A Mathematical Conjecture on the Wavefunctions of Quantum Mechanics

Gregory Pierpoint

Quantum mechanics presents a reality that defies classical intuitions, with the universal wavefunction offering one of the most profound perspectives in modern physics. This paper delves into the mathematical structure of the universal wavefunction, its role in the Many-Worlds Interpretation, and the metaphysical implications for determinism, reality, and consciousness. By blending rigorous mathematical formalism with philosophical exploration, we investigate the conceptual and mathematical underpinnings of quantum reality and its relevance to the nature of existence. Recognizing the speculative nature of certain topics, we clearly distinguish established science from conjectural ideas. Additionally, we provide a critical analysis of various interpretations of quantum mechanics, compare their strengths and weaknesses, and discuss potential experimental tests and observable consequences of the universal wavefunction theory. This work also addresses challenges, such as the derivation of the Born rule and the interpretation of probability in the multiverse.

F. Selleri

Dirk John Pons, Arion Pons, Ariel M. Pons +1 more

Quantum mechanics (QM) has the problem of lacking a coherent conceptual foundation, even if its quantitative algorithms are functionally adequate. This paper appraises the conceptual logic beneath quantum mechanics, using as the point of reference a novel alternative conceptual framework called the cordus conjecture. If the cordus conjecture is correct then the comparison suggests that quantum mechanics is conceptually fallacious in several areas: (1) Particles need not be zero-dimensional points after all. (2) Bell�s theorem is refuted as being not universally applicable, and the principle of locality also fails. (3) The wavefunction is a mathematical approximation of a deeper reality, and superposition is not a physical state. (4) Superposition confounds positional and causal (temporal) variability, and this causes the weirdness of the QM interpretations. (5) Cordus identifies the factors that cause decoherence and (6) explains why quantum mechanics does not scale up to macroscopic objects. (7) It is fallacious to consider fields and particles as independent phenomena. Instead they are closely coupled in the cordus, and this explains the measurement context. Several core principles of QM are thereby refuted. The paradox of Schr�dinger�s Cat is explained as an artefact of these flawed premises. The paper also explains why the mathematical machinery of quantum mechanics is a reasonable approximation to reality, even if the concepts are not. The mathematics works, at least within a certain scale-range where: (a) things look like particles and the proposed cordus structure is not evident (i.e. not too small) and (b) where body-coherence is attainable (i.e. not too large). Outside of that range quantum mechanics seems neither conceptually nor mathematically relevant. The same analysis predicts QM is unlikely to scale down to the next deeper level of physics. The implications are that QM is profoundly deficient in its conceptual foundations, and is only an approximation of a deeper and more logically consistent mechanics.

Won-Young Hwang, Jeong‐Young Ji, Jongbae Hong

The concept of wavefunction reduction should be introduced to standard quantum mechanics in any physical processes where effective reduction of wavefunction occurs, as well as in the measurement processes. When the overlap is negligible, each particle obey Maxwell-Boltzmann statistics even if the particles are in principle described by totally symmetrized wavefunction [P.R.Holland, The Quantum Theory of Motion, Cambridge Unversity Press, 1993, p293]. We generalize the conjecture. That is, particles obey some generalized statistics that contains the quantum and classical statistics as special cases, where the degree of overlapping determines the statistics that particles should obey among continuous generalized statistics. We present an example consistent with the conjecture.

Weder, Ricardo, Pavel Exner