With the emergence of quantum technologies such as quantum computing, quantum communications, and quantum sensing, new potential has emerged for smart manufacturing and Industry 4.0. These technologies, however, present ethical concerns that must be addressed in order to ensure they are developed and used responsibly. This article outlines some of the ethical challenges that quantum technologies may raise for Industry 4.0 and presents the value sensitive design methodology as a strategy for ethics-by-design of (...) class='Hi'>quantum computing in Industry 4.0. This research further investigates the potential ethical difficulties that may come from the use of quantum technologies in Industry 4.0, such as concerns about privacy, security, accountability, and the influence of these technologies on workers and society as a whole. The article argues, based on current literature, that these issues necessitate a proactive and comprehensive approach to ethics-by-design. (shrink)

Describes my book from the first bias creating belief in male superiority, to developing language with a massive number of names embedding male bias to guarantee patriarchy's survival, creating belief supplanting knowledge. Suggests changing language with evidence-based, neutral, inclusive and specific names reducing, and perhaps, eliminating male dominance.

Capacity of conscious agents to perform genuine choices among future alternatives is a prerequisite for moral responsibility. Determinism that pervades classical physics, however, forbids free will, undermines the foundations of ethics, and precludes meaningful quantification of personal biases. To resolve that impasse, we utilize the characteristic indeterminism of quantum physics and derive a quantitative measure for the amount of free will manifested by the brain cortical network. The interaction between the central nervous system and the surrounding environment is shown (...) to perform a quantum measurement upon the neural constituents, which actualize a single measurement outcome selected from the resulting quantum probability distribution. Inherent biases in the quantum propensities for alternative physical outcomes provide varying amounts of free will, which can be quantified with the expected information gain from learning the actual course of action chosen by the nervous system. For example, neuronal electric spikes evoke deterministic synaptic vesicle release in the synapses of sensory or somatomotor pathways, with no free will manifested. In cortical synapses, however, vesicle release is triggered indeterministically with probability of 0.35 per spike. This grants the brain cortex, with its over 100 trillion synapses, an amount of free will exceeding 96 terabytes per second. Although reliable deterministic transmission of sensory or somatomotor information ensures robust adaptation of animals to their physical environment, unpredictability of behavioral responses initiated by decisions made by the brain cortex is evolutionary advantageous for avoiding predators. Thus, free will may have a survival value and could be optimized through natural selection. (shrink)

This paper focuses on stakeholder identification as per the value sensitive design (VSD) approach applied to the context of quantum technologies (QT). We provide two comprehensive lists of stakeholders as starting points for VSD researchers and practitioners. These lists encompass a diverse range of organizations, including private companies, government agencies, NGOs, partnerships, and professional/trade organizations. Our aim is to facilitate the recognition, legitimation, and understanding of stakeholder interactions in the development of QT. These stakeholder lists can serve as (...) a foundation for designing and implementing policies and strategies that promote the ethical and responsible development of QT, considering the values and interests of various stakeholders. Furthermore, these lists can enable empirical and technical studies on specific QT innovations using an ethics-by-design approach like VSD. Overall, this paper contributes to a better understanding of the complex and dynamic nature of the QT landscape and highlights the importance of stakeholder engagement and collaboration in shaping its future. (shrink)

This paper shows how the classical finite probability theory (with equiprobable outcomes) can be reinterpreted and recast as the quantum probability calculus of a pedagogical or toy model of quantum mechanics over sets (QM/sets). There have been several previous attempts to develop a quantum-like model with the base field of ℂ replaced by ℤ₂. Since there are no inner products on vector spaces over finite fields, the problem is to define the Dirac brackets and the probability calculus. (...) The previous attempts all required the brackets to take values in ℤ₂. But the usual QM brackets <ψ|ϕ> give the "overlap" between states ψ and ϕ, so for subsets S,T⊆U, the natural definition is <S|T>=|S∩T| (taking values in the natural numbers). This allows QM/sets to be developed with a full probability calculus that turns out to be a non-commutative extension of classical Laplace-Boole finite probability theory. The pedagogical model is illustrated by giving simple treatments of the indeterminacy principle, the double-slit experiment, Bell's Theorem, and identical particles in QM/Sets. A more technical appendix explains the mathematics behind carrying some vector space structures between QM over ℂ and QM/Sets over ℤ₂. (shrink)

Practical quantum computing devices and their applications to AI in particular are presently mostly speculative. Nevertheless, questions about whether this future technology, if achieved, presents any special ethical issues are beginning to take shape. As with any novel technology, one can be reasonably confident that the challenges presented by "quantum AI" will be a mixture of something new and something old. Other commentators (Sevilla & Moreno 2019), have emphasized continuity, arguing that quantum computing does not substantially affect (...) approaches to value alignment methods for AI, although they allow that further questions arise concerning governance and verification of quantum AI applications. In this brief paper, we turn our attention to the problem of identifying as-yet-unknown discontinuities that might result from quantum AI applications. Wise development, introduction, and use of any new technology depends on successfully anticipating new modes of failure for that technology. This requires rigorous efforts to break systems in protected sandboxes, and it must be conducted at all stages of technology design, development, and deployment. Such testing must also be informed by technical expertise but cannot be left solely to experts in the technology because of the history of failures to predict how non-experts will use or adapt to new technologies. This interplay between experts and non-experts may be particularly acute for quantum AI because quantum mechanics is notoriously difficult to understand. (As Richard Feynman quipped, "Anyone who claims to understand quantum mechanics is either lying or crazy.") We will discuss the extent to which the difficulties in understanding the physics underlying quantum computing challenges attempts to anticipate new failure modes that might be introduced in AI applications intended for unsupervised operation in the public sphere. (shrink)

The idea of self-measurement by a quantum-mechanical automaton is presented, and the conclusions that are typically reached about what we can come to know from doing self-measurements are shown to be mistaken. Specifically, it is shown that, while we are capable of _predicting_ and _measuring_ the values of two incompatible observables, we are incapable of _knowing_ both these values simultaneously. This is an example of the interesting limitations quantum mechanics places on knowledge.

