It is argued that the key concepts of quantum theory—Planck’s quantum proposal, de Broglie’s wave–particle dualism and Schrodinger’s wave function idea—are neither incontestable nor integrated seamlessly into the fabric of quantum theory. In fact, it is doubtful whether classical wave treatments can serve as the basis for analysing (purported) matter waves at all. Also, an element of circular reasoning apparently surrounds the wave function concept, as the Hamiltonian-based Schrodinger equation is constrained to lead to the discrete solutions that represent quantization. These ambiguities appear particularly damning against the backdrop of the dubious Rayleigh–Jeans–Planck analysis of black body radiation, and the discredited evidence for the wave theory of radiation (based on purported diffraction phenomena). These considerations raise intriguing questions about the role of mathematical modelling in the study of natural phenomena (not to mention certain pedagogical quandaries). Thus, quantum theory—cloaked though it is in forbidding mathematical rigor—must submit to a dispassionate analysis of its extent and compass, particularly in view of its ostensible subversion of common-sense notions of reality.
It is argued that the key concepts of quantum theory—Planck’s quantum proposal, de Broglie’s wave–particle dualism and Schrodinger’s wave function idea—are neither incontestable nor integrated seamlessly into the fabric of quantum theory. In fact, it is doubtful whether classical wave treatments can serve as the basis for analysing (purported) matter waves at all. Also, an element of circular reasoning apparently surrounds the wave function concept, as the Hamiltonian-based Schrodinger equation is constrained to lead to the discrete solutions that represent quantization. These ambiguities appear particularly damning against the backdrop of the dubious Rayleigh–Jeans–Planck analysis of black body radiation, and the discredited evidence for the wave theory of radiation (based on purported diffraction phenomena). These considerations raise intriguing questions about the role of mathematical modelling in the study of natural phenomena (not to mention certain pedagogical quandaries). Thus, quantum theory—cloaked though it is in forbidding mathematical rigor—must submit to a dispassionate analysis of its extent and compass, particularly in view of its ostensible subversion of common-sense notions of reality.
It is argued that the wave-mechanical formalism that serves as the basis of quantum theory is fundamentally flawed on several counts. Primarily, the de Broglie equation is manifestly invalid as it implies that even macroscopic objects would acquire a substantial wavelength as they approach resting velocities. Furthermore, ostensible diffraction phenomena are not only logically dubious but also amenable to alternative explanations (including in the case of Newton’s rings). A subliminal thread apparently links diverse observations via the standing-wave idea, with the Planck treatment of black body radiation likely having inspired the particle-in-a-box model, which serves as the gateway to quantum chemistry via a quantum mechanical analogue of the Bohr orbits. These arguments apparently indicate that quantum theory is best regarded as an empirical model for dealing with certain natural phenomena, but also raise epistemological questions as to whether natural phenomena can at all be modelled by exact theories.
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work undertakes to investigate the issue of reality, treading a more fundamental route from the Hamilton-Jacobi equation of classical mechanics to the Schrodinger equation of quantum mechanics. Motivation for this is a similar approach from the eikonal equation in geometrical optics to the wave equation in electromagnetic theory. We rewrite the classical Hamilton-Jacobi equation as a wave equation and seek to generalise de Broglie's wave particle duality by demanding that both particle and light waves have the freedom of being described by any square-integrable function. This generalisation, which allows superposition also for matter wave functions, helps us to obtain the Schrodinger equation, whose solution can be seen to be as much objective as the classical mechanics wave function. Several other equations which one writes in quantum mechanics, including the eigenvalue equations for observables, series expansion of energy states in terms of eigenstates of observables other than energy, etc., can be written in the classical case too. Absence of any collapse of the wave function, entanglement, etc. in the classical realm have their origin in the nonlinearity of the classical wave equation. These considerations indicate that many of the puzzles in quantum mechanics are present also in classical mechanics in a dormant form, which fact shall help to demystify quantum mechanics to a great extent.
Intriguing questions from the early history of quantum theory (QT) raise serious doubts about the accepted theory of black body radiation. (The Planck theory builds on the apparently flawed Rayleigh-Jeans approach.) Furthermore, the validity of the theory of diffraction, the basis of the wave theory of radiation and matter, seems uncertain. Together, these raise fundamental questions about the foundations of QT and its current status. The apparently symbiotic relationship between QT and the theory of atomic and molecular structure, a key paradigm of modern scientific thought, may be a misleading indicator of the validity of QT. The protocols deriving from the Schrodinger equation lead to quantized states, but only along with certain assumptions. It is argued that QT applies uniquely to the interaction of electromagnetic radiation with matter, and that its scope is not universal: thus, it is best regarded as a quasi-empirical formalism. It is possible that the uncertainty surrounding QT is a legacy of the troubled historical period during which it was founded. This apparently has fascinating implications for the history and philosophy of science in general.
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
The odd concepts of quantum physics are nearly a century old. They may seem difficult and forbidding at first sight, but the barrier to understanding is not their difficulty but their differentness . Unlike classical models, quantum theory does not attempt to simulate Nature. It gives us information about observations of Nature. But it does contain a “theoretical entity” that claims to contain all information, observation notwithstanding, namely the quantum state vector in Hilbert space. Scientists routinely use the language of Hilbert space, and nonscientists do not use it at all, which is understandable but unfortunate. A sort of baby-talk has become the lingua franca for much of the popular journalism of quantum physics, an awkward patois that combines some of the early groping language of Bohr, de Broglie, Schrödinger, and Heisenberg with more modern words about symmetries and states. Earnest amateurs still ask me about the mystery of Bohr orbits. There is no mystery because there are no orbits, except as historical curiosities. Same for “wave–particle duality.” Same for “quantum jumps.” A friend once asked me to address a philosophy seminar about the “paradoxes of quantum mechanics.” He said he had approached C. N. Yang first, who replied “What paradoxes?” There are some mathematical and logical rough spots in our current best theory of matter, and perhaps some of them can be framed as paradoxes. But the theory is actually rather straightforward, and it has a perfectly clear interpretation linked to experiments that, in their simplest form, anyone can perform (and students do routinely in college laboratories). No empirical observations are known that are inconsistent with the quantum framework.
Introduction Quantum mechanics is based on the intuition that the essential difference between atomic physics and classical physics is the occurrence of discontinuities (see in particular [1,4,58–63]). Quantum mechanics should thus be considered a direct continuation of the quantum theory founded by Planck, Einstein and Bohr. Bohr in particular stressed repeatedly, already before the birth of quantum mechanics, that the discontinuities must lead to the introduction of new kinematical and mechanical concepts, so that indeed classical mechanics and its corresponding conceptual scheme should be abandoned [1,4]. Quantum mechanics tries to introduce the new concepts through a precise analysis of what is ‘observable in principle’. In fact, this does not mean setting up the principle that a sharp division between ‘observable’ and ‘unobservable’ quantities is possible and necessary. As soon as a conceptual scheme is given, one can infer from the observations to other facts that are actually not observable directly, and the boundary between ‘observable’ and ‘unobservable’ quantities becomes altogether indeterminate. But if the conceptual scheme itself is still unknown, it will be expedient to enquire only about the observations themselves, without drawing conclusions from them, because otherwise wrong concepts and prejudices taken over from before will block the way to recognising the physical relationships [Zusammenhänge].