Abstract
In this paper, Kaluza–Klein theory is revisited and its implications are elaborated. We show that electromagnetic 4-potential can be considered as a shearing-like deformation of a 5-dimensional (5D) manifold along the fifth (5th) axis. The charge-to-mass ratio has a physical meaning of the ratio between the movement along the direction of the 5th axis and the movement in the 4D space-time. In order to have a 5D matter which is consistent with the construction of the 5D manifold, a notion of particle-thread is suggested. Examinations on the compatibility of reference frames reveal a covariance breaking of the 5th dimension. The field equations which extend Einstein’s field equations give the total energy-momentum tensor as a sum of that of matter, electromagnetic field, and the interaction between electric current and electromagnetic potential. Finally, the experimental implications are calculated for the weak potential case.
Highlights
It has been nearly a hundred years since the attempt for a unified field theory was first made
Our model inherits the qualitative features of general relativity but in 5-dimensions, so that the 5D manifold is described by 5D metric and the metric is affected by 5D energy-momentum
We consider a 5D manifold which is constructed by dragging the space-time to the direction of the 5th axis so that the 4D part of 5D metric is independent of the 5th coordinate
Summary
It has been nearly a hundred years since the attempt for a unified field theory was first made. Kaluza constructed a 5D metric including a new scalar field and the whole metric was independent of the 5th dimension. He assumed the source-free condition for 5-dimensions. Where φ was a scalar field and the repeating boundary condition was imposed along the 5th dimension This is what we call as the Kaluza–Klein metric. Even though the metric has the same form, the construction of the metric for the 5D manifold and the 4D space-time (throughout the present paper, space-time will mean 4D spacetime) is different from both Kaluza’s original idea and Klein’s version. The 5D manifold used throughout this paper is constructed and the interpretation of electro magnetic 4-potential is given at section 3.
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