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Unitarity and the Incompleteness of Non-informational, Time-Invariant Dynamics

Ignacio Ospino

Published Mar 27, 2026• 0 citations
Publisher

Abstract

Information is treated by classical physics, relativity theory, and quantum mechanics as an epistemic variable, with no significance in their mathematical models. All currently accepted conceptions of information and entropy are subjective, observer-related. We have proposed (Ospino 2026) considering information as an ontic category with energy equivalence and energetic meaningfulness, and making it part of the complete balance of physical evolution. The history of science is the history of useful but incomplete models derived under the reliance of approximations and simplifications. Every such model was contemporarily considered complete until the contrary fact was demonstrated. Unitarity and determinism are generally regarded as a complete understanding of physical evolution. The empirical success and practical usefulness of such assumptions is undeniable, as every model before was also for a certain time, until it was not. Motivated by the information-energy equivalence (Landauer, Vopson), and by the possibility of resolving some open questions not explainable under the current understanding, we introduced ontic information into consideration, and we are presenting here some derived conclusions for further analysis and discussion. We emphasize that the epistemic nature of information and entropy as per Shannon and von Neumann (and related approaches) needs to be consequently updated with the ontic understanding, or else the analysis will be flawed when using epistemic approaches. Also, since unitarity is the concept in question here, we rely on acceptance, for the purpose of the discussion, that unitarity could be incomplete.

DOI
10.5281/zenodo.19264319

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Per Östborn

The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive QM from more basic principles, these principles should be of general, philosophical nature. Here, we derive the formalism of QM from well-motivated epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. First, an epistemic formalism is developed, using concepts like knowledge and potential knowledge, identifying a physical state $S$ with the potential knowledge of the physical world. It is demonstrated that QM emerges from this formalism. However, Hilbert spaces, wave functions and probabilities are defined in certain well-defined observational contexts only. This means that the epistemic formalism is broader than QM. In the fundamental layer of description, the physical state $S$ is a subset of a state space $\mathcal{S}=\{Z\}$, such that $S$ always contains many elements $Z$. These elements correspond to unattainable states of complete knowledge of the world. The evolution of $S$ cannot be determined in terms of the individual evolution of the elements $Z$, unlike the evolution of an ensemble in classical phase space. The evolution of $S$ is described in terms of sequential time $n\in \mathbf{\mathbb{N}}$, which is updated according to $n\rightarrow n+1$ each time an event occurs, each time potential knowledge changes. Sequential time $n$ can be separated from relational time $t$, which describes distances between events in space-time. There is an entire space-time associated with each $n$, in which $t$ represents the knowledge at sequential time $n$ about the temporal relations between present and past events.

arXiv:1601.00680•Jan 4, 2016•1 citation

Quantum information theory

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The astute reader might have formed the impression that quantum in formation science is a rather qualitative discipline because we have not, as yet, explained how to quantify quantum information. There are three good reasons for leaving this important question until the final chapter. Firstly, quantum information theory is technically demanding and to treat it at an earlier stage might have suggested that our subject was more complicated than it is. Secondly, there is the fact that many of the ideas in the field, such as teleportation and quantum circuits, are unfamiliar and it was important to present these as simply as possible. Finally, and most importantly, the theory of quantum information is not yet fully developed. It has not yet reached, in particular, the level of completeness of its classical counterpart. For this reason we can answer only some of the many questions we would like a quantum theory of information to address. Having said this, we can say that however, there are beautiful and useful mathematical results and it seems certain that these will continue to form an important part of the theory as it develops. We noted in the introduction to Chapter 1 that ‘quantum mechanics is a probabilistic theory and so it was inevitable that a quantum information theory would be developed’. A presentation of at least the beginnings of a quantitative theory is the objective of this final chapter. The entropy or information derived from a given probability distribution is, as we have seen, a convenient measure of the uncertainty associated with the distribution. If many of the probabilities are large, so that many of the possible events are comparably likely, then the entropy will be large. If one probability is close to unity, however, then the entropy will be small. It is convenient to introduce entropy in quantum mechanics as a measure of the uncertainty, or lack of knowledge, of the form of the state vector. If we know that our system is in a particular pure state then the associated uncertainty or entropy should be zero. For mixed states, however, it will take a non-zero value.

