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 | >=
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 | >=
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 wavefunction 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 nonlinear on the Planck mass/energy scale. Standard linear quantum mechanics is an approximation to this nonlinear theory, valid at energy scales much smaller than the Planck scale. Using ideas based on noncommutative differential geometry, we develop such a reformulation and derive a nonlinear Schrödinger equation, which can explain collapse of the wavefunction. We also obtain an expression for the lifetime of a quantum superposition. We suggest ideas for an experimental test of this model.
This thesis takes a look at the many-worlds interpretation (MWI) and discusses if it can become the leading interpretation of quantum mechanics. Firstly the Copenhagen interpretation is outlined and its issues relating to the measurement problem are discussed while taking recent insights in decoherence theory into account. Establishing that wave-function collapse still yields interpretational issues, I discuss the ideas of Hugh Everett, who proposed the many-worlds interpretation, and David Wallace who is a prominent advocate of the MWI. In particular I discuss and review Wallace's arguments in favor of viewing the wave-function and the many worlds realistically. The next part shortly focuses on the testability of the many-worlds interpretation and the philosophical and theoretical issues relating to probability in the MWI. I end by concluding that the no-collapse interpretations are preferable to the Copenhagen interpretation, and I argue in favor of a realistic view towards all of the worlds. Furthermore, I conclude that standard textbooks on quantum mechanics should be updated to introduce students to the insight that wave-function collapse isn't needed in forming a complete theory of quantum mechanics.
There are fundamental reasons why there should exist a reformulation of quantum mechanics which does not refer to a classical space–time manifold. It follows that quantum mechanics as we know it is a limiting case of a more general nonlinear quantum theory, with the nonlinearity becoming significant at the Planck mass/energy scale. This nonlinearity is responsible for a dynamically induced collapse of the wave function, during a quantum measurement, and it hence falsifies the many-worlds interpretation of quantum mechanics. We illustrate this conclusion using a mathematical model based on a generalized Doebner–Goldin equation. The non-Hermitian part of the Hamiltonian in this norm-preserving, nonlinear, Schrödinger equation dominates during a quantum measurement, and leads to a breakdown of linear superposition.
Standard quantum theory is highly successful in all its applications, from photons and atoms, to semiconductors, superconductors, quarks, and so on. Yet the need to understand what the theory is really trying to tell us about the nature of the world beyond specific predictions forces us into the realm of philosophy, or, as some have dubbed it, quantum metaphysics: the study of the interpretation of quantum mechanics. There is a wide range of opinions regarding the philosophical foundations of quantum mechanics. This chapter focuses on two of the most prominent interpretations: the Copenhagen interpretation, and one alternative interpretation that has been gaining some support in recent years, the many-worlds interpretation (MWI), also known as the many universes interpretation. The central issues of contention are: firstly, that the measurement of some attribute of a quantum system generally involves the probabilistic collapse, or reduction, of the state vector where the probabilistic nature of the process is inherent—that is, not reducible to a more fundamental, deterministic explanation; and, secondly, the problem of bringing a measurement to a completion—a problem generally known as the measurement paradox.
The interpretation of quantum mechanics has been disputed ever since the advent of the theory in the 1920’s. Famous are the discussions over long time between Einstein and Bohr. Einstein refused to accept the so‐called Copenhagen interpretation, where the wave function collapses at a measurement and where the outcome of the measurement is essentially accidental (“God does not play dice”). Alternative interpretations have appeared, but the Copenhagen school has dominated the thoughts throughout the decades. One interesting interpretation was formulated in 1957 by Hugh Everett at Princeton, a student of John Wheeler, which abandons the wave‐function collapse. In this model the universe is governed entirely by the Schrödinger equation, which does not allow for any collapse. In Everett’s model after a measurement the wave function is separated into different branches that do not interact. This model was left unnoticed for long time until Bryce DeWitt took it up in 1970 and termed it “Many‐Worlds Interpretation”, a term that in some sense is misleading. Everett’s model is incomplete, and it was later supplemented by the theory of decoherence, which explains how the different branches decouple as a result of the interaction with the environment. This extended model has in recent years gained increased respect, and some believe that it is the only model made available so far that is fully consistent with quantum mechanics. This interpretation can also shed some light on the development of the universe and, in particular, on the so‐called Anthropic principle, which puts human beings at the center of the development.
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.