ABSTRACT Topos quantum theory is standardly portrayed as a kind of ‘neo-realist’ reformulation of quantum mechanics.1 1 In this article, I study the extent to which TQT can really be characterized as a realist formulation of the theory, and examine the question of whether the kind of realism that is provided by TQT satisfies the philosophical motivations that are usually associated with the search for a realist reformulation of quantum theory. Specifically, I show that the notion of (...) the quantum state is problematic for those who view TQT as a realist reformulation of quantum theory. 1Introduction 2Topos Quantum Theory 2.1Phase space 2.2Hilbert space 2.3Beyond Hilbert space 2.4Defining realism 2.5The spectral presheaf 2.6The logic of topos quantum theory 3Interpreting States in Topos Quantum Theory 4Interpreting Truth Values and Clopen Subobjects in Topos Quantum Theory 4.1Interpreting the truth values 4.2Interpreting Subcl 5Neo-realism 5.1The covariant approach 6Conclusion. (shrink)

In this contribution I will retrace the main stages of my research on the objectification problem in quantum mechanics by highlighting some personal memories of my supervisor, the theoretical physicist Giovanni Morchio. The central aim of my MSc thesis was to ask whether the hypothesis of objectification, which is currently added to the formalism, is not, at least in one case, deducible from it and in particular from the dynamics of the temporal evolution. The case study we were looking (...) for had to: 1) represent a situation similar to that in which a macroscopic system such as a measurement apparatus, following interaction with a system, assumes a well-defined state (which or for example represents the fact that the result of a measurement is a particular value), i.e becomes objective 2) represent a fact in nature in which it is not clear whether its explanation can be derived from the formalism of quantum mechanics or whether a hypothesis of objectification is necessary for its explanation. Proving that such a fact can be deduced from the time evolution of quantum mechanics allowed us to conclude that there are cases in which the hypothesis of objectification is superfluous or, in other words, obtainable from the formalism. (shrink)

To become more useful and efficient in sustaining the Earth's health, economics must undergo a paradigm shift in its thinking. From a humanistic perspective, humans should be the center of everything. However, from the standpoint of physics and the universe, this is not the case. As a species, having a planet among the millions in the universe where humans can survive and thrive is already a great fortune. Through this book, we also try to answer one of our long-standing questions: (...) why has economics learned so little from physics, the oldest and most rigorous academic discipline that studies nature? -/- Learning from the quantum and information theories, we also provide a new definition of value, which is expected to help economists relax assumptions and loosen established economic principles in order to change and evolve. The new definition is also expected to enable social scientists to address newly arising phenomena or events that are not accounted for by existing value systems, such as environmental crises, artificial intelligence (AI), and interdisciplinary information, more proactively and productively. (shrink)

As quantum technologies (QT) advance, their potential impact on and relation with society has been developing into an important issue for exploration. In this paper, we investigate the topic of democratization in the context of QT, particularly quantum computing. The paper contains three main sections. First, we briefly introduce different theories of democracy (participatory, representative, and deliberative) and how the concept of democratization can be formulated with respect to whether democracy is taken as an intrinsic or instrumental (...) class='Hi'>value. Second, we give an overview of how the concept of democratization is used in the QT field. Democratization is mainly adopted by companies working on quantum computing and used in a very narrow understanding of the concept. Third, we explore various narratives and counter-narratives concerning democratization in QT. Finally, we explore the general efforts of democratization in QT such as different forms of access, formation of grassroot communities and special interest groups, the emerging culture of manifesto writing, and how these can be located within the different theories of democracy. In conclusion, we argue that although the ongoing efforts in the democratization of QT are necessary steps towards the democratization of this set of emerging technologies, they should not be accepted as sufficient to argue that QT is a democratized field. We argue that more reflexivity and responsiveness regarding the narratives and actions adopted by the actors in the QT field and making the underlying assumptions of ongoing efforts on democratization of QT explicit, can result in a better technology for society. (shrink)

Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of (...) time is what generates choices by itself, thus quantum information and any item in the world in final analysis. The course of time generates necessarily choices so: The future is absolutely unorderable in principle while the past is always well-ordered and thus unchangeable. The present as the mediation between them needs the well-ordered theorem equivalent to the axiom of choice. The latter guarantees the choice even among the elements of an infinite set, which is the case of quantum information. The concrete and abstract objects share information as their common base, which is quantum as to the formers and classical as to the latter. The general quantities of matter in physics, mass and energy can be considered as particular cases of quantum information. The link between choice and abstraction in set theory allows of “Hume’s principle” to be interpreted in terms of quantum mechanics as equivalence of “many” and “much” underlying quantum information. Quantum information as the universal substance of the world calls for the unity of physics and mathematics rather than that of the concrete and abstract objects and thus for a form of quantum neo-Pythagoreanism in final analysis. (shrink)

