Introduction Does Schrödinger's wave function describe physical reality (“it” in John Wheeler's terminology (Wheeler 1994)) or some kind of information (“bit”)? The answer to this question must crucially depend on the definition of these terms. Is it then merely a matter of words? Not quite – I feel. Inappropriate words may be misleading, while reasonably chosen terms are helpful. A bit is usually understood as the binary unit of information, which can be physically realized in (classical) computers, but also by neuronal states of having fired or not. This traditional physical (in particular, thermodynamical) realization of information (“bit from it”) has proven essential in order to avoid paradoxes otherwise arising from situations related to Maxwell's demon. On the other hand, the concept of a bit has a typical quantum aspect: the very word quantum refers to discreteness, while, paradoxically, the quantum bit is represented by a continuum (the unit sphere in a two-dimensional Hilbert space) – more similar to an analog computer. If this quantum state describes “mere information,” how can there be real quantum computers that are based on such superpositions of classical bits? The problematic choice of words characterizing the nature of the wave function (or a general “quantum state”) seems to reflect the common uneasiness of physicists, including the founders of quantum theory, about its fundamental meaning. However, it may also express a certain prejudice.
Introduction Does Schrödinger's wave function describe physical reality (“it” in John Wheeler's terminology (Wheeler 1994)) or some kind of information (“bit”)? The answer to this question must crucially depend on the definition of these terms. Is it then merely a matter of words? Not quite – I feel. Inappropriate words may be misleading, while reasonably chosen terms are helpful. A bit is usually understood as the binary unit of information, which can be physically realized in (classical) computers, but also by neuronal states of having fired or not. This traditional physical (in particular, thermodynamical) realization of information (“bit from it”) has proven essential in order to avoid paradoxes otherwise arising from situations related to Maxwell's demon. On the other hand, the concept of a bit has a typical quantum aspect: the very word quantum refers to discreteness, while, paradoxically, the quantum bit is represented by a continuum (the unit sphere in a two-dimensional Hilbert space) – more similar to an analog computer. If this quantum state describes “mere information,” how can there be real quantum computers that are based on such superpositions of classical bits? The problematic choice of words characterizing the nature of the wave function (or a general “quantum state”) seems to reflect the common uneasiness of physicists, including the founders of quantum theory, about its fundamental meaning. However, it may also express a certain prejudice.
It is broadly believed that everything in the universe is found to be made from a few basic building blocks called fundamental particles, governed by four fundamental forces. However, physicists such as John Archibald Wheeler suggested that information is fundamental to the physics of the universe. According to this it from bit doctrine, all things physical are information-theoretic in origin. This doctrine is based in the old Copenhagen interpretation of quantum mechanics; an interpretation which is internally inconsistent and no applicable to the cosmos as a whole. Modern consistent interpretations of quantum mechanics eliminate the old myths about measurement processes and observers' consciousness and reintroduce the idea of a wholly physical reality, invalidating the it from bit doctrine. Utilizing a new phase space formulation of quantum mechanics developed recently by the author, the concepts of bit and it are reconsidered. We introduce the new states D as quantum bits and the new Hamiltonians H as quantum its. The new concepts of it and bit introduced in this work have a well-defined and rigorous definition, unlike Wheeler's concepts. Moreover, the new concepts apply on situations where the traditional wavefunction theory does not work. The it H is not derivable from the bit D and, as a consequence, the old it from bit doctrine gets substituted by the new it and bit. After showing why the physical entropy used in the science of thermodynamics is not a measure of the ignorance of human observers, the final part of this Essay is devoted to emphasize the importance that the bit acquires in modern science when confronted to the delicious multiplicity of the far-from-equilibrium regimes, where the certainty of Newtonian and Schrodinger motion begin to fade in favour of a complex non-geometrical, 'living', conception of Nature: an it and bit conception.
The concept of quantum information is introduced as both normed superposition of two orthogonal subspaces of the separable complex Hilbert space and invariance 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 representable 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 invariance 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 𝑈𝑈(1), 𝑆𝑆𝑆 (2), and 𝑆𝑆𝑆 (3) of the Standard model.
