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A thought experiment in many worlds

Shan Gao

Published Feb 19, 2020• 0 citations
OpenAlex

Abstract

The many-worlds interpretation of quantum mechanics (MWI) is based on three key assumptions: (1) the completeness of the physical description by means of the wave function, (2) the linearity of the dynamics for the wave function, and (3) multiplicity. In this paper, I propose a new thought experiment in which a post-measurement superposition undergoes no net change while individual branches do change under certain unitary time evolution. Moreover, I argue that MWI gives contradictory predictions for this experiment. In order to avoid the contradiction and save many worlds, it seems that we must drop one or both of the first two assumptions.

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The many-worlds interpretation of quantum mechanics (MWI) is based on three key assumptions: (1) the completeness of the physical description by means of the wave function, (2) the linearity of the dynamics for the wave function, and (3) multiplicity. In this paper, I propose a new thought experiment in which a post-measurement superposition undergoes no net change while individual branches do change under certain unitary time evolution. Moreover, I argue that MWI gives contradictory predictions for this experiment. In order to avoid the contradiction and save many worlds, it seems that we must drop one or both of the first two assumptions.
A brief (subjective) description of the state of the art of the many-worlds interpretation of quantum mechanics (MWI) is presented. It is argued that the MWI is the only interpretation which removes action at a distance and randomness from quantum theory. Limitations of the MWI regarding questions of probability which can be legitimately asked are specified. The ontological picture of the MWI as a theory of the universal wave function decomposed into a superposition of world wave functions, the important parts of which are defined in three-dimensional space, is presented from the point of view of our particular branch. Some speculations about misconceptions, which apparently prevent the MWI from being in the consensus, are mentioned.
The articles provides a phenomenological reading of the Many-Worlds Interpretation (MWI) of quantum mechanics and its answer to the measurement problem, or the question of “why only one of a wave function’s probable values is observed when the system is measured.” Transcendental-phenomenological and hermeneutic-phenomenological approaches are employed. The project comprises four parts. Parts one and two review MWI and the standard (Copenhagen) interpretation of quantum mechanics. Part three reviews the phenomenologies. Part four deconstructs the hermeneutics of MWI. It agrees with the confidence the theory derives from its (1) unforgiving appropriation of the Schrödinger equation and (2) association of branching universes with the evolution of the wave function insofar as that understanding comes from the formalism itself. Part four also reveals the hermeneutical shortcomings of the standard interpretation.
Quantum nonlocality is shown to be an artifact of the Copenhagen interpretation, in which each observed quantity has exactly one value at any instant. In reality, all physical systems obey quantum mechanics, which obeys no such rule. Locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the many-worlds interpretation (MWI). Using the MWI, I show that the quantum side of Bell's inequality, generally believed nonlocal, is really due to a series of three measurements (not two as in the standard, oversimplified analysis), all three of which have only local effects. Thus, experiments confirming "nonlocality" are actually confirming the MWI. The mistaken interpretation of nonlocality experiments depends crucially on a question-begging version of the Born interpretation, which makes sense only in "collapse" versions of quantum theory, about the meaning of the modulus of the wave function, so I use the interpretation based on the MWI, namely that the wave function is a world density amplitude, not a probability amplitude. This view allows the Born interpretation to be derived directly from the Schrödinger equation, by applying the Schrödinger equation to both the observed and the observer.
Duality in quantum mechanical wave functions is manifest through the famous measurement problem. There have been several interpretations to explain this duality, but none have seen full consensus among physicists. The Copenhagen interpretation, which is at least to some extent the most widely accepted interpretation has the 'collapse' of the wave function (or state vector reduction) during measurement, does not attribute a physical reality to the wave function. Moreover, the idea of measurement having a role in defining reality shakes the very foundation of classical physics. On the other hand, the Many worlds interpretation proposed by Everett is a very brave attempt to attribute physical significance to the wave function. Though mathematically sound and elegant, 'the splitting of the universe' in the Many Worlds Interpretation completely redefines reality as we know it. We test Everett's original thought experiment in the presence of a super observer and for sequential measurements as well. We observe that the no-clone theorem helps the Many Worlds Interpretation, yet it does not provide a consistent picture for sequential measurements, unlike the Copenhagen Interpretation.
At present, there are two possible, and equally plausible, explanations for the physics of quantum measurement. The first explanation, known as the many-worlds interpretation, does not require any modification of quantum mechanics, and asserts that at the time of measurement the Universe splits into many branches, one branch for every possible alternative. The various branches do not interfere with each other because of decoherence, thus providing a picture broadly consistent with the observed Universe. The second explanation, which requires quantum mechanics to be modified from its presently known form, is that at the time of measurement the wave-function collapses into one of the possible alternatives. The two explanations are mutually exclusive, and up until now, no theoretical reasoning has been put forward to choose one explanation over the other. In this article, we provide an argument which implies that the collapse interpretation is favored over the many-worlds interpretation. Our starting point is the assertion (which we justify) that there ought to exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. The need for such a reformulation implies that quantum theory becomes non-linear on the Planck mass/energy scale. Standard linear quantum mechanics is an approximation to this non-linear theory, valid at energy scales much smaller than the Planck scale. Using ideas based on noncommutative | >=