We study the conservation of energy, or lack thereof, when measurements are performed in quantum mechanics. The expectation value of the Hamiltonian of a system changes when wave functions collapse in accordance with the standard textbook treatment of quantum measurement, but one might imagine that the change in energy is compensated by the measuring apparatus or environment. We show that this is not true; the change in the energy of a state after measurement can be arbitrarily large, (...) independent of the physical measurement process. In Everettian quantum theory, while the expectation value of the Hamiltonian is conserved for the wave function of the universe, it is not constant within individual worlds. It should therefore be possible to experimentally measure violations of conservation of energy, and we suggest an experimental protocol for doing so. (shrink)

A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions about objects in a multiplicity of worlds. In this logical framework, the continuum of worlds is treated in analogy to the continuum of time points; both “time” and “world” are considered as mutually independent modes of existence. The theory combines elements of Bohmian mechanics and (...) of Everett’s many-worlds interpretation; it has a clear ontology and a set of precisely defined postulates from where the predictions of standard quantum mechanics can be derived. Probability as given by the Born rule emerges as a consequence of insufficient knowledge of observers about which world it is that they live in. The theory describes a continuum of worlds rather than a single world or a discrete set of worlds, so it is similar in spirit to many-worlds interpretations based on Everett’s approach, without being actually reducible to these. In particular, there is no splitting of worlds, which is a typical feature of Everett-type theories. Altogether, the theory explains (1) the subjective occurrence of probabilities, (2) their quantitative value as given by the Born rule, and (3) the apparently random “collapse of the wavefunction” caused by the measurement, while still being an objectively deterministic theory. (shrink)

Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of (...) time is what generates choices by itself, thus quantum information and any item in the world in final analysis. The course of time generates necessarily choices so: The future is absolutely unorderable in principle while the past is always well-ordered and thus unchangeable. The present as the mediation between them needs the well-ordered theorem equivalent to the axiom of choice. The latter guarantees the choice even among the elements of an infinite set, which is the case of quantum information. The concrete and abstract objects share information as their common base, which is quantum as to the formers and classical as to the latters. The general quantities of matter in physics, mass and energy can be considered as particular cases of quantum information. The link between choice and abstraction in set theory allows of “Hume’s principle” to be interpreted in terms of quantum mechanics as equivalence of “many” and “much” underlying quantum information. Quantum information as the universal substance of the world calls for the unity of physics and mathematics rather than that of the concrete and abstract objects and thus for a form of quantum neo-Pythagoreanism in final analysis. (shrink)

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent’s degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the (...) general claim that probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent’s prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent’s prior beliefs. Quantum certainty is therefore always some agent’s certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system. (shrink)

The paper interprets the concept “operator in the separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined in the “classical” quantum mechanics) by that of “quantum information”. As far as wave function is the characteristic function of the probability (density) distribution for all possible values of a certain quantity to be measured, the definition of quantity in quantum mechanics means any unitary change of the probability (density) distribution. It can be represented as a particular case (...) of “unitary” qubits. The converse interpretation of any qubits as referring to a certain physical quantity implies its generalization to non-Hermitian operators, thus neither unitary, nor conserving energy. Their physical sense, speaking loosely, consists in exchanging temporal moments therefore being implemented out of the space-time “screen”. “Dark matter” and “dark energy” can be explained by the same generalization of “quantity” to non-Hermitian operators only secondarily projected on the pseudo-Riemannian space-time “screen” of general relativity according to Einstein's “Mach’s principle” and his field equation. (shrink)

Relational Quantum Mechanics is an interpretation of quantum mechanics proposed by Carlo Rovelli. Rovelli argues that, in the same spirit as Einstein’s theory of relativity, physical quantities can only have definite values relative to an observer. Relational Quantum Mechanics is hereby able to offer a principled explanation of the problem of nested measurement, also known as Wigner’s friend. Since quantum states are taken to be relative states that depend on both the system and the observer, there (...) is no inconsistency in the descriptions of the observers. Federico Laudisa has recently argued, however, that Rovelli’s description of Wigner’s friend is ambiguous, because it does not take into account the correlation between the observer and the quantum system. He argues that if this correlation is taken into account, the problem with Wigner’s friend disappears and, therefore, a relativization of quantum states is not necessary. I will show that Laudisa’s criticism is not justified. To the extent that the correlation can be accurately reflected, the problem of Wigner’s friend remains. An interpretation of quantum mechanics that provides a solution to it, like Relational Quantum Mechanics, is therefore a welcome one. (shrink)

