ON THE NOTION OF PROPOSITION IN CLASSICAL AND QUANTUM MECHANICS

When the 5th Solvay conference on quantum theory took place in Brussels in 1927, the quantum community had undergone 2 years of rapid development and intense debate. Within the period from 1925 to 1927, matrix and wave mechanics had been developed independently of each other. The two theories were proven to be mathematically equivalent and turned out to be two formulations of an overarching quantum mechanical formalism. During this time, the new theories were applied to various problems that had long resisted solution and extended to new phenomena that were beyond their initial scope. Concurrently with this development, the proponents of wave mechanics and matrix mechanics, Erwin Schrodinger, Werner Heisenberg and the physicists from Gottingen and Copenhagen, first entered a heated debate on the meaning of quantum mechanics. At the heart of their discussion were the fundamental changes that the new quantum mechanics implied for physical theories in general. Basic elements of classical mechanics and the old quantum theory, such as the ability to visualize an abstract mathematical formalism in space and time, were missing in the developing theory. It was uncertain whether quantum mechanics in general could be understood in these terms, well established in classical mechanics. At first, the founders of matrix mechanics, Werner Heisenberg, Max Born and Pascual Jordan, found these questions rather unimportant. They believed, that the abstract mathematical formalism of quantum mechanics provided all that was required from a physical theory, and that the lack of physical models was unavoidable. Erwin Schrodinger and Louis de Broglie, on the other hand, were unwilling to accept the abandonment of the former aims of the physical theory and questioned whether progress within quantum mechanics was even possible without the most powerful tools for understanding natural phenomena.

Classical statistical average values are generally generalized to average values of quantum mechanics. It is discovered that quantum mechanics is a direct generalization of classical statistical mechanics, and we generally deduce both a new general continuous eigenvalue equation and a general discrete eigenvalue equation in quantum mechanics, and discover that a eigenvalue of quantum mechanics is just an extreme value of an operator in possibility distribution, the eigenvalue f is just classical observable quantity. A general classical statistical uncertain relation is further given, and the general classical statistical uncertain relation is generally generalized to the quantum uncertainty principle; the two lost conditions in classical uncertain relation and quantum uncertainty principle, respectively, are found. We generally expound the relations among the uncertainty principle, singularity and condensed matter stability, discover that the quantum uncertainty principle prevents the appearance of singularity of the electromagnetic potential between nucleus and electrons, and give the failure conditions of the quantum uncertainty principle. Finally, we discover that the classical limit of quantum mechanics is classical statistical mechanics, the classical statistical mechanics may further be degenerated to classical mechanics and we discover that merely stating that the classical limit of quantum mechanics is classical mechanics is a mistake. As application examples, we deduce both the Schrödinger equation and the state superposition principle, and deduce that there exists a decoherent factor from a general mathematical representation of the state superposition principle; the consistent difficulty between statistical interpretation of quantum mechanics and determinant property of classical mechanics is overcome.

A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's information regarding a physical system. This is seen as the main difference from classical mechanics, where an observer's information regarding a physical system obeys classical probability theory. Quantum mechanics is then viewed purely as a mathematical framework for the probabilistic description of noncommutative information, with the projection postulate being a noncommutative generalization of conditional probability. This view clarifies many problems surrounding the interpretation of quantum mechanics, particularly problems relating to the measuring process.

Two types of prediction in Newtonian and quantum mechanics

Different approaches to the study of open linear freely-jointed (unhindered) threedimensional macromolecular chains at thermal equilibrium, based upon either Classical Hamiltonian Dynamics with constraints (namely, a formulation equivalent to Kramers' one) or Quantum Mechanics (with stiff harmonic springs), are reviewed and discussed in detail. Results from those approaches are compared to those arising from the standard Gaussian model. Fraenkel's approach, based upon Classical Mechanics (with stiff harmonic springs) and its comparison with the Gaussian model are also treated. It is argued that the quantum formulation is required in order that the treatment of the high-frequency vibrations be consistent. The role of the uncertainty principle is discussed, in support of the quantum-mechanical approach. At a later stage, internal rotations can be treated through Classical Statistical mechanics, under certain conditions. The quantum-Mechanics-based model appears to be consistent with the Gaussian model, while the one based upon constrained Hamiltonian Dynamics yields certain discrepancies with the latter. Classical and quantum-mechanical approaches to open linear freely-rotating (hindered) threedimensional macromolecular chains are also treated: the consistency of the quantum-mechanics-based model is displayed by deriving approximately the existence of a persistence length. It is argued that the possible advantages of the quantum-mechanical formulation should be expected not at large scales but at shorter ones. The specific topics to be treated are described in the summary of contents given below.

