Construal of observable facts or events, that is, the manner in which we understand reality, is based not only on mathematical formulas of a theory suggested as a reasonable explanation for physical phenomena (like general relativity or quantum mechanics), but also on a mathematical model of reasoning used to analyze and appraise statements regarding the objective world (for example, logic of one type or the other). Hence, every time that a certain construal of reality encounters a problem, there is a choice between a modification to the mathematical formalism of the physical theory and a change in the model of reasoning. A case in point is negative construal of quantum superposition causing the problem of definite outcomes. To be sure, according to the said construal, it is not the case that a system being in a superposition of states is exclusively in one of the states constituting the superposition, which in turn implies that macroscopically differing outcomes of observation may appear all at once. The usual approach to the problem of definite outcomes is to modify the quantum mathematical formalism by adding to it some extra postulates (for instance, the postulate of wave function collapse). However, since none of the extra postulates proposed so far has gained broad acceptance, one may try another avenue to resolve the problem, namely, to replace logic with an alternative mathematical model of reasoning. This possibility is studied in the present paper.
Construal of observable facts or events, that is, the manner in which we understand reality, is based not only on mathematical formulas of a theory suggested as a reasonable explanation for physical phenomena (like general relativity or quantum mechanics), but also on a mathematical model of reasoning used to analyze and appraise statements regarding the objective world (for example, logic of one type or the other). Hence, every time that a certain construal of reality encounters a problem, there is a choice between a modification to the mathematical formalism of the physical theory and a change in the model of reasoning. A case in point is negative construal of quantum superposition causing the problem of definite outcomes. To be sure, according to the said construal, it is not the case that a system being in a superposition of states is exclusively in one of the states constituting the superposition, which in turn implies that macroscopically differing outcomes of observation may appear all at once. The usual approach to the problem of definite outcomes is to modify the quantum mathematical formalism by adding to it some extra postulates (for instance, the postulate of wave function collapse). However, since none of the extra postulates proposed so far has gained broad acceptance, one may try another avenue to resolve the problem, namely, to replace logic with an alternative mathematical model of reasoning. This possibility is studied in the present paper.
I take a pragmatist perspective on quantum theory. This is not a view of the world described by quantum theory. In this view quantum theory itself does not describe the physical world, nor our observatons, experiences or opinions of it. Instead, the theory offers reliable advice on when to expect an event of one kind or another, and on how strongly to expect each possible outcome of that event. The actual outcome is a perspectival fact: a fact relative to a physical context of assessment. Measurement outcomes and quantum states are both perspectival. By noticing that each must be relativized to an appropriate physical context one can resolve the measurement problem and the problem of nonlocal action. But if the outcome of a quantum measurement is not an absolute fact, then why shoud the statistics of such outcomes give us any objective reason to accept quantum theory? One can describe extensions of the scenario of Wigner's friend in which a statement expressing the outcome of a quantum measurement would be true relative to one such context but not relative to another. However, physical conditions in our world prevent us from realizing such scenarios. Since the outcome of every actual quantum measurement is certified at what is essentially a single context of assessment, the outcome relative to that context is an objective fact in the only sense that matters for science. We should accept quantum theory because the statistics these outcomes display are just those it leads us to expect.
The non-classical nature of quantum theory has led to a number of efforts to formalize the logic of statements whose universe of discourse is the subatomic (see, for example, [3], [6], [8], and [10]).It might be hoped that ideally the fruit of such efforts would be a formalism not totally divorced from the classical logic, but incorporating or incorporated in it in such a manner as to unify the logic of the micro-and the macro-worlds.Indeed, this has been the general direction taken by these efforts, including that which we principally examine and expand upon here.*Josef Jauch, [6], pp.67-89, developed a "propositional calculus of quantum mechanics".He objected to calling a system like his a "logic of quantum mechanics"; however, our use of 'logic' here is not, I think, the use to which Jauch objected.A logic, for our present purposes, is a mathematical formalism having a reasonable interpretation as a theory of deduction; its actual application as normative of argumentation in reality is a matter of empirical judgment.This seems close to the way Jauch wished to use "propositional calculus" but more general, allowing for extension to a quantification theory of quantum mechanics, for example.Although Jauch's presentation of a propositional calculus of quantum mechanics is mathematically interesting and suggestive, there are a number of problems connected with it.It is our purpose to engage some of these problems and to present a rigorously defined formalism intended to come close to doing the job intended by Jauch for his logic.The success or lack of success of this effort as related to actual application of this formalism in the foundations of quantum theory is, I think, a matter for the physicists to decide; the empirical judgment involved in this application is not in the scope of this paper.If a formalism is to have a reasonable interpretation as a theory of deduction, it seems clear that it must include a relation which, when it holds between two elements of the formalism, may be reasonably interpreted as expressing that one of the elements 'follows from' the other, in •The author wishes to thank Robert Piziak for advice and comments in the course of research for this paper.
