Law of Probability Equilibrium (LPE) and Bounded Randomness: Light in the Universe, Photon Emission and Black Holes

The relationship between chance and determinism has been analyzed by philosophy, mathematics, and physics. With the aim of identifying the intersection between the two, the Law of Probability Equilibrium (LPE) was demonstrated. When the probabilities of natural phenomena differ from zero and one, the LPE shows that the observed probability is empirical and that the cumulative probability functions of these phenomena measure the imminence of their occurrence (“energy concentration”). These functions behave like waves that carry information about the probabilistic (“energetic”) potential for the materialization of such phenomena. Probability functions exhibit properties analogous to quantum systems, such as complementarity, superposition, uncertainty, collapse, duality, interference, and entanglement. The findings indicate that chance and determinism converge at a cumulative limit of ？, forming a self-regulating equilibrium within the probabilistic field. This implies both the certainty of occurrence and the unpredictability of its timing. Even events with infinitesimal probabilities will inevitably occur. The LPE shows that the probability potential decreases until it reaches zero (“maximum entropy”). Accumulated randomness is restricted to a maximum value of ？, allowing for causal processes (e.g., emission and absorption). Each probabilistic event, before being observed, exists in two superposed states: presence and absence, and it possesses a simultaneous and distinct probabilistic duality. One of these values is derived from the density function at the final instant, while the other is accumulated and remains stationary at ？. Upon measurement, the two probability density functions collapse into presence or absence (1 or 0) (“particle modality”). Meanwhile, the two cumulative probability distribution functions remain entangled, each stabilizing at ？ (“wave modality”). The LPE unifies principles of classical and quantum physics through a probabilistic view of the universe. The probability of light detection in the universe is 3.33 × 10^-9 s/m, a universal parameter that suggests the existence of approximately 8.01 × 10²⁶ stars in the visible universe.