One of the most striking features of quantum mechanics is the profound effect exerted by measurements alone. Sophisticated quantum control is now available in several experimental systems, exposing discrepancies between quantum and classical mechanics whenever measurement induces disturbance of the interrogated system. In practice, such discrepancies may frequently be explained as the back-action required by quantum mechanics adding quantum noise to a classical signal. Here, we implement the "three-box" quantum game [Aharonov Y, et al. (1991) J Phys A Math Gen 24(10):2315-2328] by using state-of-the-art control and measurement of the nitrogen vacancy center in diamond. In this protocol, the back-action of quantum measurements adds no detectable disturbance to the classical description of the game. Quantum and classical mechanics then make contradictory predictions for the same experimental procedure; however, classical observers are unable to invoke measurement-induced disturbance to explain the discrepancy. We quantify the residual disturbance of our measurements and obtain data that rule out any classical model by ≳7.8 standard deviations, allowing us to exclude the property of macroscopic state definiteness from our system. Our experiment is then equivalent to the test of quantum noncontextuality [Kochen S, Specker E (1967) J Math Mech 17(1):59-87] that successfully addresses the measurement detectability loophole.

The irreversible process of ‘wave packet collapse’ in quantum measurement contradicts the reversible characteristics of the Schrödinger equation and the entire quantum mechanics. This contradiction is actually the origin of measurement problems in quantum mechanics. How to resolve this contradiction is related to the understanding of some philosophical concepts. The Copenhagen School embraces the reversible/irreversible contradictions in quantum measurement through the principle of complementarity. Both von Neumann's measurement hypothesis and Everett's many world explanation adhere to the ‘universal position of the Schrödinger equation’, but due to their detachment from the thermodynamic mechanism analysis of quantum measurement processes, they fall into the dilemma of subjectivism or possible state materialization in ontology. Decoherence theory is a natural extension of dissipative structure theory in quantum mechanics, which helps to solve quantum measurement problems by combining the study of classical conversion mechanisms between reversibility and irreversibility in statistical mechanics. Due to the common statistical roots of the time arrow problem in classical mechanics and quantum mechanics, decoherence theory cannot be seen as a measurement theory that fully implements the ‘universal Schrödinger position’. Many contradictions in quantum mechanics may need to be cleverly resolved through various contradictions in classical physics.

Human-Brain Artificial-Intelligence Matrix  is a new technology that aims to connect the human brain with the machine in order to enable the human brainto perform defined functions even if it becomes unable to perform them such as performing the function of vision in case of blindness, the function of hearing in case of deafness, Performing the function of motion in case of paralysis and many other functions.  This technology will be based on the Cognition Theory, in which I suggest that the entire cognition process may be treated quantum-mechanically. Quantum mechanics  is  a  cornerstone  theory in physics that concerns with a description of any physical phenomena at the scale of atoms and subatomic particles. The interactions inside the nervous system are mediated by the action potential, which is in its simplest model, can be described as a bunch of electrons; sort of the subatomic particles. Hence, this phenomena is within the scale which is properly described by Quantum mechanics. The cognition starts when a neuron sends data to be processed in the brain and ends in an effector to respond. The data “action potential” is a current of particles which can be described quantum-mechanically as a wave-impulse based on the dual nature of the particles. In both classical and quantum mechanics, neurons are a network of entangled cells. Quantum mechanical potential wells and barriers are created when the action potential modifies the potential of the neurons. The action potential perfectly transmits in and out the neurons through quantum mechanical tunnels. The form of energy before processing is not the same after, but the amount of energy is always conserved. Since the neurons are entangled during the action potential transmission, the brain and effector will be entangled during the action potential processing. The effector’s cognition of data must be a discrete cognition of single-valued data from its self-adjoint matrix which entangled with brain matrix.

Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se, suffers from a very limited understanding that is even more severe than that of quantum mechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces.

There is a great deal of justified concern about continuity through scientific theory change. Our thesis is that, particularly in physics, such continuity can be appropriately captured at the level of conceptual frameworks (the level above the theories themselves) using conceptual space models. Indeed, we contend that the conceptual spaces of three of our most important physical theories—Classical Mechanics (CM), Special Relativity Theory (SRT), and Quantum Mechanics (QM)—have already been so modelled as phase-spaces. Working with their phase-space formulations, one can trace the conceptual changes and continuities in transitioning from CM to QM, and from CM to SRT. By offering a revised severity-ordering of changes that conceptual frameworks can undergo, we provide reasons to doubt the commonly held view that CM is conceptually closer to SRT than QM.

In this paper, Prof, van Fraassen proposes a formal model for a class of physical theories which generalizes the formalisms used in classical and quantum mechanics. He shows how semantic analysis of his model, inspired by the work of Beth, leads to a study of the logic of the theory, here defined as the study of the relations of validity and entailment between the propositions, or elementary statements, of the theory and their logical compositions. He shows that this logic, or rather these logics, share many features with the quantum logics which have been the subject of much recent discussion. He is thus led to raise the question whether there is anything very useful about the quantum logic approach to quantum theory, since many of its features are not specific to that theory.

