In this work, we derive the standard formalism of quantum theory by analyzing the behavior of single-variable systems under measurements. These systems, with minimal information capacity, exhibit indeterministic behavior in independent measurements while yielding probabilistically predictable outcomes in dependent measurements. Enforcing probability conservation in the probability transformations leads to the derivation of the Born rule, which subsequently gives rise to the Hilbert space structure and the Schrödinger equation. Additionally, we show that preparing physical systems in coherent states —crucial for observing (...) quantum phenomena— effectively reduces the number of independent variables to one. This first-principles derivation of quantum theory from probability conservation in single-variable systems offers new insights into the physical meaning of quantum theory and clarifies its domain of applicability. (shrink)

The mathematical formalism of quantum theory has been established for nearly a century, yet its physical foundations remain elusive. In recent decades, connections between quantum theory and information theory have garnered increasing attention. This study presents a physical derivation of the mathematical formalism quantum theory based on information-theoretic considerations in physical systems. We postulate that quantum systems are characterized by single independent adjustable variables. Utilizing this physical postulate along with the conservation of total probability, we derive the standard Hilbert space (...) formalism of quantum theory, including the Born probability rule. This comprehensive derivation of quantum theory offers a clear and concise physical foundation for the mathematical formalism of quantum mechanics. (shrink)

The relationship between language and consciousness has been debated since ancient times, but the details have never been fully articulated. Certainly, there are animals that possess the same essential auditory and vocal systems as humans, but acquiring language is seemingly uniquely human. In this essay, we investigate the relationship between language and consciousness by demonstrating how language usage implies the self-awareness of the user. We show that the self-awareness faculty encompasses the language faculty and how this self-awareness, that is uniquely (...) human, enables us to create social realities through utilizing the social character of the language. We conclude that it is self-awareness that empowers humans to form collective intentionality and to structure societies. Establishing the relationship between self-awareness, language and society sheds light on connections between philosophy of mind, philosophy of language and philosophy of society. (shrink)

The number of independent messages a physical system can carry is limited by the number of its adjustable properties. In particular, systems that have only one adjustable property cannot carry more than a single message at a time. We demonstrate this is the case for the single photons in the double-slit experiment, and the root of the fundamental limit on measuring the complementary aspect of the photons. Next, we analyze the other ‘quantal’ behavior of the systems with a single adjustable (...) property, such as noncommutativity and no-cloning. Finally, we formulate a mathematical theory to describe the dynamics of such systems and derive the standard Hilbert-space formalism of quantum mechanics. Our derivation demonstrates the physical foundation of the quantum theory. (shrink)

Simultaneous observation of the wave-like and particle-like aspects of the photon in the double-slit experiment is unallowed. The underlying reason behind this limitation is not understood. In this paper, we explain this unique behavior by considering the communicational properties of the photons. Photons have three independently adjustable properties (energy, direction, and spin) that can be used to communicate messages. The double-slit experiment setup fixes two of these properties and confines the single photon’s capacity for conveying messages to no more than (...) one message. With such a low communication capacity, information theory dictates that measurements associated only with one proposition can obtain consistent results, and a second measurement associated with an independent proposition must necessarily lead to randomness. In the double-slit example, these are the wave or particle properties of the photon. The interpretation we offer is based on the formalism of information theory and does not make use of Heisenberg’s uncertainty relation in any form. (shrink)

Physical systems can store information and their informational properties are governed by the laws of information. In particular, the amount of information that a physical system can convey is limited by the number of its degrees of freedom and their distinguishable states. Here we explore the properties of the physical systems with absolutely one degree of freedom. The central point in these systems is the tight limitation on their information capacity. Discussing the implications of this limitation we demonstrate that such (...) systems exhibit a number of features, such as randomness, no-cloning, and non-commutativity, which are peculiarities attributed to quantum mechanics (QM). After demonstrating many astonishing parallels to quantum behavior, we postulate an interpretation of quantum physics as the physics of systems with a single degree of freedom. We then show how a number of other quantum conundrum can be understood by considering the informational properties of the systems and also resolve the EPR paradox. In the present work, we assume that the formalism of the QM is correct and well-supported by experimental verification and concentrate on the interpretational aspects of the theory. (shrink)