I have a question about the definition of mass. In general relativity mass is closely related the curvature of spacetime, which indicates that mass might be interpreted as a geometric concept (maybe related with the connection defined on some fibre bundle structures above spacetime). I found only Gonzalez-Martin's related work on this topic in his book "physical geometry".
Gonzalez-Martin's work was quite old and two of his papers related to this topic are:
- Physical Geometry: A Unified Theory of Gravitation, Electromagnetism and Other Interactions
- A Geometric Definition of Mass
His book including these two papers can be found here: Physical geometry.
But I did not catch his idea. Can anybody help to explain his idea or provide other alternative work in this direction? BTW, I wonder if a geometric description of spacetime is valid, if the discrete space (~Planck length) somehow be related with the isoholonomic problem, which aims to find out the minimal loop to generate a given holonomy.