The concept of quantum information is introduced as both normed superposition of two orthogonal sub-spaces of the separable complex Hilbert space and in-variance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen. The separable complex Hilbert space is considered as the free variable of quantum information and any point in it (a wave (...) function describing a state of a quantum system) as its value as the bound variable. A qubit is equivalent to the generalization of ‘bit’ from the set of two equally probable alternatives to an infinite set of alternatives. Then, that Hilbert space is considered as a generalization of Peano arithmetic where any unit is substituted by a qubit and thus the set of natural number is mappable within any qubit as the complex internal structure of the unit or a different state of it. Thus, any mathematical structure being reducible to set theory is re-presentable as a set of wave functions and a subspace of the separable complex Hilbert space, and it can be identified as the category of all categories for any functor represents an operator transforming a set (or subspace) of the separable complex Hilbert space into another. Thus, category theory is isomorphic to the Hilbert-space representation of set theory & Peano arithmetic as above. Given any value of quantum information, i.e. a point in the separable complex Hilbert space, it always admits two equally acceptable interpretations: the one is physical, the other is mathematical. The former is a wave function as the exhausted description of a certain state of a certain quantum system. The latter chooses a certain mathematical structure among a certain category. Thus there is no way to be distinguished a mathematical structure from a physical state for both are described exhaustedly as a value of quantum information. This statement in turn can be utilized to be defined quantum information by the identity of any mathematical structure to a physical state, and also vice versa. Further, that definition is equivalent to both standard definition as the normed superposition and in-variance of Hamilton and Lagrange interpretation of mechanical motion introduced in the beginning of the paper. Then, the concept of information symmetry can be involved as the symmetry between three elements or two pairs of elements: Lagrange representation and each counterpart of the pair of Hamilton representation. The sense and meaning of information symmetry may be visualized by a single (quantum) bit and its interpretation as both (privileged) reference frame and the symmetries of the Standard model. (shrink)

A recent study suggests that value and quantum states seem to be governed by the same underlying mechanisms. In our recent book titled "Better economics for the Earth: A lesson from quantum and information theories," specifically Chapter 5, we have proposed an informational entropy-based notion of value, drawing on the granular worldview and primary features of quantum mechanics, Shannon’s information theory, and the mindsponge theory. Specifically, the notion suggests that values are created through the interactions (...) of information. But how do information and its interactions lead to values? This research note aims to contribute to the answer to this question. (shrink)

A familiar interpretation of quantum mechanics (one of a number of views sometimes labeled the "Copenhagen interpretation'"), takes its empirical apparatus at face value, holding that the quantum wave function evolves by the Schrödinger equation except on certain occasions of measurement, when it collapses into a new state according to the Born rule. This interpretation is widely rejected, primarily because it faces the measurement problem: "measurement" is too imprecise for use in a fundamental physical theory. We argue (...) that this is a weak objection, as there may be many ways of making "measurement" precise. However, measurement-collapse interpretations face a more serious objection: a dilemma tied to the quantum Zeno effect. Is measurement itself an observable that can enter superpositions? If yes, then the standard measurement-collapse dynamics is ill-defined. If no, then (at least if measurement is an observable), measurements can never start or finish. The best way out is to deny that measurement is an observable, but this leads to strong and revisionary consequences. This reinforces the view that there is no nonrevisionary interpretation of quantum mechanics. (shrink)

The cosmos may well be perceived as chiefly power respecting its unfathomable vastness and amount of energy, and under this form referred to the cyclic model and to its self-referentiality. The levels of power to therein inhere are accordingly meant to be subject to a drastic variation. These can be quantified according to physical-metaphysical criteria propounded as Quanta of Power. Their imperceptible value is deemed to define the amount of actual ontological power to be found in each relevant event, (...) nature or situation: The more the presence of Quanta of Power, the more the capability of power found intrinsic to such an event, nature or situation. While at a nonhuman level they focalize on the Big Bang and the Big Crunch in causing one another (and in thus proving, conceptually, one cosmic entity), touching the anthropic principle the process at issue reaches its crowning moment in an ultimate superhuman frame. (shrink)

We review some results in the theory of non-relativistic quantum unstable systems. We account for the most important definitions of quantum resonances that we identify with unstable quantum systems. Then, we recall the properties and construction of Gamow states as vectors in some extensions of Hilbert spaces, called Rigged Hilbert Spaces. Gamow states account for the purely exponential decaying part of a resonance; the experimental exponential decay for long periods of time physically characterizes a resonance. We briefly (...) discuss one of the most usual models for resonances: the Friedrichs model. Using an algebraic formalism for states and observables, we show that Gamow states cannot be pure states or mixtures from a standard view point. We discuss some additional properties of Gamow states, such as the possibility of obtaining mean values of certain observables on Gamow states. A modification of the time evolution law for the linear space spanned by Gamow shows that some non-commuting observables on this space become commuting for large values of time. We apply Gamow states for a possible explanation of the Loschmidt echo. (shrink)

The basic idea of quantum mechanics is that the property of any system can be in a state of superposition of various possibilities. This state of superposition is also known as wave function and it evolves linearly with time in a deterministic way in accordance with the Schrodinger equation. However, when a measurement is carried out on the system to determine the value of that property, the system instantaneously transforms to one of the eigen states and thus we (...) get only a single value as outcome of the measurement. Quantum measurement problem seeks to find the cause and exact mechanism governing this transformation. In an attempt to solve the above problem, in this paper, we will first define what the wave function represents in real world and will identify the root cause behind the stochastic nature of events. Then, we will develop a model to explain the mechanism of collapse of the quantum mechanical wave function in response to a measurement. In the process of development of model, we will explain Schrodinger cat paradox and will show how Born’s rule for probability becomes a natural consequence of measurement process. (shrink)

