E. Schrödinger’s early ideas on interpreting quantum mechanics, as well as their later reformulation, have been recently reexamined by historians and revived among philosophers of quantum mechanics. The neo‐Schrödingerian doctrines of relational holism and emergentism share with both Schrödinger’s earlier and later views the common assumption that the corpuscular properties of quantum systems can be successfully discarded, and the discontinuities related to measurements successfully reformulated in wave‐mechanical terms or within the framework of quantum field theory. I argue that these doctrines fail to acknowledge the significance of the experimental results concerning electron scattering, in the face of which Schrödinger himself abandoned his 1926 interpretation, and which haunted his return to these ideas in the 1930s. I conclude that the neo‐Schrödingerian trend should be cautioned by these experimental results, in which the corpuscular properties may not be “explained away” in wave‐mechanical terms.
E. Schrödinger’s early ideas on interpreting quantum mechanics, as well as their later reformulation, have been recently reexamined by historians and revived among philosophers of quantum mechanics. The neo‐Schrödingerian doctrines of relational holism and emergentism share with both Schrödinger’s earlier and later views the common assumption that the corpuscular properties of quantum systems can be successfully discarded, and the discontinuities related to measurements successfully reformulated in wave‐mechanical terms or within the framework of quantum field theory. I argue that these doctrines fail to acknowledge the significance of the experimental results concerning electron scattering, in the face of which Schrödinger himself abandoned his 1926 interpretation, and which haunted his return to these ideas in the 1930s. I conclude that the neo‐Schrödingerian trend should be cautioned by these experimental results, in which the corpuscular properties may not be “explained away” in wave‐mechanical terms.
A recent rethinking of the early history of Quantum Mechanics deemed the late 1920s agreement on the equivalence of Matrix Mechanics and Wave Mechanics, prompted by Schrödinger’s 1926 proof, a myth. Schrödinger supposedly failed to achieve the goal of proving isomorphism of the mathematical structures of the two theories, while only later developments in the early 1930s, especially the work of mathematician John von Neumman (1932) provided sound proof of equivalence. The alleged agreement about the Copenhagen Interpretation, predicated to a large extent on this equivalence, was deemed a myth as well. If such analysis is correct, it provides considerable evidence that, in its critical moments, the foundations of scientific practice might not live up to the minimal standards of rigor, as such standards are established in the practice of logic, mathematics, and mathematical physics, thereby prompting one to question the rationality of the practice of physics. In response, I argue that Schrödinger’s proof concerned primarily a domain-specific ontological equivalence, rather than the isomorphism. It stemmed initially from the agreement of the eigenvalues of Wave Mechanics and energy-states of Bohr’s Model that was discovered and published by Schrödinger in his First and Second Communications of 1926. Schrödinger demonstrated in this proof that the laws of motion arrived at by the method of Matrix Mechanics could be derived successfully from eigenfunctions as well (while he only outlined the reversed derivation of eigenfunctions from Matrix Mechanics, which was necessary for the proof of isomorphism of the two theories). This result was intended to demonstrate the domain-specific ontological equivalence of Matrix Mechanics and Wave Mechanics, with respect to the domain of Bohr’s atom. And although the full-fledged mathematico-logical equivalence of the theories did not seem out of the reach of existing theories and methods, Schrödinger never intended to fully explore such a possibility in his proof paper. In a further development of Quantum Mechanics, Bohr’s complementarity and Copenhagen Interpretation captured a more substantial convergence of the subsequently revised (in light of the experimental results) Wave and Matrix Mechanics. I argue that both the equivalence and Copenhagen Interpretation can be deemed myths if one predicates the philosophical and historical analysis on a narrow model of physical theory which disregards its historical context, and focuses exclusively on its formal aspects and the exploration of the logical models supposedly implicit in it.
