Classical reality is described in terms of objects and things and their mutual relationships. On the other hand, in the case of quantum reality, the collapse of the state in an interaction assigns a unique position to the observer. These two disparate views are based on different logics of representation. In this paper, we first summarize the early evolution of these ideas and then go beyond the implicit dependence of the quantum theory framework on the mathematical apparatus of calculus and vector spaces, by delving one layer deeper to an information-theoretic understanding of symbol representation. We examine some epistemic implications of the fact that, mathematically, e-symbol representation is optimal and 3 symbols are more efficient that 2 symbols, and this optimality leads to the idea that space itself is e-dimensional, and not 3-dimensional. We also discuss the principle of veiled nonlocality as a way to understand the split between the observer and the physical process.
Classical reality is described in terms of objects and things and their mutual relationships. On the other hand, in the case of quantum reality, the collapse of the state in an interaction assigns a unique position to the observer. These two disparate views are based on different logics of representation. In this paper, we first summarize the early evolution of these ideas and then go beyond the implicit dependence of the quantum theory framework on the mathematical apparatus of calculus and vector spaces, by delving one layer deeper to an information-theoretic understanding of symbol representation. We examine some epistemic implications of the fact that, mathematically, e-symbol representation is optimal and 3 symbols are more efficient that 2 symbols, and this optimality leads to the idea that space itself is e-dimensional, and not 3-dimensional. We also discuss the principle of veiled nonlocality as a way to understand the split between the observer and the physical process.
Classical reality is described in terms of objects and things and their mutual relationships. On the other hand, in the case of quantum reality, the collapse of the state in an interaction assigns a unique position to the observer. These two disparate views are based on different logics of representation. In this paper, we first summarize the early evolution of these ideas and then go beyond the implicit dependence of the quantum theory framework on the mathematical apparatus of calculus and vector spaces, by delving one layer deeper to an information-theoretic understanding of symbol representation. We examine some epistemic implications of the fact that, mathematically, e -symbol representation is optimal and 3 symbols are more efficient that 2 symbols, and this optimality leads to the idea that space itself is e -dimensional, and not 3-dimensional. We also discuss the principle of veiled nonlocality as a way to understand the split between the observer and the physical process.
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
Our sense of reality is different from its mathematical basis as given by physical theories. Although nature at its deepest level is quantum mechanical and nonlocal, it appears to our minds in everyday experience as local and classical. Since the same laws should govern all phenomena, we propose this difference in the nature of perceived reality is due to the principle of veiled nonlocality that is associated with consciousness. Veiled nonlocality allows consciousness to operate and present what we experience as objective reality. In other words, this principle allows us to consider consciousness indirectly, in terms of how consciousness operates. We consider different theoretical models commonly used in physics and neuroscience to describe veiled nonlocality. Furthermore, if consciousness as an entity leaves a physical trace, then laboratory searches for such a trace should be sought for in nonlocality, where probabilities do not conform to local expectations.
According to the no-signaling theorem, the nonlocal collapse of the wavefunction of an entangled particle by the measurement on its twin particle at a remote location cannot be used to send useful information. Given that experiments on nonlocal correlations continue to have loopholes, we propose a stronger principle that the nonlocality of quantum mechanics itself is veiled. In practical terms, decoherence and noise compels us to view the wavefunction as representing knowledge of potential outcomes rather than the reality. Experimental evidence in favor of naked nonlocality would support the view of the wavefunction as an objective description of physical reality.
The Semiotic Interpretation (SI) of QM pushes further the Von Neumann point of view that `experience only makes statements of this type: an observer has made a certain observation; and never any like this: a physical quantity has a certain value.' The supposition that the observables of a system `possess' objective values is purely idealistic. According to the SI view, the state- vector collapse cannot result from the Schroedinger evolution of a system (even with its environment), but only from the empirical production of a mathematical symbol, irreducible to the quantum level. The production of a symbol always takes some time. Thus the state-vector collapse cannot be instantaneous (Schneider 1994), a specific prediction of the present model. From this interpretation of Quantum Mechanics, the appearances of the body are the result of state-vector collapses of several types, i.e. the production of different kinds of symbols. In fact the universe of symbols is very rich: a symbol can have a conceptual `value' (like in physics and then give rise to a measurement), or other qualitative values (like in many human behaviors). In the latter case, the Semiotic Interpretation of QM gives a way to understand how a mental representation can modify the state of the body.
The concept of information is not different in quantum theory from its counterpart in classical physics: a sui generis quantum information concept is not needed. However, the quantum world is radically different from its classical counterpart. This difference in structure of the material world has important consequences for the amounts of information that can be stored in physical systems and for the possibilities of information transfer. In many cases, overlap between quantum states (non-orthogonality of states) blurs distinctions and impedes efficient information transfer. However, the other typical quantum feature, entanglement, makes new and seemingly mysterious ways of transporting information possible. In this article, we suggest an interpretational scheme of quantum mechanics in terms of perspectival physical properties that may provide an intelligible account of these novel quantum possibilities, while staying close to the mathematical formalism of quantum mechanics.