In the Critique of Pure Reason Kant argues that the empirical knowledge of the world depends on a priori conditions of human sensibility and understanding, i. e., our capacities of sense experience and concept formation. The objective knowledge presupposes, on one hand, space and time as a priori conditions of sensibility and, on another hand, a priori judgments, like the principle of causality, as constitutive conditions of understanding. The problem is that in the XX century the physical science completely changed (...) how we conceive our knowledge of the world. Face to this new situation, what was changed in our classical reason? However, if the transcendental point of view is adopted, in the specific case of quantum mechanics, we have to wonder about the general conditions of this theory that make possible such knowledge, which predictive value is much more accurate than the classical physics. The aim of this work is firstly to show the Kantian implications on Bohr’s interpretation of quantum phenomena and secondly to provide an overview of the key elements for understanding the transcendental locus of ordinary language in the quantum mechanics context, in order to give support to a transcendental pragmatic position in the analysis of science. (shrink)

It is not so long ago that philosophers and scientists thought of science as an objective and value-free enterprise. But since the heyday of positivism, it has become obvious that values, norms, and standards have an indispensable role to play in science. You may even say that these values are the real issues of the philosophy of science. Whatever they are, these values constrain science at an ontological, a cognitive, a methodological, and a semantic level for the purpose of (...) making science a rational pursuit of knowledge. I think, however, that a good place to look for them is in the rise of quantum mechanics and in the debate between Bohr and Einstein on its interpretation, not because similar cognitive values are not shaping scientific rationality elsewhere, but because they surface in the debate whenever a new revolutionary paradigm is about to take over the scene. (shrink)

This paper develops a Fragmentalist theory of Presentism and shows how it can help to develop a interpretation of quantum mechanics. There are several fragmental interpretations of physics. In the interpretation of this paper, each quantum system forms a fragment, and fragment f1 makes a measurement on fragment f2 if and only if f2 makes a corresponding measurement on f1. The main idea is then that each fragment has its own present (or ‘now’) until a mutual quantum (...) measurement—at which time they come (‘become’) to share the same ‘now’. The theory of time developed here will make use of both McTaggart’s A-series (in the form of future-present-past) and B-series (earlier-times to later-times). An example of an application is that a Bell pair of electrons does not take on definite spin values until measurement because the measuring system and the Bell pair do not share the same present (‘now’) until mutual quantum measurement, i.e. until they ‘become’ to share the same A-series. Before that point the ‘now’ of the opposing system is not in the reference system’s fragment. Relativistic no-signaling is preserved within each fragment, which will turn out to be sufficient for the general case. Several issues in the foundations of quantum mechanics are canvassed, including Schrodinger’s cat, the Born rule, modifications to Minkowski space that accommodate both the A-series and the B-series, and entropy. (shrink)

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete (...) set of orthogonal quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories. (shrink)

In this review, we present a rigorous construction of an algebraic method for quantum unstable states, also called Gamow states. A traditional picture associates these states to vectors states called Gamow vectors. However, this has some difficulties. In particular, there is no consistent definition of mean values of observables on Gamow vectors. In this work, we present Gamow states as functionals on algebras in a consistent way. We show that Gamow states are not pure states, in spite of their (...) representation as Gamow vectors. We propose a possible way out to the construction of averages of observables on Gamow states. The formalism is intended to be presented with sufficient mathematical rigor. (shrink)

Despite its enormous practical success, many physicists and philosophers alike agree that the quantum theory is full of contradictions and paradoxes which are difficult to solve consistently. Even after 90 years, the experts themselves still do not all agree what to make of it. The area of disagreement centers primarily around the problem of describing observations. Formally, the so-called quantum measurement problem can be defined as follows: the result of a measurement is a superposition of vectors, each representing (...) the quantity being observed as having one of its possible values. The question that has to be answered is: how this superposition can be reconciled with the fact that in practice we only observe one value. How is the measuring instrument prodded into making up its mind which value it has observed? Among some alternatives to resolve the above QM measurement problem, a very counterintuitive one was suggested by Hugh Everett in his 1955 Princeton dissertation, which was subsequently called the Many-Worlds Interpretation of QM (MWI). In this paper we will not discuss all possible scenarios to solve the measurement problem, but we will only shortly discuss Everett’s MWI, because it has led to heated debates on possibility of multiverses, beyond the Universe we live in. We also discuss two alternatives against MWI proposal: (a) the so-called scale symmetry theory, (b) the Maxwell-Dirac isomorphism. In last section, we also discuss shortly MWI hypothesis from philosophical perspective. (shrink)

The concepts of choice, negation, and infinity are considered jointly. The link is the quantity of information interpreted as the quantity of choices measured in units of elementary choice: a bit is an elementary choice between two equally probable alternatives. “Negation” supposes a choice between it and confirmation. Thus quantity of information can be also interpreted as quantity of negations. The disjunctive choice between confirmation and negation as to infinity can be chosen or not in turn: This corresponds to set-theory (...) or intuitionist approach to the foundation of mathematics and to Peano or Heyting arithmetic. Quantum mechanics can be reformulated in terms of information introducing the concept and quantity of quantum information. A qubit can be equivalently interpreted as that generalization of “bit” where the choice is among an infinite set or series of alternatives. The complex Hilbert space can be represented as both series of qubits and value of quantum information. The complex Hilbert space is that generalization of Peano arithmetic where any natural number is substituted by a qubit. “Negation”, “choice”, and “infinity” can be inherently linked to each other both in the foundation of mathematics and quantum mechanics by the meditation of “information” and “quantum information”. (shrink)

Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two entanglement measures for all quantum states, however, allows for meaningful conceptualization of sensitivity to entanglement, which will be greater for the entanglement measure that produces the larger numerical values. Here, we have investigated the partial order between the normalized versions of four entanglement measures (...) based on Schmidt decomposition of bipartite pure quantum states, namely, concurrence, tangle, entanglement robustness and Schmidt number. We have shown that among those four measures, the concurrence and the Schmidt number have the highest and the lowest sensitivity to quantum entanglement, respectively. Further, we have demonstrated how these measures could be used to track the dynamics of quantum entanglement in a simple quantum toy model composed of two qutrits. Lastly, we have employed state-dependent entanglement statistics to compute measurable correlations between the outcomes of quantum observables in agreement with the uncertainty principle. The presented results could be helpful in quantum applications that require monitoring of the available quantum resources for sharp identification of temporal points of maximal entanglement or system separability. (shrink)

Since the release of OpenAI's ChatGPT, the world has entered a race to develop more capable and powerful AI, including artificial general intelligence (AGI). The development is constrained by the dependency of AI on the model, quality, and quantity of training data, making the AI training process highly costly in terms of resources and environmental consequences. Thus, improving the effectiveness and efficiency of the AI training process is essential, especially when the Earth is approaching the climate tipping points and planetary (...) boundaries. It is evident that AI can function better when trained to mimic certain human mental processes. Based on insights from quantum mechanics and the informational entropy-based notion of value, we suggest AI developers can enhance the AI training processes' effectiveness and efficiency by creating and implementing parameter systems that are capable of effectively assigning probabilities to informational quanta. Such systems can help reduce entropy within the system, which lowers the energy required for data storage and processing while decreasing the likelihood of information loss during training. Successfully applying the concept of information entropy-based value in AI development will be crucial for advancing generative AI and achieving AGI in a sustainable manner. (shrink)

One can construct a mapping between Hilbert space and the class of all logic if the latter is defined as the set of all well-orderings of some relevant set (or class). That mapping can be further interpreted as a mapping of all states of all quantum systems, on the one hand, and all logic, on the other hand. The collection of all states of all quantum systems is equivalent to the world (the universe) as a whole. Thus that (...) mapping establishes a fundamentally philosophical correspondence between the physical world and universal logic by the meditation of a special and fundamental structure, that of Hilbert space, and therefore, between quantum mechanics and logic by mathematics. Furthermore, Hilbert space can be interpreted as the free variable of "quantum information" and any point in it, as a value of the same variable as "bound" already axiom of choice. (shrink)

“Better Economics for the Earth: A Lesson from Quantum and Information Theories” is a synthesis of ideas that promise to revolutionize our understanding of economics. Authors Quan-Hoang Vuong and Minh-Hoang Nguyen nurture a refreshing perspective by intertwining complex scientific theories with the intricate dance of economic systems. Their exploration goes beyond the traditional frameworks, engaging readers in a journey that teases the intellect while whispering secrets of the universe that are intimately tied to our everyday lives. The book earns (...) a glowing 5 out of 5 stars for its audacious approach to expanding economic thought, its emotional resonance, and its ability to captivate the intellect. Vuong and Nguyen have crafted a narrative that is not only timely but also timeless, as it invites readers to be part of a dialogue that could transform our world. This book is essential reading for anyone eager to explore the nexus of science and economics, pushing boundaries while maintaining an engaging and humane touch. (shrink)

This book, “Better Economics for the Earth,” offers a fresh take on how economics can evolve to better address modern challenges like environmental crises and AI. It draws on ideas from physics and quantum theory to redefine value and encourages economists to rethink traditional approaches. I really liked some of the figures and illustrations used to explain complex concepts—they really helped clarify the ideas presented.

A new non-Archimedean approach to interacted quantum fields is presented. In proposed approach, a field operator φ(x,t) no longer a standard tempered operator-valued distribution, but a non-classical operator-valued function. We prove using this novel approach that the quantum field theory with Hamiltonian P(φ)_4 exists and that the corresponding C^*­ algebra of bounded observables satisfies all the Haag-Kastler axioms except Lorentz covariance. We prove that the λ(φ^2n )_4,n≥2 quantum field theory models are Lorentz covariant.

We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the A(Si) and i,±1 N Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum (...) mechanics. In detail we realize a bare bone skeleton of quantum mechanics recovering all the basic foundations of this theory on an algebraic framework. We give proof of the quantum like Heisenberg uncertainty relations using only the basic support of the Clifford algebra. In addition we demonstrate the well known phenomenon of quantum Mach Zender interference using the same algebraic framework, as well as we give algebraic proof of quantum collapse in some cases of physical interest by direct application of the theorem that we derive to elaborate the i,±1 N algebra. We also discuss the problem of time evolution of quantum systems as well as the changes in space location, in momentum and the linked invariance principles. We are also able to re-derive the basic wave function of standard quantum mechanics by using only the Clifford algebraic approach. In this manner we obtain a full exposition of standard quantum mechanics using only the basic axioms of Clifford algebra. We also discuss more advanced features of quantum mechanics. In detail, we give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR paradox only using the Clifford algebra. By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that, as it is well known, are interpreted as logical statements, following the basic von Neumann results. Von Neumann realized a matrix logic on the basis of quantum mechanics. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic. Therefore, it seems that we may conclude that quantum mechanics, as it appears when investigated by the Clifford algebra, is a two-faced theory in the sense that it looks from one side to “matter per se”, thus to objects but simultaneously also to conceptual entities. We advance the basic conclusion of the paper: There are stages of our reality in which we no more can separate the logic ( and thus cognition and thus conceptual entity) from the features of “matter per se”. In quantum mechanics the logic, and thus the cognition and thus the conceptual entity-cognitive performance, assume the same importance as the features of what is being described. We are at levels of reality in which the truths of logical statements about dynamic variables become dynamic variables themselves so that a profound link is established from its starting in this theory between physics and conceptual entities. Finally, in this approach there is not an absolute definition of logical truths. Transformations , and thus … “redefinitions”…. of truth values are permitted in such scheme as well as the well established invariance principles, clearly indicate . (shrink)