Oxford University Press eBooks•May 28, 2009•24 citations

Multipartite Nonlocality in Ontological Models of Quantum Theory

Fumiaki Morikoshi

Quantum nonlocality has been a long-standing and fascinating problem in the foundations of quantum theory since its proof by the Bell inequality. It seems to contradict our intuitive picture of space-time and thus urges us to reconsider its foundation. With the advent of quantum information science, it has attracted renewed interest from a fundamental point of view as well as from a quantum information-theoretic one. Another fundamental question on the nature of quantum theory is how we understand what quantum states represent. (Quantum states hereafter refer to pure states.) This is also a long-standing problem since the early days of quantum theory. Roughly speaking, there are two conflicting views on this matter: one is ontology and the other is epistemology. Ontological models of quantum theory are models in which we assume some underlying reality for physical systems and require that all the predictions of quantum theory should be reproduced. The ontological models are divided into two categories, depending on which views the models are based on, ontology or epistemology. In the models based on ontology, quantum states represent the underlying reality in some sense, and different quantum states correspond to different realities. In the models based on epistemology, quantum states do not necessarily correspond to the underlying realities, and even different quantum states can be consistent with a common underlying reality. The former type of ontological models of quantum theory is called 1⁄4-ontic. The latter is called 1⁄4-epistemic. Thus, it might be rather confusing that ontological models are classified further into 1⁄4-ontic models and 1⁄4-epistemic ones. We use these terms here in accordance with the recent literature on quantum foundations. (For details of these notions in the ontological models of quantum theory, see the paper by Harrigan and Spekkens.) Quite recently, the question just mentioned has been answered by Pusey et al., and one of the above models has been refuted. It was shown that 1⁄4-epistemic models are inconsistent with the predictions of quantum theory. In other words, epistemological views on quantum states turned out to be false as long as we assume some underlying reality for physical systems. Therefore, only 1⁄4-ontic models of quantum theory are valid for describing quantum systems. This significantly advances our understanding on the nature of quantum states. It is expected that various conclusions will be drawn from this fact. In this paper, we will discuss a connection with nonlocality. The above two fundamental questions, nonlocality and the nature of quantum states, are intimately connected, and the connection was first implicitly recognised by Einstein in the early days of quantum theory. In a private correspondence with Schrodinger, Einstein constructed a fascinating argument that relates the above two. (That argument is distinctly different from the well-known EPR argument.) Recently, it was revisited and reconstructed in accordance with more rigorous notions in quantum foundations. Nonlocality is usually shown by violations of Bell inequalities. (Bell inequalities hereafter include all the subsequent developments such as the CHSH inequality.) Even if it is not clear whether the models of quantum theory are 1⁄4-ontic or 1⁄4-epistemic, we can prove nonlocality just by showing the violation of Bell inequalities. However, the above argument originated by Einstein implies that if we know the models are 1⁄4-ontic in advance (as we do now), we can prove nonlocality in a simpler way without Bell inequalities. (This argument had been known in quantum foundations before the refutation of 1⁄4-epistemic models.) Nonlocality is rigorously defined as a violation of the notion of local causality defined by Bell. Showing the violation of Bell inequalities is one way of demonstrating the violation of local causality. Since the simpler proof initiated by Einstein directly demonstrates the violation of local causality, it is a more straightforward proof of nonlocality from a conceptual point of view. In the following, we will see that this simple argument of nonlocality without Bell inequalities can be used to show multipartite nonlocality as well. Before moving onto multipartite cases, first let us define the necessary notions for presenting our result. First of all, we assume that there exists a complete specification of the properties of a physical system, which we refer to as the ontic state of that system. The ontic states represent the underlying realities and are not necessarily equal to ordinary quantum states. (In other words, the ontic states correspond to hidden variables.) Ontological models of quantum theory are models that assume ontic states and reproduce all the predictions of quantum theory. An important question is how ontic states correspond to quantum states in quantum theory. In order to frame the question accurately, we need the notion of an epistemic state, which represents the relation between them. Suppose we prepare a physical system in a quantum state 1⁄4. Although the system is uniquely specified as 1⁄4 in quantum theory, there still remains a possibility that it allows a more detailed specification in the ontic state space, in which case many different ontic states turn out to be consistent with 1⁄4. The relation between ontic states and the preparation procedure, P1⁄4, is described by a conditional probability distribution over the ontic state space, pð jP1⁄4Þ, which we refer to as an epistemic state. In general, the preparation P can be a preparation of a physical system in a mixed sate. Unless there exists a one-to-one correspondence between ontic states and quantum states, the probability distribution spreads over . (See Fig. 1.) The question of whether an ontological model is 1⁄4-ontic or 1⁄4-epistemic is concerned with the behaviour of the epistemic states for two distinct preparations of quantum states. Consider two distinct preparations of quantum states, Journal of the Physical Society of Japan 82 (2013) 055003

Journal of the Physical Society of Japan•Apr 23, 2013•0 citations

On Certain Questions Related to Information and Symmetries - In Physics From Certain View of Philosophy of Science

