Lying in the core of the conceptual scheme of current quantum theory, the notion of quantum superposition is a consequence of the quantum-mechanical superposition principle. However, relying on precise but not attainable space or time coordinates, quantum superposition makes little sense physically if we use it to describe or explain experimental results obtained by measurement. Space or time is usually modeled by a metric space endowed with the usual distance function. Irrelevant to instrument precision and measurement accuracy, unattainability of precise coordinates is a well-established mathematical fact following from properties of the corresponding metric topology, and hence rules out completely, in principle, the possibility for us to obtain precise coordinates by measurement in actually performed experiments. In classical mechanics, unattainability of precise coordinates is hardly noticeable, and measurement results obtained in classical physics can still be reasonably explained even though precise coordinates are unattainable. However, when we explain measurement results obtained in quantum physics, unattainability of precise coordinates should not be omitted. In the conceptual scheme of current quantum theory, omission of unattainability of precise coordinates is an unfortunate flaw, which is largely responsible not only for the invalidity of quantum superposition in description of the physical world but also for various ineligible applications of quantum mechanics. Nevertheless, in no sense does the flaw imply quantum mechanics as a successful theory failing to be correct. As shown in this article, the flaw is repairable. By taking into account unattainability of precise coordinates, we can reinterpret the meaning of quantum superposition to repair the flaw without affecting eligible applications of quantum mechanics while avoiding all the ineligible applications.
Lying in the core of the conceptual scheme of current quantum theory, the notion of quantum superposition is a consequence of the quantum-mechanical superposition principle. However, relying on precise but not attainable space or time coordinates, quantum superposition makes little sense physically if we use it to describe or explain experimental results obtained by measurement. Space or time is usually modeled by a metric space endowed with the usual distance function. Irrelevant to instrument precision and measurement accuracy, unattainability of precise coordinates is a well-established mathematical fact following from properties of the corresponding metric topology, and hence rules out completely, in principle, the possibility for us to obtain precise coordinates by measurement in actually performed experiments. In classical mechanics, unattainability of precise coordinates is hardly noticeable, and measurement results obtained in classical physics can still be reasonably explained even though precise coordinates are unattainable. However, when we explain measurement results obtained in quantum physics, unattainability of precise coordinates should not be omitted. In the conceptual scheme of current quantum theory, omission of unattainability of precise coordinates is an unfortunate flaw, which is largely responsible not only for the invalidity of quantum superposition in description of the physical world but also for various ineligible applications of quantum mechanics. Nevertheless, in no sense does the flaw imply quantum mechanics as a successful theory failing to be correct. As shown in this article, the flaw is repairable. By taking into account unattainability of precise coordinates, we can reinterpret the meaning of quantum superposition to repair the flaw without affecting eligible applications of quantum mechanics while avoiding all the ineligible applications.
Lying at the heart of quantum mechanics, the notion of quantum superposition causes enormous difficulty in understanding the problem of quantum measurement, which concerns the Einstein-Bohr debate on the conceptual foundations of the quantum theory. According to Bell’s theorem, Einstein’s viewpoint in his debate with Bohr seems to be wrong. In the present paper, a new principle (referred to as the general principle of measurements) is introduced and proved as a mathematical theorem. Based on this principle, various forms of quantum superposition (including quantum entanglement) and the corresponding experiments are scrutinized. The main findings are as follows. (a) Einstein’s viewpoint is correct and Bell’s theorem is problematic. (b) Measurement outcomes of any actual experiment with individual microscopic objects described in a form of quantum superposition, in particular, the experimental results of testing Bell inequalities, are all erroneously explained. (c) Bell inequalities failed to capture the essence of the Einstein-Bohr debate, i.e., whether quantum superposition is legitimate for describing individual microscopic objects. (d) All kinds of quantum superposition violate the general principle of measurements and hence are illegitimate. (e) Quantum mechanics can be completed by using disjunction (“or”) as the logical relation between the orthonormal vectors that span an arbitrarily given Hilbert space for describing a single microscopic object, and the mathematical setting will remain essentially unchanged; hidden-variable theories are irrelevant to the real world. (f) After completing quantum mechanics as above, the difficulty in understanding the problem of quantum measurement disappears naturally. Implications of the findings are also discussed.