This paper re-opens the debate on the failure of quantum mechanics to provide an understandable view of micro-reality. A critique is offered of the commonly accepted ‘Copenhagen Interpretation’ of a theory that is only a mathematical approach to the level of reality characterized by atoms and electrons. This critique is based on the oldest approach to thinking about nature for over 2500 years, known as Natural Philosophy. Quantum mechanics (QM) was developed over the first quarter of the 20th Century, when scientists were enthralled by a new philosophy known as Positivism, whose foundations were based on the assumption that material objects exist only when measured by humans – This central assumption conflates epistemology (knowledge) with ontology (existence). The present critique rejects this human-centered view of reality by assuming material reality has existed long before (and will persist long after) human beings (“Realism”). The defensive view that the micro-world is too different to understand using regular thinking (and only a mathematical approach is possible) is rejected totally. At least 12 earlier QM interpretations are critically analyzed, indicating the broad interest in “what does QM mean?” The standard theory of quantum mechanics is thus constructed on only how the micro-world appears to macro measurements - as such, it cannot offer any view of how the foundations of the world are acting when humans are not observing it - this has generated almost 100 years of confusion and contradiction at the very heart of physics. Significantly, we live in a world that is not being measured by scientists but is interacting with itself and with us. QM has failed to provide explanations: only recipes (meaningless equations), not insights. Physics has returned to the pre-Newtonian world of Ptolemaic phenomenology: only verifiable numbers without real understanding. The focus needs to be on an explicit linkage between the micro-world, when left to itself, and our mental models of this sphere of material reality, via the mechanism of measurement. This limits the role of measurement to confirming our mental models of reality but never confusing these with a direct image of ‘the thing in itself’. This implies a deep divide between reality and appearances. This paper proposes that it is the attempt to preserve continuum mathematics (especially calculus), which drives much of the mystery and confusion behind all attempts to understand quantum mechanics. The introduction of discrete mathematics is proposed to help analyze the discrete interactions between the quintessential quantum objects: the electrons and their novel properties. Additionally, several hidden major assumptions have been present in Classical Mechanics (represented by continuum mathematics) since its inception by Newton that are blocking progress and understanding of quantum mechanics. A related paper demonstrates that it is possible to create a point-particle theory of electrons that explains all their peculiar (and ‘paradoxical’) behavior without introducing the continuum mathematical ideas of fields or waves. * Surrey, B.C. Canada (604) 542-2299 spsi99@telus.net Version 1.195 10-07-2016 Begun 23-06-2008 {pp. 80, 70.4 Kw; 800 KB}
The interpretation of quantum mechanics has been disputed ever since the advent of the theory in the 1920’s. Famous are the discussions over long time between Einstein and Bohr. Einstein refused to accept the so‐called Copenhagen interpretation, where the wave function collapses at a measurement and where the outcome of the measurement is essentially accidental (“God does not play dice”). Alternative interpretations have appeared, but the Copenhagen school has dominated the thoughts throughout the decades. One interesting interpretation was formulated in 1957 by Hugh Everett at Princeton, a student of John Wheeler, which abandons the wave‐function collapse. In this model the universe is governed entirely by the Schrödinger equation, which does not allow for any collapse. In Everett’s model after a measurement the wave function is separated into different branches that do not interact. This model was left unnoticed for long time until Bryce DeWitt took it up in 1970 and termed it “Many‐Worlds Interpretation”, a term that in some sense is misleading. Everett’s model is incomplete, and it was later supplemented by the theory of decoherence, which explains how the different branches decouple as a result of the interaction with the environment. This extended model has in recent years gained increased respect, and some believe that it is the only model made available so far that is fully consistent with quantum mechanics. This interpretation can also shed some light on the development of the universe and, in particular, on the so‐called Anthropic principle, which puts human beings at the center of the development.
Abstract While the theory proved successful at describing a broad range experimental results, from the black body spectrum to the hydrogen atom, the question arose as to what the theory was telling us about the nature of physical reality. Schrödinger’s attempt to represent particles as wave packets failed because of the spreading of the wave packets. Max Born, investigating how the theory could be applied to scattering processes, was led to introduce the probability interpretation of the wave function. In an attempt to summarize the physical meaning of the theory, Heisenberg introduced the uncertainty principle. Niels Bohr and his Copenhagen school developed the philosophical position known as “complementarity.” There was a bitter dispute between Schrödinger and the “Copenhageners” over the necessity of quantum jumps in the theory.
The physical meaning of Schrödinger’s wave function remains afoundational interpretive question in quantum mechanics. This paperseparates two questions that are often introduced together: what thewave function describes during propagation, and why experimentaloutcomes obey Born statistics. Rather than taking∣Ψ∣2 as the starting definition of Ψ, we begin from theoperational structure of early electron-scattering and transmissionexperiments surrounding the emergence of wave mechanics and Born’s1926 collision theory. Davisson and Kunsman measured angle-dependent collected current,Ramsauer measured energy-dependent electron transmission throughgases, and Dymond later resolved the energy and angular redistributionof electrons after collisions. In each case, the apparatus returnedphysical signals---charge, current, or flux---from which reproducibleoutcome distributions were reconstructed. From this common structure we propose a deliberately limitedinterpretation: for a single nonrelativistic particle, Ψ may beread first as a complex-amplitude representation of thespatial--directional organization of quantum propagation. Thisproposal is anchored not only in the experimental sequence but also inthe mathematics of the wave function. Its Fourier representationresolves propagation into wave-vector components, while theSchrödinger continuity relation defines a conserved density--currentpair; in polar formΨ=Rexp(iS/ℏ),the associated current is proportional toR2∇S. These facts show that Ψ contains both spatial weighting anddirectional phase structure before any additional ontological claim ismade. We do not infer a material wave medium, deterministic particletrajectories, hidden variables, or an alternative dynamics. Nor do wederive the Born rule. Instead, we isolate a separate mapping problem:how does a structured propagation state, through a specific detectorinteraction, become the observed statistics of localized or collectedparticle events? In scattering, any acceptable account must recover the standard fluxand cross-section relations. The contribution of the present paper istherefore interpretive and programmatic: it identifies a constrainedphysical reading of Ψ and states precisely what remains to beexplained.
Chapter 2 explains how in constructing quantum mechanics, old ideas had to be discarded and well-established principles had to be modified or even abandoned. First it was necessary to be convinced of the physical reality of the atomic structure of matter; then to show that Newtonian mechanics is not directly applicable to the study of the atom; later to show that Maxwell’s electrodynamics alone does not describe all the elementary processes of interaction between an atom and other quantum particles. The chapter takes us from Planck’s energy quantum to Einstein’s quantization as a universal phenomenon, from Bohr’s quantum atom model, and the early quantization rules, to de Broglie’s waves associated with corpuscles in motion. It ends with a corollary on the electrodynamic nature of quantum mechanics.