The Born’s rule to interpret the square of wave function as the probability to get a specific value in measurement has been accepted as a postulate in foundations of quantum mechanics. Although there have been so many attempts at deriving this rule theoretically using different approaches such as frequency operator approach, many-world theory, Bayesian probability and envariance, literature shows that arguments in each of these methods are circular. In view of absence of a convincing theoretical proof, recently some (...) researchers have carried out experiments to validate the rule up-to maximum possible accuracy using multi-order interference (Sinha et al, Science, 329, 418 [2010]). But, a convincing analytical proof of Born’s rule will make us understand the basic process responsible for exact square dependency of probability on wave function. In this paper, by generalizing the method of calculating probability in common experience into quantum mechanics, we prove the Born’s rule for statistical interpretation of wave function. (shrink)

Since 2019, I have been accompanying the development of the Mindsponge Theory (MT). In 2023, the book Mindsponge Theory was officially published, marking a significant milestone. During this period, I completed my doctoral research and explored new methods to enhance work efficiency. The journey was filled with challenges. Surprisingly, the difficulties arose from concepts that seemed small and basic, almost taken for granted as "already known." I was entrusted by my co-author—the father of the mindsponge mechanism—with the task of further (...) developing the theory. He was not satisfied with what seemed like the final form, encapsulating Mindsponge theory as an information mechanism of biological systems. This was a significant challenge because the next form could only be approached using scientific information from quantum physics, as predicted by Erwin Schrödinger. Indeed, our exploration traversed many realms of physics and information. This journey was greatly supported by books like Reality Is Not What It Seems by Rovelli and On the Origin of Time by Hertog, along with Shannon's principles of information theory. The more valuable information we gathered, the more we realized the vast contributions left by countless brilliant minds, highlighting our own limitations. I was driven by a seemingly simple yet profoundly challenging question: • What is value? What approach is needed to reach its deepest essence? (shrink)

In quantum mechanics, the wavefunction predicts probabilities of possible measurement outcomes, but not which individual outcome is realised in each run of an experiment. This suggests that it describes an ensemble of states with different values of a hidden variable. Here, we analyse this idea with reference to currently known theorems and experiments. We argue that the ψ-ontic/epistemic distinction fails to properly identify ensemble interpretations and propose a more useful definition. We then show that all local ψ-ensemble interpretations which (...) reproduce quantum mechanics violate Statistical Independence. Theories with this property are commonly referred to as superdeterministic or retrocausal. Finally, we explain how this interpretation helps make sense of some otherwise puzzling phenomena in quantum mechanics, such as the delayed choice experiment, the Elitzur-Vaidman bomb detector, and the Extended Wigner's Friends Scenario. (shrink)

If you’re looking for a fresh take on solving our planet's environmental issues, “Better Economics for the Earth” by Vuong and Nguyen is a must-read. This book is not just another dense economic text; it’s a riveting exploration into how quantum physics and information theory can totally transform our approach to economics, making it more suited to tackle today’s ecological crises.

Through the lens of the informational entropy-based notion of value, I attempt to provide explanations for the aspects of cultural additivity that I could not explain previously: the additivity limit and the drawbacks of cultural additivity.

Entanglement has been called the most important new feature of the quantum world. It is expressed in the quantum formalism by the joint measurement formula. We prove the formula for projection valued observables from a plausible assumption, which for spacelike separated measurements is an expression of relativistic causality. The state reduction formula is simply a way to express the joint measurement formula after one measurement has been made, and its result known.

The well-definedness of particles of any kind depends on the limits, approximations, or other conditions that may or may not be involved, for example, whether there are interactions and whether ostensibly related energy is localizable. In particular, their theoretical status differs between its non-relativistic and relativistic versions: One can properly define interacting elementary particles in single-system non-relativistic quantum mechanics, at least in the case of non-zero mass systems; by contrast, one is severely challenged to define even these properly in (...) the relativistic quantum field theories that now underlie the study of particle physics. Here, the impact of localizability on this status is reviewed in relation to the work of Paul Busch on positive operator valued measures that significantly probes the relevance of quantum unsharpness to it. (shrink)

It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible taking into account the logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum propositions within the context of the fuzzy sets is here more useful for (...) systemics. In conclusion we propose an example of formal quantum coherence. (shrink)