György Darvas

Introduction My presentation aims at answering a part of the questions posted in the invitation to the session. The questions arose in and originated from the FIS discussion on Physical informatics … in October 2014. No doubt, they were formulated in provocative manner. The goal was to challenge discussion. I plan to illustrate my personal answers with a few examples quoted from the history of 20th c. physics. My answers to the questions are not intended to be enunciations and to provide final solutions, rather they serve as arguments and indicate that nothing is closed, the discussion is open. Methods 1 What do we consider physical information? Can one speak about physical information when there is no live percipient to accept, evaluate and use it? Can one speak about physical information (e.g., signal exchange) between inanimate physical objects (cf., e.g., Feynman diagrams)? And if so, what is it for? Is (physical) information a passive phenomenon, or its existence presumes activity? Interpretation of ‘activity’ plays important role in the possible answers. One of the interpretations says that activity is an antropomorph phenomenon. It is a privilege of the human mind, which is able to perceive and process information, able to teleologically evaluate its possible consequences and (re)act accordingly. Another interpretation says that there is inanimate activity, that means, reception of information between physical agents and their reaction to it. I argue for the latter concept. Let us see the example of the interaction between two (electric) charges. There were two approaches in the classical age of developing these theories (1928-33). When two electric charges interact, there appear two types of interaction. One is a Coulomb-type repulsion/attraction (according to their mutual signs) governed by their scalar potential, and the other is a Lorentz-type one governed by their vector potential depending on their relative velocity to each other. One type of the theories considered first the interaction between the scalar potentials and calculated the effect of the vector potentials as perturbation. It considered two charges approaching to each other from the infinity, when in first approximation they have got information on the amount of the Coulomb charge of the other, but not its velocity and the caused Lorentz force. The latter was considered in the perturbation process. The other type of the theories considered first the effect of the Lorentz force of the approaching charges, and took into consideration the effect of the Coulomb force in course of the perturbation. Representatives of both types of theories agreed that the roles of the interacting electric charges must be symmetrical, but Christian Møller. Møller [7], who belonged to the latter type of theoreticians, applied scattering matrices (1931). He showed that there appeared a component among the matrix elements that was asymmetric in respect to the two interacting charges. H. Bethe (that time a doctoral student of E. Fermi, 1932) could not accept this asymmetry and ‘corrected’ Møller’s theory. He ‘symmetrised’ those matrix elements artificially [1]. That was a rough and unjustified involvement in Møller’s equation, but due to the later attained high authority of both Bethe and Fermi, the physics community accepted the apparently convenient symmetrisation of the theory without discussion and has not treated it until the recent years. Thus any possible distinction between (roles and properties of) interacting charges were unrevealed until the past decade. However, the question can be formulated so: how do the charges, ready to interact, get information from each other? All theories agree that interaction between two charges take place by the exchange of a boson. In case of electromagnetic interaction this boson is a photon. Which of them emits the first photon towards the other? Did this emitter receive any information from the direction of the partner charge prior to the photon emission? What else is this if not an asymmetry between the roles, and possibly between properties of the two interacting charges? The distinction between the interacting charges was introduced by the isotopic field-charge theory, and the notion of ‘isotopic field-charge’ made the distinction between the properties of the two charges [2],[3],[4],[5]. The latter led to the proof of the gauge invariance under rotation of a newly introduced property, the isotopic field-charge spin, in an abstract field, and its conservation. This conservation is a result of a symmetry. Neverthe-less, this mechanism argues for activity between physical objects without an animated (human) agent. 2 What are the limits between (closed and open) systems, from the aspects of information and of symmetries? Further, if so, how wide can we extend the meaning of activity to be still accepted for generating information? What are the roles of different appearances of symmetries in taking a stand in the mentioned questions? What kinds of symmetry (or their absence) may play a role in making decision in the listed problems? The ‘classical’ (20th c.) relativity theories demanded that all physical laws were invariant under the Lorentz transformation. This was established first in the special theory of relativity that was formulated for electromagnetic interactions [6]. Lorentz invariance of physical laws was in fact a symmetry principle (conservation of the form of the laws during reference frame change) [9]. This invariance proved to hold for many other physical laws, so later also the symmetry principle was extended to other physical laws as well. The Lorentz invariant relativity theory included another consequence: there is no distinct (odd) reference frame in nature. In other words, all reference frames are equivalent. Aren’t they? Based on Noether’s theorems [8], one can show that conservation laws hold in all reference frames. However, the quantity of the conserved property (e.g., mass, charge, etc.) may change in the different reference frames. E.g., the amount of mass of matter in a closed system depends on the velocity of the observer relative to that system where the mass is to be measured. One can always find a reference frame from which the amount of the measured mass is minimal. This fact contradicts to the absence of a distinct (odd) reference frame. And there are more. Is there any invariance that compensates this lost equivalence of all reference frames? The observer can be not only a human agent who measures with instruments and reads the records. It can be another inanimate mass that perceives information about the mass from the observed system. Its ‘activity’ is that this information can be obtained by experiencing a force. This force can be gravitational or inertial. According to the general theory of relativity the ‘observer mass’ is unable to make distinction whether the experienced force is of ‘inertial’ or ‘gravitational’ origin. At the same time, the inertial mass changes its value according to its relative velocity to the observer, while the gravitational mass does not. Thus the ‘observer mass’ in different reference frames will experience different inertial forces originating from the ‘observed mass’. Something similar distinction can be made between the Coulomb charges and the Lorentz-type (current) charges. They are sources of the Coulomb force and the Lorentz force, respectively, and similar to the two types of masses, originate from the scalar potential and from the vector potential of the Hamiltonian of the charged object, respectively. The two types of masses and the two types of electric charges are called isotopic field-charge pairs, respectively. They are subject of the same gauge invariance. As such, they can exchange their roles (switch into each other) by the exchange of a gauge boson (in addition to the graviton and the photon, respectively), called delta bosons in the theory. As a consequence of the additional invariance and the corresponding additional mediating gauge boson, the respective systems of the two interacting isotopic field-charges (masses or electric charges) are not subjects of the Lorentz invariance alone. They are subjects of a convolution of the Lorentz- and this additional invariance. One can conclude two things. First, along with the development of physics, there is no more enough to demand invariance under the Lorentz transformation. At extended conditions, one should demand the invariance under a combination of the Lorentz invariance and an additional invariance. In short, we demand invariance under (the applicable) transformations. Secondly, when two charges (let they be either gravitational, electric, or other field-charges) interact, they make a distinction between each other. The system, composed of the interacting two field-charges, follow the Pauli principle. That means, the two interacting field-charges must be in different quantum states. Since this state in which they differ cannot be characterized by any of the earlier known properties, it must be a characteristic of the newly introduced property. It must be one of the two stable positions of the isotopic field-charge that are rotated into each other by the SU(2) symmetry group in the isotopic field-charge field. These two stable positions are called, by an analogically given name, the isotopic field-charge spin (not identical either with the angular momentum spin or the isotopic spin). According to its proven invariance, the isotopic field-charge spin is a conserved property. When two field-charges interact, they must be in the opposite isotopic field-charge spin states. The information that they exchange about each other is about this state: they check whether the partner is in the opposite state. Otherwise they are ‘not allowed’ to interact (Pauli’s exclusion principle). The information exchange takes place by the exchange of a delta boson (called also dion) between them, in addition to the exchange of the traditional mediating bosons (like graviton, photon, weak charged and neutral bosons, or gluons). That delta boson switches the emitting charge from inertial to potential state, and the absorbing charge from potential to inertial state. Conclusions The asymmetry of the interacting charges has been explained. It was subject of information exchange between the interacting particle partners. In order to meet the Pauli principle, physical objects should exchange information about the (opposite) states of each other before getting into active interaction. The explanation led to the loss of an invariance property. However, this loss has been restored by introducing a new physical property (isotopic field-charge spin), by proving its conservation, and completing the Lorentz invariance with the respective invariance attributed to the newly proven conservation. References Bethe, H., Fermi, E., Über die Wechselwirkung von zwei elektronen, Zeitschrift für Physik, 77 (1932), 5-6, 296-306. Darvas, G., The Isotopic Field Charge Spin Assumption, International Journal of Theoretical Physics, 50 (2011), 10, 2961-2991.DOI: 10.1007/s10773-011-0796-9 Darvas, G., The Isotopic Field-Charge Assumption Applied to the Electromagnetic Interaction, Int J Theor Phys, 52 (2013a), 11, 3853-3869, DOI 10.1007/s10773-013-1693-1. Darvas, G., A symmetric adventure beyond the Standard Model – Isotopic field-charge spin conservation in the electromagnetic interaction, Symmetry: Culture and Science, 24 (2013b), 1-4, 17-40. Darvas, G., Electromagnetic Interaction in the Presence of Isotopic Field-Charges and a Kinetic Field, Int J Theor Phys, 53 (2014), 1, 39-51, DOI 10.1007/s10773-013-1781-2. Einstein, A., Zur Elektrodynamik bewegter Körper, Annalen der Physik, 17:891 (1905); English translation: On the electrodynamics of moving bodies, in: The Principle of Relativity, (1923), London: Methuen and Co. Møller, C., Über den Stoß zweier Teilchen unter Berücksichtigung der Retardation der Kräfte, Zeitschrift für Physik, 70 (1931), 11-12, 786-795. Noether, E. A., Invariante Variationsprobleme, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen: Mathematisch-physikalische Klasse, (1918) 235-257. Wigner, E.P. , Events, laws of nature and invariance principles, pp. 38-50, in: Wigner, Symmetries and Reflections, Bloomington: Indiana University Press (1967).