Modern quantum mechanics, despite its flawless mathematical apparatus, has been in a deep ontological crisis for over a century. The traditional Copenhagen interpretation has introduced philosophical mysticism and absurd paradoxes into the description of the microworld, such as the famous mental experiments of "Schrödinger's cat." The orthodox claim that a particle exists simultaneously in multiple mutually exclusive states before measurement (quantum superposition) contradicts the most fundamental ontological law of existence. We have built this paper on a new, solid, realistic postulate, which at the same time represents an ontological axiom: Any object at a given moment in time exists only in one specific and definite physical state. Superposition is not an objective reality—it represents merely a mathematical tool for describing the system. Instead of splitting the universe into two, where the macro- and microworlds operate by different logics, we propose a unified causal model. The fundamental substance of the microworld is a continuous quantum field, the vibration of which before measurement manifests as a real physical wave. The act of measurement is not a "passive observation," but rather a harsh physical intervention. When a macroscopic instrument touches the wave structure of the field, an instantaneous non-linear reaction is born—a quantum spasm (a local phase transition), which instantly condenses the wave into a point-like particle. This article describes in detail the mechanism of this spasm and its connection with the structural deformation of the quantum field.
The concept of “objective reality” is addressed, and an ontological model is suggested, in which correlations of events in the configuration space of the wave function are considered invariant with respect to changes of observer. It is suggested that these statements make the best sense when considered from within a fifth-dimensional framework, extrapolated from the four dimensions of spacetime in a direct way. A pair of postulates is then suggested which strengthens two current models of quantum theory into a broader picture, giving a physical interpretation of Macroscopic Quantum Superposition (MQS) states. Relational Quantum Mechanics (RQM) from Rovelli and Consistent Histories (“CH”) from Griffiths are discussed and related to the postulates. By dropping the assumption that unobserved macroscopic events are “in a definite state” determined independently of an observer, a surprising but consistent theory of quantum macroscopic reality is arrived at (with fewer fundamental assumptions about everyday reality) that does not contradict experiment or everyday experience. As a result, a concept herein termed “retroactive event determination” is extended from a quantum principle (in CH) to a macroscopic principle. Macroscopic events that have not been observed by a particular observer are free to be retroactively determined. The feasibility of applying the physics of quantum operators to macro systems is analyzed using the concept of “macro projectors.” Various concerns with this model are addressed, such as solipsism and decoherence of the wave function for macro objects. A discussion is also made of the philosophical context of the ideas suggested. Some experimental ideas are offered.Keywords: Macroscopic quantum superposition—MQS—consistent histories—relational quantum mechanics—time—spacetime—retrocausation—framework—single-framework rule—macro pointers—synchronicity—meaningful coincidence—positivism—observer effect—measurement problem—delayed choice experiment—retroactive event determination—existential behavior—Many-Worlds model
THE PROBLEM IN A NUTSHELL CONCLUSION This poster points out an internal tension between quantum collapse and expressions which set eigenstates equal to superposition states in a different basis and thereby imply that pre-measurement and immediate post-measurement states are of the same kind. Its resolution appears to be either to discard the collapse postulate or to consider such states to be of distinct kinds with respect to their association with a superposition of properties. OVERVIEW Quantum collapse is a postulate in orthodox quantum mechanics, but it is poorly understood, though much has been written about it [1]. Here we point out that it also leads to a subtle internal tension in the theory when it is considered in conjunction with expressions that equate eigenstates with superposition states in a different basis because such expressions are consistent with a symmetry between states and observables under quantum superposition that is broken by quantum collapse. The tension can be relieved either by discarding the collapse postulate or by keeping it and considering pre-measurement and immediate post-measurement states to be of distinct kinds, in which case quantum collapse must be considered a transformation between two kinds of states. The basic strategy employed here is to convert a standard quantum mechanical relation into a logical equivalence, and then show that the imposition of the collapse postulate makes it possible to formulate an argument such that the truth value of the conclusion depends on which of the implications that are part of the equivalence is used, from which it is then possible to derive a contradiction.
Quantum mechanics have always shown great predictive successes, but also some weird aspects concerning the mathematics-reality correspondence, such as superposition of contradictory events, like a dead and alive cat. Although physicists claim that we have to live with these contradictions, a psycho-biological analysis could propose another explanation. Observation of extra-mental reality is based on direct physical contact between an object, its corresponding sense organ and its mental representation in the brain. In contrast, prediction of the future is no longer directly linked to extra-mental reality, but projects possible observations from the memory of the past into the future. Due to the uncertainty of the future, predictions require mental potentiality, meaning that it may or may not happen in extra-mental reality. Nevertheless, if past observations are regular as in classical physics, they allow predictions with high reliability, whereas if they are irregular as in quantum physics, they are limited to uncertainty and probability. Superposition in classical physics increases space or time units accordingly, whereas quantum superposition considers multiple space locations for the same object at the same time. Thus, the quantum mechanical formalism is in direct contradiction to the philosophical law of non-contradiction, which does not allow considering it as extra-mental reality. However, it has all characteristics of mental potentiality, which allows prediction of future outcomes with probability. The consideration of quantum mechanics as mental potentiality would solve the superposition problem, as well as the measurement and the non-locality problem. According to the regularity or irregularity of observation, classical or quantum mechanical formalism has to be applied for prediction of future dynamics. There is no collapse or continuation of superposition in the wave function, but simply the replacement of an uncertain prediction model by the more certain observation. With this interpretation some weird aspects could be completely eliminated.