Dear Ramesh, you pose an interesting question and an approach to answering it. My approach is to apply Peter Rowlands' duality principle which regards the gauge forces and gravitational fields as inverses which I like to write in the following way: gauge (+) gravity = Z, a zero-totality condition. Gauge forces are responsible for inertial conditions. My paper on this topic and Peter's work are available through ResearchGate.

Dear Ramesh, I have attached a document that could perhaps be useful on issues that you raise.

Dear Jesus Alvarez Lobo,

Unable to read your attachment 'ON THE ORIGN OF THE INERTIA'.

Regards

Ramesh Chandra

It is in PDF format. You need acrobat reader (it is free) or other reader of PDF. It is the most commonly used format for sharing documentation.

Thank you Jesús for the PDF. Kevin Brown has a similar perspective. See: http://www.mathpages.com/home/kmath588/kmath588.htm

Thank Sabah for your information.

Dear Sabah E. Karam,

Sorry for late reply due to unavoidable circumstances.

According to your advise, I am trying to read about the gauge field but, unable to read. According to my knowledge, a gauge field may not be incorporated in special relativity and in general relativity without modifying the structures of the special relativity and the general relativity.

My question is very simple. We consider an inertial frame F. The geometrical structure of the frame is Minkowskian. Now, we consider a frame F' which is accelerating relative to the frame F. The geometrical structure of the frame F' is neither Minkowskian similar to the inertial frame F nor a Riemannian structure similar to the general relativity. For simplicity, we consider a constant acceleration of the frame F' relative to the inertial frame F. We want to know the geometrical structure of the frame F' and the relations between the coordinates of the frames F and F'.

Regards

Dear Mohammad Hassani, I think it is clear which theory Ramesh is talking about. The theory of special relativity (SR) as proposed by Einstein in his 1905 paper was built on a concept of inertia and inertial reference frames developed by Galileo and Newton. SR applied to systems where no acceleration was present. In 1916 this limitation was overcome in general relativity (GR) where both inertial and noninertial (accelerated) reference frames Were considered. A new concept called "curvature of spacetime" was introduced replacing the concept of Newtonian forces.

The Newtonian concept of "inertia" was also replaced by "geodesic deviations." Einstein never defined inertia and failed to incorporate Mach's principle. Rather, he redefined gravity to be a linkage between spacetime and matter. Space and time had been linked by Minkowski, motion of planets and gravitational forces on earth were linked by Newton, stationary and inertial motion were linked by Galileo. You can see how the linkage of continuous and discrete concepts have emerged over a 400 year period of time. NOTE: My paper presented at a GR Conference in Moscow in July 2017 (See: PIRT.info) argues that it is spacetime quantum forces (applying Newtonian terminology to GR) that curve matter rather than the other way around.

Dear Sabah E. Karam,

Thank you very much for your explanation of my question.Now I am eagerly waiting for your reply on my question.

With best regards

Ramesh Chandra

Dear Ramesh,

Please excuse my delayed response. I have been working on other projects and wanted to present my thoughts in an organized fashion. I am still considering your Question and want you to know that I am still thinking about it. Here is a link to a 2005 paper that is relevant to my current research and may give insight into your question.------ https://arxiv.org/ftp/physics/papers/0501/0501060.pdf ------- "Empty space-time, general relativity principle and covariant ether theories" by Alexander L. Kholmetskii, Department of Physics, Belarus State University, E-mail:[email protected]

Dear Sabah E. Karam,

Thank you very much for your response. I will try to see the reference advised by you but, I am not sure about it according to my present situation.

Regards

Ramesh Chandra

Dear M. Hassani,

I am waiting for your responce on my question " In the Einstein's theory......what is an inertial force?"

Regards

Ramesh Chandra