The basic assumption underlying various quantum information technologies, such as quantum computation and quantum communication, is that qubits are physical objects. However, this assumption is false. A qubit is a quantum superposition, which is a purely mathematical entity in a Hilbert space for description of a two-level quantum system. There is no theoretical or experimental evidence for quantum superpositions in general, and for qubits in particular, having physical counterparts in the real world, although quantum systems themselves are all physical objects. Nevertheless, quantum superpositions failing to be physical objects does not necessarily imply quantum mechanics failing to be correct. Hilbert spaces differ essentially from the three-dimensional Euclidean space; the latter is the model of space in which we live and measure physical quantities. Associated with time or space coordinates, measurements of all quantum systems must be performed in the real world. However, precise time and space coordinates are not attainable by measurement. Based on a comparison between the Euclidean space and Hilbert spaces, this paper shows that no quantum systems in the real world can realize qubits, and hence, quantum information technologies are not physically realizable; their so-called advantages over classical information technologies make little sense.
Quantum Mechanics represents one of the greatest triumphs of the scientific enterprise of the twentieth century. The stunning success of quantum theory has led to many revolutionary inventions and its extraordinary concepts describe the heart of several important real world applications like transistors and lasers. The theory makes accurate predictions about a wide range of physical phenomena and has historically withstood the tests and scrutiny of every experimental investigation. However, inspite of the fact that quantum theory is widely regarded by the scientific establishment as the fundamental theory of nature and is immensly successful and useful, its conceptual framework makes many predictions which are difficult to comprehend “classically. The theory is, pardoxically, powerful and confusing at the same time. Quantum theory’s unusual predictions originate from its basic formailsm which involves concepts like probability amplitudes and the linear superposition principle(Dirac, 1947). The quantum view appears abstract and counterintuitive and at odds with classical perceptions. Many of the conceptual problems of quantum mechanics are encompassed in what is known as the quantum measurement problem(Peres, 1986; von Neumann, 1932; Wheeler & Zurek, 1983). Conventionally, the measurement paradox is supposedly ’resolved’ by forcing a notion of a sudden collapse of the state vector of the system being measured. However, the nature of this mechanism is at odds with the basic tenets of quantum mechanics and hence may lie outside its realm thus questioning the validity of the theory it self. Closely related with the problem of measurement in quantum mechanics is the question of its connection with the emergence of classicality and the elusive boundary between quantum and classical worlds. What is the connection between the ‘classical’ and the ‘quantum’ worlds? Is there a definite relationship? Are classical mechanics and quantum mechanics two mutually exclusive incompatible theories or are they two aspects of the same underlying philosophy? Classical objects are eventually composed of elements of the microworld which can be described quantum mechanically. So, how and where can there be a boundary between the two worlds? In the following section we begin by introducing the quantum measurement problem. In the next section we will discuss attempts to understand and explain away the underlying paradoxes in quantum theory as highlighted in the quantum measurement problem and the question of the quantum-classical connection. From among the various explanations that seek a resolution to the conceptual problems of quantum mechanics, we focus on the ‘environment induced decoherence theory’ an approach that employs the methods developed by several authors to analyse the quantum mechanics of Measurement in Quantum Mechanics: Decoherence and the Pointer Basis
We take it for granted that our physical environment communicates information, making things observable and measurable. However, there are very strong constraints on the fundamental physics of any universe that can do this. Measuring or communicating any kind of information always requires an appropriate interactive context, and these contexts are necessarily complex, involving other kinds of information determined in different contexts. This makes measurement hard to grasp theoretically, since every measurement depends on other kinds of measurements. Even so, we can identify some basic functional requirements for a physics that determines and communicates facts. These are sufficient to explain the peculiar features of quantum mechanics, combining the unitary evolution of superpositions with the mysterious "collapse" that occurs whenever the context allows new facts to be defined. Moreover, the precise determinism of classical physics can be understood on the same basis. It seems likely, in fact, that most of the complexity and fine-tuning we see in our most fundamental theories is needed to make any kind of information measurable.
