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

(40) The Equations(6), (32) and (34) can be written in tensor presentation as the 4-Dimensional Relativistic Quantum Mechanical Dirac Equation: [3] (Equation 102, page 213) (41) VI. H eisenberg’s U ncertainty R elationship a) The Inertia of Confined Electromagnetic Radiation According to the insights derived from equation (23), the solutions of the Schrödinger wave equation depict confined electromagnetic waves characterized by a distinct 90-degree phase shift between the electric and magnetic fields. This segment delves into exploring the concept of inertia associated with confined electromagnetic waves. To elucidate the calculation of inertia pertaining to confined electromagnetic radiation, a hypothetical scenario involving electromagnetic radiation trapped between two perfectly reflective mirrors will be considered. The radiation beams emanating from these mirrors, referred to as the emitted radiation, can be likened to light emitted from a source of electromagnetic radiation. In this scenario, when an observer moves towards the emitter, the intensity of light at the observer's position undergoes a transformation in accordance with the Lorentz transformation formula, where "v" signifies the relative velocity between the emitter and the observer. At relatively low velocities, the term in the Lorentz transformation equation simplifies to 1, reflecting the behavior observed in this regime. When the observer moves away from the emitter, the intensity of the light at the location of the observer will decrease with ( ) 1 - v / c γ according the Lorentz transformation. At low velocities the Lorentz contraction term: 2 2 1 = v 1 - c γ (42) will equal 1 (“v” equals the relative velocity between object and observer and c equals the speed of light). In the scenario where light is confined between two perfectly reflective mirrors, a significant observation emerges: the speeds of both mirrors remain consistently equal relative to each other. This equilibrium ensures that the radiation pressures exerted on each mirror are also in balance; these opposing radiation pressures effectively cancel each other out. Consequently, the system—comprising the two perfect mirrors and the confined electromagnetic radiation—will either remain at rest or continue moving at a uniform speed. This dynamic equilibrium underscores the intricate interplay between the confined electromagnetic radiation and the reflective surfaces in this conceptual framework. i. The Resulting Radiation Pressure for accelerated or decelerated confined electromagnetic radiation In the context of acceleration, an interesting phenomenon arises where the time taken for light to travel between the mirrors at the speed of light can introduce variations. If we designate one mirror as the emitter and the other as the observer, the apparent speeds of the emitter and observer differ due to the time delay inherent in light propagation during acceleration. This time discrepancy gives rise to a situation where the opposing radiation pressures on the mirrors are no longer balanced, leading to an imbalance in forces. This disparity in radiation pressures may engender a resultant force as per Newton's second law of motion during acceleration. To embark on this analysis, an imaginary experiment is envisioned. Two perfectly reflective mirrors, labeled as B and A and situated opposite each other in the x-y plane at a specific distance, serve as the setting. Within this framework, a single harmonic electromagnetic wave is confined between the mirrors, giving rise to a "Standing Electromagnetic Wave" akin to the solution described in equation (23). This standing 0 0 = and = 0 0 ab ab δ σ α β δ σ         −     ( ) 4 (41.1) i m c 1 x + . = - h c t ψ ψ β α ∂ ∂  ∇     0 2 3 2 1 E 1 ( ) ( ) - x x x E E t c ε Η ∂ ∂ + ∇ . ×           0 0 0 ( ) ( ) ( ) (41.2) g ( g ) g ( g ) 0 0 E E µ µ ε γ γ + ∇ . − × ∇ × + = − × ∇ × + 0 Η Η Η Η ∇ . − × ∇ × Global Journal of Science Frontier Research ( A ) XXIV Issue IV Version I Year 2024 64 © 2024 Global Journals A Reinterpretation of Quantum Physics