Classical dynamics is usually considered to be the first level in the development of our understanding of the physical laws in Nature, which today is based on quantum theory. Despite the many successes of quantum theory in describing basic physical phenomena, it is continually running into difficulties in some specific physical situations. Thus, all attempts to quantize the theory of gravity have encountered serious difficulties. In order to find a solution to these problems, it seems to be useful to reconsider the fundamental principles of classical dynamics. In this context, the principles of Hamiltonian dynamics are seen to be of great importance not only for a basic understanding of classical theory, but also for its quantization.
Classical dynamics is usually considered to be the first level in the development of our understanding of the physical laws in Nature, which today is based on quantum theory. Despite the many successes of quantum theory in describing basic physical phenomena, it is continually running into difficulties in some specific physical situations. Thus, all attempts to quantize the theory of gravity have encountered serious difficulties. In order to find a solution to these problems, it seems to be useful to reconsider the fundamental principles of classical dynamics. In this context, the principles of Hamiltonian dynamics are seen to be of great importance not only for a basic understanding of classical theory, but also for its quantization.
Despite its successes, quantum mechanics (QM) has remained mysterious to all who have encountered it. Starting with Bohr and progressing into the present, the departure from intuitive, physical reality has widened. The connection between QM and reality is more than just a “philosophical” issue. It reveals that QM is not a correct or complete theory of the physical world and that inescapable internal inconsistencies and incongruities arise when attempts are made to treat it as physical as opposed to a purely mathematical “tool.” Some of these issues are discussed in a review by F. Laloe [Am. J. Phys. 69, 655 (2001)]. In an attempt to provide some physical insight into atomic problems and starting with the same essential physics as Bohr of e moving in the Coulombic field of the proton and the wave equation as modified by Schrodinger, a classical approach is explored that yields a remarkably accurate model and provides insight into physics on the atomic level. The proverbial view, deeply seated in the wave-particle duality notion, that there is no large-scale physical counterpart to the nature of the electron may not be correct. Physical laws and intuition may be restored when dealing with the wave equation and quantummechanical problems. Specifically, a theory of classical quantum mechanics (CQM) is derived from first principles that successfully applies physical laws on all scales. Rather than using the postulated Schrodinger boundary condition “Ψ → 0 as r → ∞,” which leads to a purely mathematical model of the electron, the constraint is based on experimental observation. Using Maxwell’s equations, the classical wave equation is solved with the constraint that the bound (n = 1)state electron cannot radiate energy. By further application of Maxwell’s equations to electromagnetic and gravitational fields at particle production, the Schwarzschild metric is derived from the classical wave equation, which modifies general relativity to include conservation of spacetime in addition to momentum and matter/energy. The result gives a natural relationship among Maxwell’s equations, special relativity, and general relativity. CQM holds over a scale of spacetime of 85 orders of magnitude — it correctly predicts the nature of the universe from the scale of the quarks to that of the cosmos. A review is given by G. Landvogt [Internat. J. Hydrogen Energy 28, 1155 (2003)].
In only 150 pages, not counting appendices, references, or the index, this book is one author's perspective of the massive theoretical and philosophical hurdles in the no-man's-land separating the classical and quantum domains of physics. It ends with him emphasizing his own theoretical contribution to this area. In his own words, he has attempted to answer: 1. 'How can we obtain the quantum dynamics of open systems initially described by the equations of motion of classical physics (quantization process)? 2. 'How can we retrieve classical dynamics from the quantum mechanical equations of motion by means of a classical limiting process (dequantization process)?' However, this monograph seems overly ambitious. Although the publisher's description refers to this book as 'an accessible entrée', we find that this author scrambles too hastily over the peaks of information that are contained in his large collection of 272 references. Introductory motivating discussions are lacking. Profound ideas are glossed over superficially and shoddily. Equations morph. But no new convincing understanding of the physical world results. The author takes the viewpoint that physical systems are always in interaction with their environment and are thus not isolated and, therefore, not Hamiltonian. This impels him to produce a method of quantization of these stochastic systems without the need of a Hamiltonian. He also has interest in obtaining the classical limit of the quantized results. However, this reviewer does not understand why one needs to consider open systems to understand 'quantum-classical correspondence'. The author demonstrates his method using various examples of the Smoluchowski form of the Fokker--Planck equation. He then renders these equations in a Wigner representation, uses what he terms 'an infinitesimality condition', and associates with a constant having the dimensions of an action. He thereby claims to develop master equations, such as the Caldeira--Leggett equation, without use of a Hamiltonian. However, his procedure is seriously flawed. For example, he considers a case of anomalous Brownian motion using a Kolmogorov stochastic equation, and two cases of Brownian motion, the first with a constant force and the second with a linear force. In each of these three cases, his alleged solutions for a function F(x,p,t), which he wishes to interpret as a probability density, are not in fact solutions of their respective evolution equations. The author, in order to interpret these as probability densities, appears to have obtained the correct solutions of these equations, but then has normalized each of them with a time-dependent function, so that their integrals over the whole phase space remains unity for all time. However, an integration of the original equations over phase space demonstrates that an integral of their solutions over the whole phase space must be time-dependent. Despite the poor editing of this monograph, in which errors in equations abound, and in which the dimensionality of quantities is occasionally incorrect, this reviewer's interest in this subject was not extinguished. We are thus thankful for its extensive bibliography.
The previous chapters contain many examples of the successful application of quantum mechanics to the solution of real physical problems. These represent only a small sample of the wide range of experimental results, spanning just about all areas of physics and chemistry and beyond, that have been successfully explained by quantum theory. So far at least, no quantum-mechanical prediction has been experimentally falsified. Despite these successes, however, many scientists have considered the basic conceptual framework of the subject to be unsatisfactory, and repeated attempts have been made to reinterpret quantum mechanics, or even replace it with a different theory whose philosophical and conceptual basis could be considered more acceptable. In the present chapter we shall explain the reasons for this dissatisfaction and outline some of the reinterpretations and alternative approaches that have been devised. Inevitably many of the questions that arise in this area are matters of opinion rather than fact and, for this reason, some physicists consider that they belong more properly to the realm of philosophy than of physics. However, the conceptual basis of quantum mechanics is so fundamental to our whole understanding of the nature of the physical universe that it should surely be important for physicists to understand the nature of the problems involved, if nothing else.1,2 16.1 THE CONCEPTUAL PROBLEMS In this section we outline some of the main areas of difficulty with a view to more detailed discussion later in the chapter.
Despite the extraordinary successes the two great bastions of 20th century science (Quantum Theory and General Relativity) are troubled with serious conceptual and mathematical difficulties. As a result, further growth of fundamental science is at stake. Is this the end of science? Optimistic answer is ``NOT''! In this work, it is argued that science must continue its cruise, but with anew strategy -- a thorough recourse into the grass-root level working of science is inevitable. In fact, our conventional scientific methods are based upon ordinary sense perception, which keeps the outer physical universe as a separate entity, that is something quite independent of the observer. Basically, it is the observer -- the knower (human mind) -- which makes perception possible. It makes a person or scientist to recognize or refute the existence of an object or a phenomenon. It is also tempted to evince that working of human mind is epistemically scientific and can, in principle, be completely deciphered. It's inclusion in scientific theories, although tedious, can certainly spark a revolution in our understanding of nature and reality.