Introduction Of John Wheeler's “Really Big Questions,” the one on which the most progress has been made is “It from bit?” – does information play a significant role at the foundations of physics? It is perhaps less ambitious than some of the other questions, such as “How come existence?”, because it does not necessarily require a metaphysical answer. And unlike, say, “Why the quantum?”, it does not require the discovery of new laws of nature: there was room for hope that it might be answered through a better understanding of the laws as we currently know them, particularly those of quantum physics. And this is what has happened: the better understanding is the quantum theory of information and computation. How might our conception of the quantum physical world have been different if “It from bit” had been a motivation from the outset? No one knows how to derive it (the nature of the physical world) from bit (the idea that information plays a significant role at the foundations of physics), and I shall argue that this will never be possible. But we can do the next best thing: we can start from the qubit. Qubits To a classical information theorist, a bit is an abstraction: a certain amount of information. To a programmer, a bit is a Boolean variable. To an engineer, a bit is a “flip-flop” – a piece of hardware that is stable in either of two physical states.
Quantum mechanics was reformulated as an information theory involving a generalized kind of information, namely quantum information, in the end of the last century. Quantum mechanics is the most fundamental physical theory referring to all claiming to be physical. Any physical entity turns out to be quantum information in the final analysis. A quantum bit is the unit of quantum information, and it is a generalization of the unit of classical information, a bit, as well as the quantum information itself is a generalization of classical information. Classical information refers to finite series or sets while quantum information, to infinite ones. Quantum information as well as classical information is a dimensionless quantity. Quantum information can be considered as a “bridge” between the mathematical and physical. The standard and common scientific epistemology grants the gap between the mathematical models and physical reality. The conception of truth as adequacy is what is able to transfer “over” that gap. One should explain how quantum information being a continuous transition between the physical and mathematical may refer to truth as adequacy and thus to the usual scientific epistemology and methodology. If it is the overall substance of anything claiming to be physical, one can question how different and dimensional physical quantities appear. Quantum information can be discussed as the counterpart of action. Quantum information is what is conserved, action is what is changed in virtue of the fundamental theorems of Emmy Noether (1918). The gap between mathematical models and physical reality, needing truth as adequacy to be overcome, is substituted by the openness of choice. That openness in turn can be interpreted as the openness of the present as a different concept of truth recollecting Heidegger’s one as “unconcealment” (ἀλήθεια). Quantum information as what is conserved can be thought as the conservation of that openness
Quantum mechanics was reformulated as an information theory involving a generalized kind of information, namely quantum information, in the end of the last century. Quantum mechanics is the most fundamental physical theory referring to all claiming to be physical. Any physical entity turns out to be quantum information in the final analysis. A quantum bit is the unit of quantum information, and it is a generalization of the unit of classical information, a bit, as well as the quantum information itself is a generalization of classical information. Classical information refers to finite series or sets while quantum information, to infinite ones. Quantum information as well as classical information is a dimensionless quantity. Quantum information can be considered as a “bridge” between the mathematical and physical. The standard and common scientific epistemology grants the gap between the mathematical models and physical reality. The conception of truth as adequacy is what is able to transfer “over” that gap. One should explain how quantum information being a continuous transition between the physical and mathematical may refer to truth as adequacy and thus to the usual scientific epistemology and methodology. If it is the overall substance of anything claiming to be physical, one can question how different and dimensional physical quantities appear. Quantum information can be discussed as the counterpart of action. Quantum information is what is conserved, action is what is changed in virtue of the fundamental theorems of Emmy Noether (1918). The gap between mathematical models and physical reality, needing truth as adequacy to be overcome, is substituted by the openness of choice. That openness in turn can be interpreted as the openness of the present as a different concept of truth recollecting Heidegger’s one as “unconcealment” (ἀλήθεια). Quantum information as what is conserved can be thought as the conservation of that openness.
Whoever it was who first contracted the words 'binary digit' to form 'bit' can hardly have realised that he (she?) was coining a term not only for the smallest unit of information but also for the smallest unit of 'being' – or so the general relativist John Archibald Wheeler would have us believe. 'It from bit' is his declamation of the ultimate fount of significance of every physical quantity: all we can know about photons, fields, black holes – you name 'it' – depends at root, he emphasizes, on yes-or-no indications. Pursuing the implications of this observation through quantised strings, quantum measurement theory, computational representations of physical laws, information theory, thermodynamic entropy, evolution... those, he says, are routes to that happy state of perceived simplicity and beauty when we finally know the Final Answer to the question: 'How come existence?'