In this paper we discuss the notions of adequacy and truth functionality in quantum logic from the point of view of a non-deterministic semantics. We give a characterization of the degree of non-functionality which is compatible with the propositional structure of quantum theory, showing that having truth-functional connectives, together with some assumptions regarding the relation of logical consequence, commits us to the adequacy of the interpretation sets of these connectives. An advantage of our proof is that it is (...) independent of the number of truth values involved, generalizing previous works. We also show the failure of the adequacy of every Nmatrix that is a model of the non-distributive lattice of quantum propositions. En este trabajo discutimos las nociones de adecuación y veritativo-funcionalidad en la lógica cuántica, desde el punto de vista de una semántica no determinista. Damos una caracterización del grado de no-funcionalidad compatible con la estructura proposicional de la teoría cuántica, mostrando que tener conectivos veritativo-funcionales, junto con algunos presupuestos relativos a la relación de consecuencia lógica, nos compromete con la adecuación de los conjuntos de interpretación de estos conectivos. Un punto ventajoso de nuestra prueba es que se independiza de la cantidad de valores de verdad involucrados, generalizando trabajos previos. Probamos también que falla la adecuación de cualquier Nmatriz que sirva como modelo para el retículo no distributivo de proposiciones cuánticas. (shrink)

Biomolecules and particularly proteins and DNA exhibit some mysterious features that cannot find satisfactory explanation by quantum mechanical modes of atoms. One of them, known as a Levinthal’s paradox, is the ability to preserve their complex three-dimensional structure in appropriate environments. Another one is that they possess some unknown energy mechanism. The Basic Structures of Matter Supergravitation Unified Theory (BSM-SG) allows uncovering the real physical structures of the elementary particles and their spatial arrangement in atomic nuclei. The resulting physical (...) models of the atoms are characterized by the same interaction energies as the quantum mechanical models, while the structure of the elementary particles influence their spatial arrangement in the nuclei. The resulting atomic models with fully identifiable parameters and angular positions of the quantum orbits permit studying the physical conditions behind the structural and bonding restrictions of the atoms connected in molecules. A new method for a theoretical analysis of biomolecules is proposed. The analysis of a DNA molecule leads to formulation of hypotheses about the energy storage mechanism in DNA and its role in the cell cycle synchronization. This permits shedding a light on the DNA feature known as a C-value paradox. The analysis of a tRNA molecule leads to formulation of a hypothesis about a binary decoding mechanism behind the 20 flavors of the complex aminoacyle-tRNA synthetases - tRNA, known as a paradox. (shrink)

I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an assignment of chance values is possible if and only if it is given by a pure state on a given algebra, your estimates for chances avoid accuracy-dominance if and only if they are given by a state on that algebra. When your estimates avoid accuracy-dominance (roughly: when you cannot guarantee that other (...) estimates would be more accurate), I say that they are sufficiently coherent. In formal epistemology and quantum foundations, the notion of rational coherence that gets more attention requires that you never allow for a sure loss (or “Dutch book”) in a given sort of betting game; I call this notion full coherence. I characterize when these two notions of rational coherence align, and I show that there is a quantum state giving estimates that are sufficiently coherent, but not fully coherent. (shrink)

The paper discusses Hilbert mathematics, a kind of Pythagorean mathematics, to which the physical world is a particular case. The parameter of the “distance between finiteness and infinity” is crucial. Any nonzero finite value of it features the particular case in the frameworks of Hilbert mathematics where the physical world appears “ex nihilo” by virtue of an only mathematical necessity or quantum information conservation physically. One does not need the mythical Big Bang which serves to concentrate all the (...) violations of energy conservation in a “safe”, maximally remote point in the alleged “beginning of the universe”. On the contrary, an omnipresent and omnitemporal medium obeying quantum information conservation rather than energy conservation permanently generates action and thus the physical world. The utilization of that creation “ex nihilo” is accessible to humankind, at least theoretically, as long as one observes the physical laws, which admit it in their new and wider generalization. One can oppose Hilbert mathematics to Gödel mathematics, which can be identified as all the standard mathematics until now featureable by the Gödel dichotomy of arithmetic to set theory: and then, “dialectic”, “intuitionistic”, and “Gödelian” mathematics within the former, according to a negative, positive, or zero value of the distance between finiteness and infinity. A mapping of Hilbert mathematics into pseudo-Riemannian space corresponds, therefore allowing for gravitation to be interpreted purely mathematically and ontologically in a Pythagorean sense. Information and quantum information can be involved in the foundations of mathematics and linked to the axiom of choice or alternatively, to the field of all rational numbers, from which the pair of both dual and anti-isometric Peano arithmetics featuring Hilbert arithmetic are immediately inferable. Noether’s theorems (1918) imply quantum information conservation as the maximally possible generalization of the pair of the conservation of a physical quantity and the corresponding Lie group of its conjugate. Hilbert mathematics can be interpreted from their viewpoint also after an algebraic generalization of them. Following the ideas of Noether’s theorem (1918), locality and nonlocality can be realized both physically and mathematically. The “light phase of the universe” can be linked to the gap of mathematics and physics in the Cartesian organization of cognition in Modernity and then opposed to its “dark phase”, in which physics and mathematics are merged. All physical quantities can be deduced from only mathematical premises by the mediation of the most fundamental physical constants such as the speed of light in a vacuum, the Planck and gravitational constants once they have been interpreted by the relation of locality and nonlocality. (shrink)