TITLE:
Relativistic Mechanics in Positive and Negative Subspace-Time according to the Inverse Relativity Model
AUTHORS:
Michael Girgis
KEYWORDS:
4D Velocity Vector Analysis, Positive Subspace, Negative Subspace, Negative Relativistic Mechanics, Positive Tensor of Energy and Momentum, Inverse Theory of Relativity
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.12 No.11,
November
21,
2024
ABSTRACT: In the second paper on the inverse relativity model, we explained in the first paper [1] that analyzing the four-dimensional displacement vector on space-time according to a certain approach leads to the splitting of space-time into positive and negative subspace-time. Here, in the second paper, we continue to analyze each of the four-dimensional vectors of velocity, acceleration, momentum, and forces on the total space-time fabric. According to the approach followed in the first paper. As a result, in the special case, we obtain new transformations for each of the velocity, acceleration, momentum, energy, and forces specific to each subspace-time, which are subject to the positive and negative modified Lorentz transformations described in the first paper. According to these transformations, momentum remains a conserved quantity in the positive subspace and increases in the negative subspace, while the relativistic total energy decreases in the positive subspace and increases in the negative subspace. In the general case, we also have new types of energy-momentum tensor, one for positive subspace-time and the other for negative subspace-time, where the energy density decreases in positive subspace-time and increases in negative subspace-time, and we also obtain new gravitational field equations for each subspace-time.