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Conservation Laws in the Many-Worlds Interpretation of Quantum Mechanics

Lev Vaidman A

Published Apr 15, 2026• 0 citations
Publisher

Abstract

Abstract Although the basic approach of the many-worlds interpretation is that the ontology of our universe is a unitarily evolving highly entangled wavefunction, we live in a world in which we only perceive a tiny part of the global wavefunction, and the quantum state corresponding to our world does not evolve unitarily, making our world an effectively open system. Recently, the common approach that within a world conservation laws hold only for an ensemble of measurements was questioned. This chapter analyses how this can affect viewing worlds as open systems and proposes a possible resolution of the unitarity puzzle.

DOI
10.1093/9780198929277.003.0016

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Abstract Although the basic approach of the many-worlds interpretation is that the ontology of our universe is a unitarily evolving highly entangled wavefunction, we live in a world in which we only perceive a tiny part of the global wavefunction, and the quantum state corresponding to our world does not evolve unitarily, making our world an effectively open system. Recently, the common approach that within a world conservation laws hold only for an ensemble of measurements was questioned. This chapter analyses how this can affect viewing worlds as open systems and proposes a possible resolution of the unitarity puzzle.
Ontological questions, concerning the nature of reality, continue to be argued in both the scientific and general literature, and new experiments may be proposed to move ontological questions into the instrumental category for resolution. This chapter contends that all interpretations of quantum mechanics are weird when considered from classical, everyday viewpoints. Readers holding classical world views should not expect to find intuitively-pleasing explanations of quantum mechanics; scientists much smarter than us have failed in this quest over the past century.
Hugh Everett thought it was preposterous to accept the Schrodinger equation as a fundamental law of quantum physics, but then assert that it is usually violated in any observation of quantum phenomena. Demanding that the Schrodinger equation always holds led him to the 'many worlds' interpretation. To avoid this conclusion, I propose that the Schrodinger equation is not fundamental, but that one should instead regard as primary a von Neumann version of the equation which lets the density matric evolve unitarily, but where conclusions reached concerning measurements always involve the non-unitary step of tracing out environmental degrees of freedom which always exist even if the system in question is the entire observable universe.
Abstract What does realism about the quantum state imply? What follows when quantum theory is applied without restriction, if need be, to the whole universe? These are the questions which are debated in this book. All the chapters start from the point of realism, and based on the need, or the aspiration, for a theory that unites micro- and macroworlds, at least in principle. But the further claim argued by some is that if you allow the Schrödinger equation unrestricted application, supposing the quantum state to be something physically real, then this universe is one of countlessly many others, constantly branching in time, all of which are real. The result is the many worlds theory, also known as the Everett interpretation of quantum mechanics. The contrary claim sees this picture of many worlds as in no sense inherent in quantum mechanics, even when the latter is allowed unrestricted scope and even given that the quantum state itself is something physically real. For this picture of branching worlds fails to make physical sense, let alone common sense, even on its own terms. The status of these worlds, what they are made of, is never adequately explained. Ordinary ideas about time and identity over time become hopelessly compromised. The concept of probability itself is brought into question. This picture of many branching worlds is inchoate, it is a vision, an error. There are realist alternatives to many worlds, some even that preserve the Schrödinger equation unchanged. Twenty chapters, accompanied by commentaries and discussions, examine these claims and counterclaims in depth. They focus first on the question of ontology, the existence of worlds, second on the interpretation of probability, and third on alternatives or additions to many worlds. The introduction offers a helpful guide to the arguments for the Everett interpretation, particularly as they have been formulated in the last two decades.
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.