ISIS Summit: The Information Society at the Crossroads•Jun 30, 2015•0 citations

Quantum Mechanics: 44 Admissible Questions? -Not only Fapp-

Michele Caponigro, Helen Lynn

The words: determinism, hidden variables, subjectivism, information, objectivism, informational-theoretic axioms,observers have some connection with physical reality? What we mean with "description" of physical reality? When we say that we understand this reality? Certain parameters:position, velocity are sufficient? We will focus only to conceptual considerations regarding the relation between the "questions" and the relative "answers" in general and specifically in quantum mechanics. It is usually believed that the answers are more important of the questions, for this reason we can read many answers everywhere and in different field of knowledge. We need to add and clarify some things: (i) usually an answers require a question, (ii) but, as we know, their relation is not so simple and immediate, (iii) For instance: a)an epistemic questions give us ontic answers? b)the answer has a connection with the question and vice versa? c)we could to infer a question starting from an answer? d)there are answers without questions? These answers could be in some framework considered as ontic answers? The relative scientific works are the same time ontic? Speaking of quantum mechanics we see around many answers in the meantime we do not see the correspondent questions, these answers seem completely independent, and this seem a right road, the road of the independent nature unlinked from human thoughts. We retain instead that questions can affect the possible answers. Exist "something" before the question?

arXiv:quant-ph/0606032•Prespacetime journal•Jun 5, 2006•0 citations

About the Nature of Quantum Information

Olímpia Lombardi

Although the interpretation of the concept of information is not clear, even in the classical framework, new interpretive problems have arisen with the advent of the so-called quantum information, which combine the difficulties in understanding the concept of information with the well-known foundational puzzles derived from quantum mechanics itself. The aim of this paper is to consider some arguments traditionally put forward to support the idea that quantum information is qualitatively different from classical information. The final conclusion is that there are no reasons to admit the existence of quantum information as qualitatively different from classical information: there is only one kind of information, physically neutral, which can be encoded by means of classical or quantum states.

