Abstract

This paper proposes a novel framework in which time is not a fundamental dimension but an emergent property arising from the probabilistic unfolding of events governed by a universal decay function. Each universe is characterized by its own decay function $D_{U}$ , which normalizes and hierarchically organizes event probabilities. Within this framework, phenomena such as free will, dreams, and movement are reinterpreted as manifestations of localized probability collapses. Moreover, we extend the model to address extraterrestrial contact: rather than traversing astronomical distances via conventional spacecraft, advanced entities might manipulate their probability distributions to appear on Earth without traditional travel. This perspective not only challenges conventional space–time paradigms but also provides testable predictions linking quantum mechanics, cognitive science, and cosmology.

1. Introduction

Traditional physics views time as a linear dimension and space as a continuous backdrop through which entities travel. However, recent developments in quantum theory and cosmology suggest that time might be an emergent phenomenon arising from the evolution of underlying probability distributions rather than existing as a primary construct. In this paper, we introduce a mathematical model based on a universal decay function $D_{U}$ that governs how event probabilities unfold and localize. This model offers fresh insights into phenomena such as free will, dreaming, and movement. Crucially, it provides a novel explanation for the possibility of extraterrestrial contact: if time and space are emergent, advanced civilizations may bypass conventional travel by “tuning” their probability profiles to manifest on Earth instantaneously.

2. The Decay Function as the Governing Principle

2.1 Mathematical Formulation

For a given universe $U$ , let ${p_{i}}_{i = 1}^{N}$ be the base probabilities associated with events $i$ . We define the decay function as:

D_{U} (p_{i}) = A_{U} \cdot p_{i}^{β_{U}} with N \sum i = 1 D_{U} (p_{i}) = 1,

where:

$A_{U}$ is a normalization constant ensuring that the probabilities sum to unity.
$β U (w i t h 0 < β U < 1)$ characterizes the decay rate, amplifying dominant probabilities while suppressing minor ones.

2.2 Hierarchical Probability Distribution

This formulation implies a hierarchical structure: events with higher base probabilities (for example, an 80% likelihood for a...

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