What is Logic? My answer consists of three steps: Logic is about Language, Language is about the World. Panlogism is the attempt to "short circuit" this process by identifying the real object and the "concrete-in-thought." It leads to the assertion: Logic is about the World. If we abandon panlogism, we see that quantum logics (note the plural!) are just different ways of reformulating the same content. The danger: is that, If we accept the idea of one unique quantum logic, that provides all the answers, this prevents us from confronting the real questions about quantum mechanics.
What is Logic? My answer consists of three steps: Logic is about Language, Language is about the World. Panlogism is the attempt to "short circuit" this process by identifying the real object and the "concrete-in-thought." It leads to the assertion: Logic is about the World. If we abandon panlogism, we see that quantum logics (note the plural!) are just different ways of reformulating the same content. The danger: is that, If we accept the idea of one unique quantum logic, that provides all the answers, this prevents us from confronting the real questions about quantum mechanics.
Why should anyone think that what is so deeply puzzling about the quantum world is really a matter of logic? Why should anyone think that studying the logic of quantum mechanics should be a route to a proper understanding of quantum mechanics? There is a tradition in the philosophy of quantum mechanics, a tradition stronger among philosophical commentators than among physicists, which sees the subject as the business of understanding quantum mechanical language and the way that language relates to the world. It is an idea more strongly held by philosophers – it comes much more naturally to them – because the analytic tradition, in which most Anglo-American philosophers of science are raised, is generally much exercised about words and how they hook on to things. The analytic tradition in the philosophy of quantum mechanics is not unreasonable. Everyone admits that we cannot picture the microphysical world, that a graphic or iconic representation of quantum systems is impossible. Therefore understanding quantum mechanics must be a matter of understanding the logic of the words and the mathematics of quantum mechanics. If this seems implausible, it is because of an ambiguity in our use of the verb ‘to understand’. We understand the physical world, and we understand physics. But physics is not the physical world. It is something of an entirely different sort, a human product, a way of representing the world.
Are there quantum objects? What are they if they are neither given nor resemble anything familiar? To answer these questions we have to abstract from the substantive features of familiar things, delineate the pure logical forms by which we acknowledge objects and show how the forms are fulfilled in quantum theories. We have to explicate, in general terms and without resorting to the given, what we mean by objects. The clear criteria will enable us to affirm the objectivity of quantum theories. Auyang 1995, p. 5 Introduction Cantor, famously, defined a set as ‘… collections into a whole of definite, distinct objects of our intuition or of our thought’ (Cantor 1955, p. 85, our emphasis). On this basis the standard formulations of set theory, and consequently much of contemporary mathematics, are erected. Reflecting upon this definition, and the underlying ontological presuppositions, the question immediately arises, how are we to treat, mathematically, collections of objects which are not distinct individuals? This question becomes particularly acute in the quantum mechanical context, of course. As Yu. I. Manin noted at the 1974 American Mathematical Society Congress on the Hilbert Problems, We should consider possibilities of developing a totally new language to speak about infinity [that is, axioms for set theory]. Classical critics of Cantor (Brouwer et al. ) argue that, say, the general choice is an illicit extrapolation of the finite case.
What do we expect of a quantum logical interpretation of quantum mechanics worthy of the name? In what sense should it resolve the paradoxes? What scope should it have? Should quantum logic, if it is successful in the micro world, replace classical logic in the macro world and in mathematics? We distinguish between two kinds of quantum logical interpretations of quantum mechanics. An example of the first kind, the activist kind, will do much more than simply rewrite the assertions that quantum mechanics makes about the quantum world in an unfamiliar notation - in the elementary language of quantum mechanics. It will offer a solution to the major puzzles of quantum mechanics. It will show that the paradoxes of quantum mechanics can be resolved if we do away with classical logic and replace it with quantum logic, at least in our descriptions of quantum phenomena. It may defend a form of quantum-mechanical realism, a sort of quantum logical particle view of quantum systems, protecting it from the paradoxes that classical logic would impose on it. The second kind of quantum logical interpretation, the passive or quietist kind, is less ambitious. A quietist interpretation offers a solution to the paradoxes only in the following sense. It will assert that quantum mechanics, when it describes quantum phenomena in the elementary language, need not generate paradox, that the so-called paradoxes are not even formulable in quantum logic.
Quantum logic is the logic of the high-level language in which we describe what is true and false of quantum systems. I use the term ‘highlevel’ in its computational sense. The language whose logic quantum logic is, is inexpressive. It has no machinery for describing probabilities, only truths and falsehoods and perhaps whatever is in between. Quantum logic conceals from its user the underlying details of the formalism of quantum mechanics, and the details (whatever they may be) of the underlying ‘machine’, the physical world. Quantum logic encourages a top-down view of the quantum world. Quantum mechanics, as done by the practising physicist, is bottom-up. The program of feeding back quantum logic into our metalevel discussion of realism fails. Quantum logic does not licence quantummechanical realism. It cannot override or rewrite the bottom-up view. The program itself is odd in that quantum logic is most naturally thought of as expressing quantum-mechanical antirealism, just as quantum mechanics itself is most naturally interpreted antirealistically. Thus quantum logic is consonant with nonlocality, in the sense that it does not allow one to derive the Bell inequalities. The conditional in quantum logic nicely expresses the effect of ideal measurements on quantum systems.
Quantum-inspired metaheuristics are solvers that incorporate principles inspired from quantum mechanics into classical-approximate algorithms using non-quantum machines. Due to the uniqueness of quantum principles, the inspiration of quantum phenomena and the way it is done in fundamentally different non-quantum systems rather than real or simulated quantum computers raise important questions about these algorithms’ design and the reproducibility of their results in real or simulated quantum devices. Thus, this work’s contribution stands in a first step towards answering those questions as an attempt to identify key findings in the existing literature that should be considered or adapted in order to build hybrid or fully-quantum algorithms that can be used in quantum machines. This is done by proposing and studying four inspired, simulated and real quantum cellular genetic algorithms that, as far as the authors’ knowledge, are the first quantum structured metaheuristics studied in the three quantum realms using a quantum simulator with 32 quantum bits and a real quantum machine employing 15 superconducting quantum bits. The users’ mobility management in cellular networks is taken as a validation problem using 13 real-world instances. The comparisons have been made against 6 diverse algorithms using 9 comparison metrics. Thorough statistical tests and parameters’ sensitivity analysis have been also conducted. The experiments allowed answering several questions, including how quantum hardware influences the studied-algorithms’ search process. They also enabled opening new perspectives in quantum metaheuristics’ design.
In order to establish the object language of quantum physics, we begin with a quantum mechanical system S (atom, nucleus, elementary particle) and consider propositions A,B,… about this system S which can be proved or disproved by measuring processes. These propositions will be called elementary propositions. We will assume here that elementary propositions are value definite, i.e.,there always exists an experimental testing procedure which decides between truth and falsity of the respective proposition. The logical connectives A ∧ B (A and B), A ∨ B (A or B), A → B (A then B) and ┐ A (not A) will be defined by means of dialogs. A dialog is a formalized kind of discussion between two participants, the proponent P who asserts a certain proposition and the opponent 0 who attempts to refute it.