International Society for the Study of Information Summit (IS4SI Summit)•Sep 19, 2021•0 citations
Information is treated by classical physics, relativity theory, and quantum mechanics as an epistemic variable, with no significance in their mathematical models. All currently accepted conceptions of information and entropy are subjective, observer-related. We have proposed (Ospino 2026) considering information as an ontic category with energy equivalence and energetic meaningfulness, and making it part of the complete balance of physical evolution. The history of science is the history of useful but incomplete models derived under the reliance of approximations and simplifications. Every such model was contemporarily considered complete until the contrary fact was demonstrated. Unitarity and determinism are generally regarded as a complete understanding of physical evolution. The empirical success and practical usefulness of such assumptions is undeniable, as every model before was also for a certain time, until it was not. Motivated by the information-energy equivalence (Landauer, Vopson), and by the possibility of resolving some open questions not explainable under the current understanding, we introduced ontic information into consideration, and we are presenting here some derived conclusions for further analysis and discussion. We emphasize that the epistemic nature of information and entropy as per Shannon and von Neumann (and related approaches) needs to be consequently updated with the ontic understanding, or else the analysis will be flawed when using epistemic approaches. Also, since unitarity is the concept in question here, we rely on acceptance, for the purpose of the discussion, that unitarity could be incomplete.
The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive QM from more basic principles, these principles should be of general, philosophical nature. Here, we derive the formalism of QM from well-motivated epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. First, an epistemic formalism is developed, using concepts like knowledge and potential knowledge, identifying a physical state SSS with the potential knowledge of the physical world. It is demonstrated that QM emerges from this formalism. However, Hilbert spaces, wave functions and probabilities are defined in certain well-defined observational contexts only. This means that the epistemic formalism is broader than QM. In the fundamental layer of description, the physical state SSS is a subset of a state space S={Z}\mathcal{S}=\{Z\}S={Z}, such that SSS always contains many elements ZZZ. These elements correspond to unattainable states of complete knowledge of the world. The evolution of SSS cannot be determined in terms of the individual evolution of the elements ZZZ, unlike the evolution of an ensemble in classical phase space. The evolution of SSS is described in terms of sequential time n∈Nn\in \mathbf{\mathbb{N}}n∈N, which is updated according to n→n+1n\rightarrow n+1n→n+1 each time an event occurs, each time potential knowledge changes. Sequential time nnn can be separated from relational time ttt, which describes distances between events in space-time. There is an entire space-time associated with each nnn, in which ttt represents the knowledge at sequential time nnn about the temporal relations between present and past events.
The astute reader might have formed the impression that quantum in formation science is a rather qualitative discipline because we have not, as yet, explained how to quantify quantum information. There are three good reasons for leaving this important question until the final chapter. Firstly, quantum information theory is technically demanding and to treat it at an earlier stage might have suggested that our subject was more complicated than it is. Secondly, there is the fact that many of the ideas in the field, such as teleportation and quantum circuits, are unfamiliar and it was important to present these as simply as possible. Finally, and most importantly, the theory of quantum information is not yet fully developed. It has not yet reached, in particular, the level of completeness of its classical counterpart. For this reason we can answer only some of the many questions we would like a quantum theory of information to address. Having said this, we can say that however, there are beautiful and useful mathematical results and it seems certain that these will continue to form an important part of the theory as it develops. We noted in the introduction to Chapter 1 that ‘quantum mechanics is a probabilistic theory and so it was inevitable that a quantum information theory would be developed’. A presentation of at least the beginnings of a quantitative theory is the objective of this final chapter. The entropy or information derived from a given probability distribution is, as we have seen, a convenient measure of the uncertainty associated with the distribution. If many of the probabilities are large, so that many of the possible events are comparably likely, then the entropy will be large. If one probability is close to unity, however, then the entropy will be small. It is convenient to introduce entropy in quantum mechanics as a measure of the uncertainty, or lack of knowledge, of the form of the state vector. If we know that our system is in a particular pure state then the associated uncertainty or entropy should be zero. For mixed states, however, it will take a non-zero value.
Quantum nonlocality has been a long-standing and fascinating problem in the foundations of quantum theory since its proof by the Bell inequality. It seems to contradict our intuitive picture of space-time and thus urges us to reconsider its foundation. With the advent of quantum information science, it has attracted renewed interest from a fundamental point of view as well as from a quantum information-theoretic one. Another fundamental question on the nature of quantum theory is how we understand what quantum states represent. (Quantum states hereafter refer to pure states.) This is also a long-standing problem since the early days of quantum theory. Roughly speaking, there are two conflicting views on this matter: one is ontology and the other is epistemology. Ontological models of quantum theory are models in which we assume some underlying reality for physical systems and require that all the predictions of quantum theory should be reproduced. The ontological models are divided into two categories, depending on which views the models are based on, ontology