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arXiv:2105.10431

Many-Worlds Quantum Mechanics is Neither Mathematically Nor Experimentally Equivalent to Standard Quantum Mechanics

Frank J. Tipler

Published May 21, 2021• 1 citation
arXivHTMLPDF

Abstract

Many-Worlds quantum mechanics differs from standard quantum mechanics in that in Many-Worlds, the wave function is a relative density of universes in the multiverse amplitude rather than a probability amplitude. This means that in Many-Worlds, the Born frequencies are approached rather than given a priori. Thus in Many-Worlds the rate of approach to the final frequencies can be calculated and compared with observation. I use Many-Worlds to derive the rate of approach in the double slit experiment, and show that it agrees with observation. Standard quantum theory has never been used to derive an approach formula because it cannot be so used, as has been tacitly acknowledged for 70 years.

DOI
10.48550/arxiv.2105.10431

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Many-Worlds quantum mechanics differs from standard quantum mechanics in that in Many-Worlds, the wave function is a relative density of universes in the multiverse amplitude rather than a probability amplitude. This means that in Many-Worlds, the Born frequencies are approached rather than given a priori. Thus in Many-Worlds the rate of approach to the final frequencies can be calculated and compared with observation. I use Many-Worlds to derive the rate of approach in the double slit experiment, and show that it agrees with observation. Standard quantum theory has never been used to derive an approach formula because it cannot be so used, as has been tacitly acknowledged for 70 years.
Quantum chemists have recorded a huge number of data points which standard quantum mechanics cannot interpret. Many-Worlds quantum mechanics can. Many-Worlds quantum mechanics differs from standard quantum mechanics because in Many-Worlds, the wave function is a relative density of universes in the multiverse amplitude rather than a probability amplitude. In Many-Worlds, the Born frequencies are approached rather than given a priori. Thus in Many-Worlds, the rate of approach to the final frequencies can be calculated and compared with observation. This is a new type of reaction rate. I show how to use Many-Worlds to analyze the breakup of Br2{\rm Br}_2Br2​. Such analysis will experimentally test Many-Worlds fermionic and time-dependent quantum mechanics. Conversely, experimental quantum chemistry has become too sophisticated to be analyzed by standard quantum mechanics. Only Many-Worlds can do the job
The Born Interpretation of the wave function gives only the relative frequencies as the number of observations approaches infinity. Using the Many-Worlds Interpretation of quantum mechanics, specifically the fact that there must exist other versions of ourselves in the multiverse, I show that the observed frequencies should approach the Born frequencies as 1/N, where N is the number of observations. In the body of the paper I state this convergence rate precisely as AN EASILY TESTABLE FORMULA. We can therefore test the central claim of the MWI by measuring the convergence rate to the final Born frequency. Conversely, the MWI allows us to calculate this convergence rate.
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I show that the classical Hamilton-Jacobi (H-J) equation can be used as a technique to study quantum mechanical problems. I first show that the the Schrödinger equation is just the classical H-J equation, constrained by a condition that forces the solutions of the H-J equation to be everywhere C2C^2C2. That is, quantum mechanics is just classical mechanics constrained to ensure that ``God does not play dice with the universe.'' I show that this condition, which imposes global determinism, strongly suggests that ψ∗ψψ^*ψψ∗ψ measures the density of universes in a multiverse. I show that this interpretation implies the Born Interpretation, and that the function space for ψψψ is larger than a Hilbert space, with plane waves automatically included. Finally, I use H-J theory to derive the momentum-position uncertainty relation, thus proving that in quantum mechanics, uncertainty arises from the interference of the other universes of the multiverse, not from some intrinsic indeterminism in nature.
The hidden variable theories are, more cumbersome and artificial—while the Copenhagen interpretation is hopelessly incomplete because of its a priori reliance on classical physics, as well as a philosophic monstrosity with a “reality” concept for the macroscopic world and denial of the same for microcosm. In recent work on the Everett (Many-Worlds) interpretation of quantum mechanics, it has increasingly been recognized that any version of the interpretation worth defending will be one in which the basic formalism of quantum mechanics is left unchanged. Properties such as the interpretation of wave-function as describing a multiverse of branching worlds, or the ascription of probabilities to the branching events, must be emergent from the unitary quantum mechanics rather than added explicitly to the mathematics. Deutsch’s strategy was to introduce a few assumptions from decision theory into the Everett interpretation and then to show how they work with quantum theory to create a natural value measure that is the same as the expectation value.
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.