Left: K is fixed and K’ is rotating along z-axis. The background is fixed in K reference frame. So K is an

inertial reference frame and K’ is non-inertial reference frame. Right: The background starts rotating such that it is

fixed in K’ reference frame. In this case K’ will become an inertial reference frame and K becomes non-inertial

reference frame.

**Santanu Das**

One of the main motivations behind formulating the general theory of relativity was to provide a mathematical description to the Machian gravity’s principle. However, soon after its formulation, it was realized that the theory does not follow Mach’s principle. As the theoretical predictions were matching with the observations, Einstein believed that the theory was correct and did not make any farther attempt to reformulate the theory to explain Mach’s principle. Later on, several attempts were made by different researchers to formulate the theory of gravity based on Mach’s principle. However most of these theories remain unsuccessful to explain different physical phenomena. In this report I have proposed a new theory of gravity which is completely based on the Mach’s principle. The theory can explain the galactic velocity profiles up to a high degree of accuracy, without demanding the existence of any dark matter component in the universe. The theory can also explain the accelerated expansion of the universe without Dark Energy. It is a metric theory and can be derived from the action principle, which guarantees energy or momentum conservation. Modern theories like TeVeS or Modified gravity give some mathematical modification of the Einstein’s equation to explain different observational phenomenon like the galactic velocity profile, accelerated expansion of the universe or CMBR power spectrum. Most of these theories don’t have any underlying logic. However, the new theory explained in this paper, is a mathematical formulation of the Mach’s principle. Therefore, the theory is not just a mathematical jugglery to explain some observed facts, but arises from a deep physical argument….

Read more: http://arxiv.org/pdf/1206.6755v1.pdf

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*Related*

Cosmological solution of Machian gravity (http://arxiv.org/abs/1205.4055)

Santanu Das

(Submitted on 17 May 2012)

The standard model of cosmology predicts that more than 95% matter in the universe consists of dark components namely dark matter and dark energy. In spite of several attempts to measure these components, there is not a single direct observational evidence for these components till date. Hence, different alternate models of cosmology have been put forward by different authors. However, most of these models have their own problems. Therefore, in this paper, a new cosmological model has been proposed. This model is based on the Machian gravity model, which will be discussed in detail in a later paper. The model can provide an exactly similar cosmology as that of the standard cosmological model without demanding any ad-hoc dark matter or dark energy components. The paper shows that when the field equations from Machian gravity (a 5 dimensional model) are projected to the 4-dimensional space-time, some new mathematical terms arise in the equations that behave exactly like dark matter and dark energy. These mathematical terms come completely from the geometry of the universe and therefore these do not have any connection with the real matter. As the General theory of Relativity does not follow Mach’s principle, the FLRW model that is based on GR, cannot provide the correct solution to the cosmological model and demands extra forms of matter and energy to give any predictions consistent with the observations.

On the wavy mechanics of particles (http://arxiv.org/abs/1206.0923)

Santanu Das

Concept of mass is one of the most complicated concepts in physics. Philosophically, the mass can be defined in three different ways and according to these definitions; there are three different kinds of masses. These are named as the active gravitational mass, passive gravitational mass and the inertial mass. Several experiments have been performed to distinguish these masses, and in all these experiments, surprisingly these masses come out to be the same. Therefore, even though conceptually these masses are different but they are considered to be same empirically. Hence, in modern physics, all these different concepts are abolished and people treat all the three masses as the same. However, in this paper the inertial mass is considered to be different from the other ones. It is thought that the inertial mass of a particle is not completely its intrinsic property and it depends on the position of the particle in the universe, or the background of the position where the particle is located. But the background of a particle keeps on fluctuating randomly due to different types of phenomenon occurring in the universe. Therefore, the exact position or the mass of a particle can not be determined at any time, without knowing the exact positions and the states of all the other particles in the universe. Hence, in this paper, the dynamics of a particle has been defined statistically, which leads to the Schrodinger equation. The mathematical formalism presented in this paper can explain the quantum mechanical phenomenon completely classically and thus it gives quantum mechanics a sense of completeness.