Challenging Randomness and Probability in a Symmetric Universe Based on the Group nZ

Challenging Randomness and Probability in a Symmetric Universe Based on the Group (nZ,+) Benchekroun Mounssif Abstract This article proposes a radical questioning of the concept of randomness and probability, based on a fundamental hypothesis: the observable universe is the symmetric counterpart of a prior universe, according to a mathematical structure founded on the discrete group (nZ,+). In this vision, every event that seems uncertain or probabilistic today is in fact the deterministic manifestation of an event already accomplished in the symmetric universe before zero. This framework offers a new interpretation of quantum phenomena, particularly entanglement and measurement, without resorting to probabilistic approximation. 1 Introduction Modern physics relies heavily on probabilistic notions, especially in quantum mechanics, where probability is perceived as intrinsic. Here, we propose an alternative: the world we perceive does not contain real indeterminacy, since events are already determined, being reflections of a symmetric universe. 2 Mathematical Foundation: The Group (nZ,+) We consider the discrete Abelian group (nZ,+), which contains all integers that are multiples of a given integer n. Here, zero represents the tipping point, the boundary between two states of existence: 1 •Negative elements of nZrepresent past events of a prior universe (before 0). •Positive elements are the symmetric reflections of these events in the current universe. Thus, every event occurring in our world is seen as the projection or symmetric repetition of an event already realized. 3 Questioning Randomness Within this framework, randomness does not exist. The apparent ignorance of the observer is due not to fundamental indeterminacy, but to a lack of knowledge of the prior symmetric state. Probabilities are therefore statistical approximation tools, but do not reflect any ontological reality. 3.1 Application to Quantum Mechanics Consider a classic example: the measurement of a particle’s state in superposition. In the standard model, a probability is associated with each outcome. But in this framework: •The final measured state corresponds to an event already accomplished in the symmetric universe. •Entanglement is not an instantaneous transmission of information, but the simultaneous manifestation of a single symmetric event shared between two entities. Thus, the wave function and its collapse are no longer necessary. The role of the observer is simply to reveal an already realized state. 4 Probability as a Human Tool What we call probability is therefore a human tool, useful to deal with ignorance. But in a perfectly symmetric and deterministic world, probability loses any fundamental meaning. 2 5 Conclusion We propose a radically deterministic interpretation of the physical world, based on a symmetry around zero in a discrete group. This approach abolishes randomness and restores logical coherence to so-called random phenomena. It is not merely a philosophy, but a mathematizable framework that may be extended to other physical quantities. Perspectives A next step would be to extend this framework to phenomena such as decoherence, the arrow of time, or the wave-particle duality, and to investigate whether the known laws of physics can be recovered from this fundamental principle. 3