In the present work, I discuss the interpretation of quantum mechanics (QM) from the viewpoint of quantum logic (QL). I regard the objects of QL to be the possible (accidental) properties that can be ascribed to a quantum system SYS. The basic idea is that, at any given moment t, SYS actualizes some properties, but not others. The micro-state of SYS at time t is identified with the set of all properties that SYS actualizes at time t.One thing an interpretation of QM is supposed to do, I believe, is delineate the admissible quantum micro-states. Since the characterization of quantum micro-states is intimately related to the characterization of quantum logical consistency, the interpretation of QM is intimately tied to the interpretation of QL.Two kinds of interpretations are discussed. Strict interpretations are based on the assumption that the properties of a system are individuated by the projection operators on the associated Hilbert space.

With considerable interest I read the article “Bohr’s molecular model, a century later” by Anatoly Svidzinsky, Marlan Scully, and Dudley Herschbach (Physics Today, January 2014, page 33). It is always interesting to see how our current understanding sheds new light on the revolutionary scientific ideas of the past. I agree with the authors that although quantum mechanics is the real basis for atomic- and molecular-physics computations, the old Bohr model that treats electrons in atoms like tiny planets moving around the sun-nucleus is intuitively clear and very attractive.As I see it, the aim of the article is to show how to use Bohr’s approach to treat not only simple atoms but molecules. An important point in that approach is reconciliation of quantum mechanics with Bohr’s ideas. The authors claim that in infinite dimensions, quantum mechanics “morphs into classical mechanics.”I cannot say, however, that the infinite-dimension system is a clarifying model to describe physical or chemical objects. I do not see that the reference to chromodynamics (and to Edward Witten’s article in Physics Today, July 1980, page 38) is a clarifying one. Far from convincing are statements like “Hence the large-D limit, where 1/D → 0, is closer to the real world (1/D = 1/3) than is the oft-used D = 1 regime. Indeed, results obtained at large D usually resemble those for D = 3.” I confess it sounds too lacking in rigor to be convincing.But the large-D limit per se is not what bothers me. Of great concern is the assumption that the radial part of the D-dimensional Schrödinger equation in Hartree units looks like this:(1)where Z is the nuclear charge and l is the angular momentum.Equation (1) has no sense for D = 1. Indeed, in one dimension, a finite angular momentum requires infinite speed of a rotating particle. Therefore, for D = 1, the correct equation is(2)which does not follow from equation (1) at D = 1.But most important is that equation (1) implies that the Coulomb potential does not depend on D. That could have been considered correct before it became clear that the Coulomb law follows from Maxwell’s equations when one considers a field generated by a point-like electric charge. So to obtain the Coulomb law for a two-dimensional space, one has to consider Maxwell equations in a two-dimensional world. For a point-like charge, those equations lead to a 1/(ln r) instead of 1/r dependence. If one takes into account the D-dependence of the Coulomb potential, derivations performed in the Physics Today article become meaningless. Indeed, when using an unrealistic equation (1), how can one believe that it illuminates Bohr’s quite realistic and physical postulates?© 2014 American Institute of Physics.

The Weyl representation in classical and quantum mechanics

Problem- There are deep unanswered questions about photon emission, specifically how the field structures of the photon emerge from the electron. While this problem cannot be answered from within quantum mechanics, due to its premise that particles are zero dimensional points, other theories of physics have better prospects. Purpose- A conceptual theory is developed for the processes of photon emission and absorption, in a non-local hidden-variable (NLHV) design called the Cordus theory. Approach- Logical inference is used to predict the structures of the discrete fields of the photon and electron under this framework. From this is extracted an explanation of how electron bonding constraints require the electron to emit its excess energy, and how the photon is created and emerges from the electron. Findings- Emission is found to be an escapement mechanism whereby matter particles that are over-prescribed in position can get rid of that energy, and the details of this are explained. The results show excellent qualitative agreement with classical electromagnetic wave theory and quantum mechanics, many conceptual features of which can be recovered. Originality- A novel conceptual theory is developed for the processes of photon emission and absorption. Particularly important here is the proposed causality whereby bonding constraints affect geometric span of the particule, which affects frequency. Hence this constrains the energy that the electron can contain, and explains why the emitted photon has a specific quantum of energy. A second contribution is the proposed differentiation between the discrete fields of the photon and electron. This yields an explanation for the exponential nature of the evanescent field, and recovery of the inverse radius squared relationship for the electro-magneto-gravitational fields. The theory also offers a physical interpretation of the fine structure constant α as a measure of the transmission efficacy of the fabric, i.e. α determines the relationship between the electric constant of the vacuum fabric, and the speed of propagation c through the fabric. There is further novelty in achieving this from the non-local hidden-variable sector of physics. Implications- Quantum mechanics originated with the observation that the movement of electrons between orbitals resulted in emission of photons with discrete quanta of energy. However it does not explain how the transitions occur. The original contribution here is showing that a solution does exist in NLHV physics. Assuming this is valid then the implications are that particles have internal structure and that quantum mechanics is merely a quantitative statistical summary of a deeper physics.