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arXiv:1908.02352

On Non-Linear Quantum Mechanics and the Measurement Problem IV. Experimental Tests

W. David Wick

Published Aug 6, 2019• 0 citations
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Abstract

I discuss three proposed experiments that could in principle locate the boundary between the classical and quantum worlds, as well as distinguish the Hamiltonian theory presented in the first paper of this series from the spontaneous-collapse theories.
DOI
10.48550/arxiv.1908.02352

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The measurement problem and the apparent collapse of the wavefunction remain the last major unresolved issues in quantum mechanics. This paper demonstrates that both phenomena emerge rigorously from the single mother equation of the Al-Ani Fabric Theory: ∂δ/∂t = D∇²δ - Γδ + (g/2)δ² + S with only two fundamental parameters Γ = 2.4×10⁻¹⁸ s⁻¹ and λ = 200 kpc (hence D = Γλ²). The deformation field δ evolves continuously and deterministically. The apparent collapse is the rapid non-linear damping of non-classical components due to the Γδ and (g/2)δ² terms when a macroscopic apparatus interacts with the system. The Born rule arises naturally as the steady-state probability distribution of the stable nodes of δ, derived from the principle of maximum entropy. The theory distinguishes clearly between decoherence (linear decay of off-diagonal elements) and collapse (non-linear selection of a single outcome). This closes the measurement problem completely from first principles using only the two fundamental parameters of the theory. No additional postulates (consciousness, many worlds, hidden variables) are required.
A particle is described as a non-spreading wave packet satisfying a linear equation within the framework of special relativity. Young's and other interference experiments are explained with a hypothesis that there is a coupling interaction between the peaked and non-peaked pieces of the wave packet. This explanation of the interference experiments provides a realistic interpretation of quantum mechanics. The interpretation implies that there is physical reality of particles and no wave function collapse. It also implies that neither classical mechanics nor current quantum mechanics is a complete theory for describing physical reality and the Bell inequalities are not the proper touchstones for reality and locality. The problems of the boundary between the macro-world and micro-world and the de-coherence in the transition region (meso-world) between the two are discussed. The present interpretation of quantum mechanics is consistent with the physical aspects of the Copenhagen interpretation, such as, the superposition principle, Heisenberg's uncertainty principle and Born's probability interpretation, but does not favor its philosophical aspects, such as, non-reality, non-objectivity, non-causality and the complementary principle.
After a summary of Bohr's views and their relation to Kant's theory of science, two fruitless lines of attack on the measurement problem are discussed: the way of the psi-ontologist and the way of the QBist. In the remainder of the paper the following results are obtained. (i) Because the testable correlations between outcomes of measurements of macroscopic positions are consistent with both the classical and the quantum laws, there is no conflict between the superposition principle and the existence of measurement outcomes. (ii) Intrinsically, each fundamental particle is numerically identical with every other fundamental particle. What presents itself here and now with these properties and what presents itself there and then with those properties is one and the same entity, herein called "Being." (iii) The distinction between a classical domain and a quantum domain is essentially a distinction between the manifested world and its manifestation. By entering into reflexive spatial relations, Being gives rise to (a) what looks like a multiplicity of relata if the reflexive quality of the relations is ignored, and (b) what looks like a substantial expanse if the spatial quality of the relations is reified. (iv) The reason why quantum mechanics is a calculus of correlations between measurement outcomes is that it concerns the progressive realization of distinguishable objects and distinguishable regions of space. (v) The key to the relation between quantum mechanics and experience is that Being does not simply manifest the world, Being manifests the world to itself. It is at once the single substance by which the world exists and the ultimate self or subject for which it exists. The question how we are related to this ultimate self or subject is discussed.