Quantum theory is the soul of contemporary physics. It was discovered in an adventurous way, under the urge to solve the puzzles posed by atomic spectra and blackbody radiation. But after its invention, it immediately became clear that it was not just a theory of specific physical systems: it was rather a new language of universal applicability. Already in 1928, the theory had received solid mathematical foundations by Hilbert, von Neumann, and Nordheim, and this work was brought to completion in the monumental work of von Neumann, in the form that we still study nowadays. The theory is extraordinarily successful, and its predictions have been confirmed to an astonishing level of precision in a large spectrum of experiments. However, almost 90 years after von Neumann's book, quantum theory remains mysterious. Its mathematical formulation – based on Hilbert spaces and self-adjoint operators – is far from having an intuitive interpretation. The association of physical systems to Hilbert spaces whose unit vectors represent pure states, the representation of transformations by unitary operators and of observables by self-adjoint operators – all such postulates look artificial and ad hoc . A slightly more operational approach is provided by the C * -algebraic formulation of quantum theory – still, this formulation relies on the assumption that observables form an algebra , where the physical meanings of the multiplication and the sum are far from clear. In short, the postulates of quantum theory impose mathematical structures without providing any simple reason for this choice: the mathematics of Hilbert spaces is adopted as a magic blackbox that “works well” at producing experimental predictions. However, in a satisfactory axiomatization of a physical theory the mathematical structures should emerge as a consequence of postulates that have a direct physical interpretation. By this we mean postulates referring, e.g., to primitive notions like physical system, measurement, or process, rather than notions like, e.g., Hilbert space, C * -algebra, unit vector, or selfadjoint operator. The crucial question thus remains unanswered: why quantum theory? Which are the principles at the basis of the theory? A case that is often invoked in contrast is that of Special Relativity theory, which directly follows from the simple understandable principle of relativity.
Considered by Einstein as “the fundamental dice-game”, the quantum-mechanical description of quantum objects in the real world is controversial. According to Einstein’s understanding of the physical world, the quantum-mechanical description is incomplete, but rendering quantum mechanics complete might be possible. Derived by resorting to a hidden-variable theory, Bell inequalities attempted to render quantum mechanics complete somehow. Unfortunately, the attempts all failed. More unfortunately, the failure and the widely accepted but erroneous interpretation of the failure resulted in giving up either or both of locality and realism, the two fundamental hypotheses for scientific research, and hence opened the door to so-called quantum information technologies. Consequently, quantum information technologies all stem from “the fundamental dice-game”. Based on an important mathematical fact irrelevant to any issue about measurement instruments or accuracies of measurement outcomes, namely, precise space and time coordinates are practically unattainable by measurements, which reflects a general principle regarding the nature of measurements (henceforth principle of measurements), this paper reports the following findings: (a) Einstein’s understanding of the physical world is correct. (b) Without resorting to any hidden-variable theory, rendering quantum mechanics complete is possible while keeping the mathematical setting for quantum mechanics (i.e., Hilbert space) essentially unchanged; therefore, eligible applications of quantum mechanics, which are all irrelevant to “the fundamental dice-game”, will also remain unchanged. (c) As fictitious results in “the fundamental dice-game” based on the problematic postulate of quantum superposition in current quantum theory, quantum information technologies are all physically unrealizable. A very regrettable conclusion then follows inevitably from the above findings: An extremely huge amount of time, effort, funding, and investment in realizing physically unrealizable quantum information technologies has been wasted because of “the fundamental dice-game”, which has seriously damaged science!