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arXiv:2301.04021

Need for "special" states in a deterministic theory of quantum mechanics

Lawrence S. Schulman

Published Jan 8, 2023• 0 citations
arXivHTMLPDF

Abstract

There are several theories or processes which may underlie quantum mechanics and make it deterministic. Some references are given in the main text. Any such theory, plus a number of reasonable assumptions, implies the existence of what I have called ``special" states. The assumptions are conservation laws, obedience (up to a point) of Schrodinger's equation, and a single world, in the sense of the many worlds interpretation (the last one a consequence of any deterministic theory). This article also, for clarity, gives an example of a ``special" state. There is an experimental test of the ``special" state theory.

DOI
10.48550/arxiv.2301.04021

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There are several theories or processes which may underlie quantum mechanics and make it deterministic. Some references are given in the main text. Any such theory, plus a number of reasonable assumptions, implies the existence of what I have called special" states. The assumptions are conservation laws, obedience (up to a point) of Schrodinger's equation, and a single world, in the sense of the many worlds interpretation (the last one a consequence of any deterministic theory). This article also, for clarity, gives an example of a special" state. There is an experimental test of the ``special" state theory.
An outline is given of the interpretation of quantum mechanical expressions if one assumes that what is called Quantum Mechanics today, refers to an underlying reality as in Chap. 2 , even if many authors claim to have evidence to the contrary, as is usually brought forward. If there exists a sub-microscopic classical world of real things, is that the same classical world as the world of large things such as planets, rocks and people? How does the notion of probability enter into quantum mechanics? These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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.
Why should special states occur as initial conditions in every physical situation in which they are needed? Half this book has been devoted to making the points that initial conditions may not be as controllable as they seem; that there may be constraints on microscopic initial conditions; that this would not have been noticed; that such constraints can arise from two-time or future conditioning; that in our universe such future conditioning may well be present, although, as remarked, cryptic . In this chapter I will take up more detailed questions: what future conditions could give rise to the need for our ‘special’ states, and why should those particular future conditions be imposed. Before going into this there is a point that needs to be made. Everything in the present chapter could be wrong and the thesis of Chapter 6 nevertheless correct. It is one thing to avoid grotesque states (and solve the quantum measurement problem) by means of special states and it is another provide a rationale for their occurrence. I say this not only to highlight the conceptual dependencies of the theses in this book, but also because there is a good deal of hand waving in the coming chapter and I don't want it to reflect unfavorably on the basic proposal. As pointed out earlier, the usual thermodynamic arrow of time can be phrased as follows: initial states are arbitrary, final states special.
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.