or epistemology. In the models based on ontology, quantum states represent the underlying reality in some sense, and different quantum states correspond to different realities. In the models based on epistemology, quantum states do not necessarily correspond to the underlying realities, and even different quantum states can be consistent with a common underlying reality. The former type of ontological models of quantum theory is called 1⁄4-ontic. The latter is called 1⁄4-epistemic. Thus, it might be rather confusing that ontological models are classified further into 1⁄4-ontic models and 1⁄4-epistemic ones. We use these terms here in accordance with the recent literature on quantum foundations. (For details of these notions in the ontological models of quantum theory, see the paper by Harrigan and Spekkens.) Quite recently, the question just mentioned has been answered by Pusey et al., and one of the above models has been refuted. It was shown that 1⁄4-epistemic models are inconsistent with the predictions of quantum theory. In other words, epistemological views on quantum states turned out to be false as long as we assume some underlying reality for physical systems. Therefore, only 1⁄4-ontic models of quantum theory are valid for describing quantum systems. This significantly advances our understanding on the nature of quantum states. It is expected that various conclusions will be drawn from this fact. In this paper, we will discuss a connection with nonlocality. The above two fundamental questions, nonlocality and the nature of quantum states, are intimately connected, and the connection was first implicitly recognised by Einstein in the early days of quantum theory. In a private correspondence with Schrodinger, Einstein constructed a fascinating argument that relates the above two. (That argument is distinctly different from the well-known EPR argument.) Recently, it was revisited and reconstructed in accordance with more rigorous notions in quantum foundations. Nonlocality is usually shown by violations of Bell inequalities. (Bell inequalities hereafter include all the subsequent developments such as the CHSH inequality.) Even if it is not clear whether the models of quantum theory are 1⁄4-ontic or 1⁄4-epistemic, we can prove nonlocality just by showing the violation of Bell inequalities. However, the above argument originated by Einstein implies that if we know the models are 1⁄4-ontic in advance (as we do now), we can prove nonlocality in a simpler way without Bell inequalities. (This argument had been known in quantum foundations before the refutation of 1⁄4-epistemic models.) Nonlocality is rigorously defined as a violation of the notion of local causality defined by Bell. Showing the violation of Bell inequalities is one way of demonstrating the violation of local causality. Since the simpler proof initiated by Einstein directly demonstrates the violation of local causality, it is a more straightforward proof of nonlocality from a conceptual point of view. In the following, we will see that this simple argument of nonlocality without Bell inequalities can be used to show multipartite nonlocality as well. Before moving onto multipartite cases, first let us define the necessary notions for presenting our result. First of all, we assume that there exists a complete specification of the properties of a physical system, which we refer to as the ontic state of that system. The ontic states represent the underlying realities and are not necessarily equal to ordinary quantum states. (In other words, the ontic states correspond to hidden variables.) Ontological models of quantum theory are models that assume ontic states and reproduce all the predictions of quantum theory. An important question is how ontic states correspond to quantum states in quantum theory. In order to frame the question accurately, we need the notion of an epistemic state, which represents the relation between them. Suppose we prepare a physical system in a quantum state 1⁄4. Although the system is uniquely specified as 1⁄4 in quantum theory, there still remains a possibility that it allows a more detailed specification in the ontic state space, in which case many different ontic states turn out to be consistent with 1⁄4. The relation between ontic states and the preparation procedure, P1⁄4, is described by a conditional probability distribution over the ontic state space, pð jP1⁄4Þ, which we refer to as an epistemic state. In general, the preparation P can be a preparation of a physical system in a mixed sate. Unless there exists a one-to-one correspondence between ontic states and quantum states, the probability distribution spreads over . (See Fig. 1.) The question of whether an ontological model is 1⁄4-ontic or 1⁄4-epistemic is concerned with the behaviour of the epistemic states for two distinct preparations of quantum states. Consider two distinct preparations of quantum states, Journal of the Physical Society of Japan 82 (2013) 055003
Introduction My presentation aims at answering a part of the questions posted in the invitation to the session. The questions arose in and originated from the FIS discussion on Physical informatics … in October 2014. No doubt, they were formulated in provocative manner. The goal was to challenge discussion. I plan to illustrate my personal answers with a few examples quoted from the history of 20th c. physics. My answers to the questions are not intended to be enunciations and to provide final solutions, rather they serve as arguments and indicate that nothing is closed, the discussion is open. Methods 1 What do we consider physical information? Can one speak about physical information when there is no live percipient to accept, evaluate and use it? Can one speak about physical information (e.g., signal exchange) between inanimate physical objects (cf., e.g., Feynman diagrams)? And if so, what is it for? Is (physical) information a passive phenomenon, or its existence presumes activity? Interpretation of ‘activity’ plays important role in the possible answers. One of the interpretations says that activity is an antropomorph phenomenon. It is a privilege of the human mind, which is able to perceive and process information, able to teleologically evaluate its possible consequences and (re)act accordingly. Another interpretation says that there is inanimate activity, that means, reception of information between physical agents and their reaction to it. I argue for the latter concept. Let us see the example of the interaction between