Theory of the Four-Dimensional Electromagnetic Universe: Derivation of the Energy-Time Uncertainty Principle for Temporal Waves and Their Stability

In this paper, we derive a specific form of the energy-time uncertainty principle as it applies to Temporal Waves (TWs) in the context of the Four-Dimensional Electromagnetic Universe (4DEU) Theory, providing further evidence of the stability of TWs from the beginning and throughout the four-dimensional (4D) universe's expansion. In this model, the universe is proposed to exist in four real spatial dimensions, with the fourth dimension, which we perceive as time, along which the cause of the 4D universe's expansion acts. TWs play a fundamental role in the formation and expansion of the 4D universe, with this expansion being caused by their radiation pressure. In this work, we derive the specific form of the uncertainty principle for TWs, demonstrating that the product of the uncertainties in the TW energy and privileged time is not merely constrained by a lower bound, as in the canonical uncertainty principle, but is exactly equal to h/4. In contrast to the canonical uncertainty principle, where the product of uncertainties is greater than or equal to h/4p, in the case of TWs this product equals precisely h/4, indicating a unique relationship in the 4DEU theory. Our findings also confirm the stability of TWs from the beginning and throughout every phase of the 4D universe's expansion, ensuring their persistence over time. This paper offers further mathematical evidence supporting the stability of TWs and strengthens the foundational principles of the Theory of the Four-Dimensional Electromagnetic Universe.