lobal Journal of Science Frontier Research, A: Physics and Space Science, Volume 24 Issue 4

(37) In which f 1 , f 2 , f 3 , represent the force densities in the 3 spatial dimensions and f 4 represent the force density (energy flow) in the time dimension (4 th dimension). Equation (37) can be written as: (38) The 4 th term in equation (38.1) can be written in the terms of the Poynting vector “S” and the energy density “w” representing the electromagnetic law for the conservation of energy (Newton’s second law of motion). b) The 4-dimensional Relativistic Dirac Equation Substituting (32) and (34) in Equation (38.1) results in The 4-Dimensional Tensor presentation for the relativistic quantum mechanical Dirac Equation (39): (39) To transform the electromagnetic vector wave function φ into a scalar (spinor or one-dimensional matrix representation), the Pauli spin matrices σ and the following matrices (Ref. 3 page 213, equation 99) are introduced: ( ) ( ) ( ) ( ) Energy-Time Domain E . E H . H 1 0 0 f . ( E ) + = 0 4 2 3- Dimen t ε µ ∂ + ⇔ ∇ × Η ∂ sional Space Domain f 3 (E ) 1 f - E ( E ) E ( E ) 2 0 0 2 f 1 t c ε ε µ     ∂ × Η   ⇔ + ∇ . − × ∇ × ∂       + ( ) ( ) 0 0 µ Η ∇ . Η − Η × ∇ × Η = 0 Energy-Time Domain Conservation of Energy ( ) B -7 w f . S + = 0 (38.1) 4 t ∂ ∇ ∂ 3-Dimensional Space Domain B -1 B -2 B -3 (E 1 - 2 f 3 f 2 f 1 c ∂             ) E ( E ) E ( E ) 0 0 B -4 B -5 ( ) ( ) 0 0 t ε ε µ µ × Η + ∇ . − × ∇ × + ∂ + Η ∇ . Η − Η × ∇ × Η = 0 (38.2) ( ) ( ) 4 3 2 1 * ( ( ( ) ( ) x . ( *) + = 0 x x ) + ) + x * * * * . t i c i c t φ φ φ φ φ φ φ φ φ φ φ φ ∂ ∂ − × ∇ × × ∇ × ∇ . + × ∂ ∂ ∇ ×           ( ) ( ) * φ φ ∇ . = 0 Global Journal of Science Frontier Research ( A ) XXIV Issue IV Version I Year 2024 63 © 2024 Global Journals A Reinterpretation of Quantum Physics