two (electric) charges. There were two approaches in the classical age of developing these theories (1928-33). When two electric charges interact, there appear two types of interaction. One is a Coulomb-type repulsion/attraction (according to their mutual signs) governed by their scalar potential, and the other is a Lorentz-type one governed by their vector potential depending on their relative velocity to each other. One type of the theories considered first the interaction between the scalar potentials and calculated the effect of the vector potentials as perturbation. It considered two charges approaching to each other from the infinity, when in first approximation they have got information on the amount of the Coulomb charge of the other, but not its velocity and the caused Lorentz force. The latter was considered in the perturbation process. The other type of the theories considered first the effect of the Lorentz force of the approaching charges, and took into consideration the effect of the Coulomb force in course of the perturbation. Representatives of both types of theories agreed that the roles of the interacting electric charges must be symmetrical, but Christian Møller. Møller [7], who belonged to the latter type of theoreticians, applied scattering matrices (1931). He showed that there appeared a component among the matrix elements that was asymmetric in respect to the two interacting charges. H. Bethe (that time a doctoral student of E. Fermi, 1932) could not accept this asymmetry and ‘corrected’ Møller’s theory. He ‘symmetrised’ those matrix elements artificially [1]. That was a rough and unjustified involvement in Møller’s equation, but due to the later attained high authority of both Bethe and Fermi, the physics community accepted the apparently convenient symmetrisation of the theory without discussion and has not treated it until the recent years. Thus any possible distinction between (roles and properties of) interacting charges were unrevealed until the past decade. However, the question can be formulated so: how do the charges, ready to interact, get information from each other? All theories agree that interaction between two charges take place by the exchange of a boson. In case of electromagnetic interaction this boson is a photon. Which of them emits the first photon towards the other? Did this emitter receive any information from the direction of the partner charge prior to the photon emission? What else is this if not an asymmetry between the roles, and possibly between properties of the two interacting charges? The distinction between the interacting charges was introduced by the isotopic field-charge theory, and the notion of ‘isotopic field-charge’ made the distinction between the properties of the two charges [2],[3],[4],[5]. The latter led to the proof of the gauge invariance under rotation of a newly introduced property, the isotopic field-charge spin, in an abstract field, and its conservation. This conservation is a result of a symmetry. Neverthe-less, this mechanism argues for activity between physical objects without an animated (human) agent. 2 What are the limits between (closed and open) systems, from the aspects of information and of symmetries? Further, if so, how wide can we extend the meaning of activity to be still accepted for generating information? What are the roles of different appearances of symmetries in taking a stand in the mentioned questions? What kinds of symmetry (or their absence) may play a role in making decision in the listed problems? The ‘classical’ (20th c.) relativity theories demanded that all physical laws were invariant under the Lorentz transformation. This was established first in the special theory of relativity that was formulated for electromagnetic interactions [6]. Lorentz invariance of physical laws was in fact a symmetry principle (conservation of the form of the laws during reference frame change) [9]. This invariance proved to hold for many other physical laws, so later also the symmetry principle was extended to other physical laws as well. The Lorentz invariant relativity theory included another consequence: there is no distinct (odd) reference frame in nature. In other words, all reference frames are equivalent. Aren’t they? Based on Noether’s theorems [8], one can show that conservation laws hold in all reference frames. However, the quantity of the conserved property (e.g., mass, charge, etc.) may change in the different reference frames. E.g., the amount of mass of matter in a closed system depends on the velocity of the observer relative to that system where the mass is to be measured. One can always find a reference frame from which the amount of the measured mass is minimal. This fact contradicts to the absence of a distinct (odd) reference frame. And there are more. Is there any invariance that compensates this lost equivalence of all reference frames? The observer can be not only a human agent who measures with instruments and reads the records. It can be another inanimate mass that perceives information about the mass from the observed system. Its ‘activity’ is that this information can be obtained by experiencing a force. This force can be gravitational or inertial. According to the general theory of relativity the ‘observer mass’ is unable to make distinction whether the experienced force is of ‘inertial’ or ‘gravitational’ origin. At the same time, the inertial mass changes its value according to its relative velocity to the observer, while the gravitational mass does not. Thus the ‘observer mass’ in different reference frames will experience different inertial forces originating from the ‘observed mass’. Something similar distinction can be made between the Coulomb charges and the Lorentz-type (current) charges. They are sources of the Coulomb force and the Lorentz force, respectively, and similar to the two types of masses, originate from the scalar potential and from the vector potential of the Hamiltonian of the charged object, respectively. The two types of masses and the two types of electric charges are called isotopic field-charge pairs, respectively. They are subject of the same gauge invariance. As such, they can exchange their roles (switch into each other) by the exchange of a gauge boson (in addition to the graviton and the photon, respectively), called delta bosons in the theory. As a consequence of the additional invariance and the corresponding additional mediating gauge boson, the respective systems of the two interacting isotopic