or chemical compositions. The explanation of these two facts without utilizing the concepts of absolute space or inertia, but taking into account the gravitational influence exerted by the distant galaxies in these two experiments, is one of the major achievements of relational mechanics.
He supports a universe in dynamical equilibrium without expansion but doesn’t go into that as much as other topics.
He notes in the Conclusion: We have found a complete equivalence between ptolemaic and copernican world systems. It is then equally valid to say that the Earth is spinning once a day relative to the stationary set of distant galaxies, or that the Earth is at rest while the set of distant galaxies is rotating once a day as a whole relative to the Earth. Both world views are now equivalent not only kinematically or visually, but also dynamically (yielding the same flattening of the Earth at the poles, the same precession of the plane of oscillation of Foucault’s pendulum relative to the ground, etc.) We have deduced the fact that all inertial forces of newtonian mechanics, like the centrifugal or Coriolis forces, are real forces acting on the test body and being exerted by the set of galaxies. These forces have a gravitational origin and appear when there is a relative rotation between the test body and the set of galaxies. This property explained the flattening of the Earth as being due to the relative rotation between the Earth and the set of galaxies. This property also justifies the fact that the plane of oscillation of Foucault’s pendulum at the North or South poles remains at rest relative to the set of galaxies, while the Earth is spinning relative to the galaxies. In the terrestrial frame of reference, on the other hand, the Coriolis force exerted gravitationally by the set of galaxies and acting on the mass connected to the pendulum rotates the plane of oscillation of the pendulum, relative to the ground. This Coriolis force causes a precession in the plane of oscillation of the pendulum, making it rotate together with the set of galaxies around the North-South axis of the Earth.