field-charges (masses or electric charges) are not subjects of the Lorentz invariance alone. They are subjects of a convolution of the Lorentz- and this additional invariance. One can conclude two things. First, along with the development of physics, there is no more enough to demand invariance under the Lorentz transformation. At extended conditions, one should demand the invariance under a combination of the Lorentz invariance and an additional invariance. In short, we demand invariance under (the applicable) transformations. Secondly, when two charges (let they be either gravitational, electric, or other field-charges) interact, they make a distinction between each other. The system, composed of the interacting two field-charges, follow the Pauli principle. That means, the two interacting field-charges must be in different quantum states. Since this state in which they differ cannot be characterized by any of the earlier known properties, it must be a characteristic of the newly introduced property. It must be one of the two stable positions of the isotopic field-charge that are rotated into each other by the SU(2) symmetry group in the isotopic field-charge field. These two stable positions are called, by an analogically given name, the isotopic field-charge spin (not identical either with the angular momentum spin or the isotopic spin). According to its proven invariance, the isotopic field-charge spin is a conserved property. When two field-charges interact, they must be in the opposite isotopic field-charge spin states. The information that they exchange about each other is about this state: they check whether the partner is in the opposite state. Otherwise they are ‘not allowed’ to interact (Pauli’s exclusion principle). The information exchange takes place by the exchange of a delta boson (called also dion) between them, in addition to the exchange of the traditional mediating bosons (like graviton, photon, weak charged and neutral bosons, or gluons). That delta boson switches the emitting charge from inertial to potential state, and the absorbing charge from potential to inertial state. Conclusions The asymmetry of the interacting charges has been explained. It was subject of information exchange between the interacting particle partners. In order to meet the Pauli principle, physical objects should exchange information about the (opposite) states of each other before getting into active interaction. The explanation led to the loss of an invariance property. However, this loss has been restored by introducing a new physical property (isotopic field-charge spin), by proving its conservation, and completing the Lorentz invariance with the respective invariance attributed to the newly proven conservation. References Bethe, H., Fermi, E., Über die Wechselwirkung von zwei elektronen, Zeitschrift für Physik, 77 (1932), 5-6, 296-306. Darvas, G., The Isotopic Field Charge Spin Assumption, International Journal of Theoretical Physics, 50 (2011), 10, 2961-2991.DOI: 10.1007/s10773-011-0796-9 Darvas, G., The Isotopic Field-Charge Assumption Applied to the Electromagnetic Interaction, Int J Theor Phys, 52 (2013a), 11, 3853-3869, DOI 10.1007/s10773-013-1693-1. Darvas, G., A symmetric adventure beyond the Standard Model – Isotopic field-charge spin conservation in the electromagnetic interaction, Symmetry: Culture and Science, 24 (2013b), 1-4, 17-40. Darvas, G., Electromagnetic Interaction in the Presence of Isotopic Field-Charges and a Kinetic Field, Int J Theor Phys, 53 (2014), 1, 39-51, DOI 10.1007/s10773-013-1781-2. Einstein, A., Zur Elektrodynamik bewegter Körper, Annalen der Physik, 17:891 (1905); English translation: On the electrodynamics of moving bodies, in: The Principle of Relativity, (1923), London: Methuen and Co. Møller, C., Über den Stoß zweier Teilchen unter Berücksichtigung der Retardation der Kräfte, Zeitschrift für Physik, 70 (1931), 11-12, 786-795. Noether, E. A., Invariante Variationsprobleme, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen: Mathematisch-physikalische Klasse, (1918) 235-257. Wigner, E.P. , Events, laws of nature and invariance principles, pp. 38-50, in: Wigner, Symmetries and Reflections, Bloomington: Indiana University Press (1967).
The words: determinism, hidden variables, subjectivism, information, objectivism, informational-theoretic axioms,observers have some connection with physical reality? What we mean with "description" of physical reality? When we say that we understand this reality? Certain parameters:position, velocity are sufficient? We will focus only to conceptual considerations regarding the relation between the "questions" and the relative "answers" in general and specifically in quantum mechanics. It is usually believed that the answers are more important of the questions, for this reason we can read many answers everywhere and in different field of knowledge. We need to add and clarify some things: (i) usually an answers require a question, (ii) but, as we know, their relation is not so simple and immediate, (iii) For instance: a)an epistemic questions give us ontic answers? b)the answer has a connection with the question and vice versa? c)we could to infer a question starting from an answer? d)there are answers without questions? These answers could be in some framework considered as ontic answers? The relative scientific works are the same time ontic? Speaking of quantum mechanics we see around many answers in the meantime we do not see the correspondent questions, these answers seem completely independent, and this seem a right road, the road of the independent nature unlinked from human thoughts. We retain instead that questions can affect the possible answers. Exist "something" before the question?
Although the interpretation of the concept of information is not clear, even in the classical framework, new interpretive problems have arisen with the advent of the so-called quantum information, which combine the difficulties in understanding the concept of information with the well-known foundational puzzles derived from quantum mechanics itself. The aim of this paper is to consider some arguments traditionally put forward to support the idea that quantum information is qualitatively different from classical information. The final conclusion is that there are no reasons to admit the existence of quantum information as qualitatively different from classical information: there is only one kind of information, physically neutral, which can be encoded by means of classical or quantum states.