Why were two theories (Matrix Mechanics and Wave Mechanics) deemed logically distinct, and yet equivalent, in Quantum Mechanics?

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

Niels Bohr’s Complementarity and Quantum Tunneling

Niels Bohr’s complementarity principle is a tenuous synthesis of seemingly discrepant theoretical approaches (the wave mechanical approach, and that of Heisenberg and early Bohr) based on a comprehensive analysis of relevant experimental results. Yet the role of complementarity, and the experimentalist-minded approach behind it, were not confined to a provisional best-available synthesis of well-established experimental results alone. They were also pivotal in discovering and explaining the phenomenon of quantum tunneling in its various forms. The core principles of Bohr’s method and the ensuing complementarity account of quantum phenomena remain highly relevant guidelines in the current controversial debate and in experimental work on quantum tunneling times

Why were two theories (Matrix Mechanics and Wave Mechanics) deemed logically distinct, and yet equivalent, in Quantum Mechanics?

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

Niels Bohr’s Complementarity and Quantum Tunneling

Niels Bohr’s complementarity principle is a tenuous synthesis of seemingly discrepant theoretical approaches (the wave mechanical approach, and that of Heisenberg and early Bohr) based on a comprehensive analysis of relevant experimental results. Yet the role of complementarity, and the experimentalist-minded approach behind it, were not confined to a provisional best-available synthesis of well-established experimental results alone. They were also pivotal in discovering and explaining the phenomenon of quantum tunneling in its various forms. The core principles of Bohr’s method and the ensuing complementarity account of quantum phenomena remain highly relevant guidelines in the current controversial debate and in experimental work on quantum tunneling times

Hybrid Product Cost Calculation Model as a Decision Support Tool

Cost calculation is of huge importance both for determining a rational and competitive price of the product and preparation of offers according to customer\u27s demand, where deadlines for sending offers are limited. In individual and small batch production, which is characterised by a wide product range, reduced quantities, and short delivery times, cost calculation in forming the price of the product according to customer requirements is of essential importance. Traditional methods of calculating the cost of products in these cases are inefficient, considering the number of offers that need to be made, timing, as well as their competitiveness in the market. For product cost calculation in individual and small batch production, it is necessary to apply modern, efficient methods and models based on the application of artificial intelligence. A wide range of products, which is characteristic of individual and small batch production in some companies, enables the development of modern costing models with the use of basic principles of group technology. The constructional and technological similarity of products enables the formation of groups of similar parts and appropriate group technological processes. Combining that with artificial intelligence, it is possible to develop appropriate cost calculation models. This paper presents a developed model for production cost calculation, based on the principles of group technology and adaptive neuralfuzzy networks (ANFIS)

When Should We Stop Investing in a Scientific Project? The Halting Problem in Experimental Physics

The question of when to stop an unsuccessful experiment can be difficult to answer from an individual perspective. To help to guide these decisions, we turn to the social epistemology of science and investigate knowledge inquisition within a group. We focused on the expensive and lengthy experiments in high energy physics, which were suitable for citation-based analysis because of the relatively quick and reliable consensus about the importance of results in the field. In particular, we tested whether the time spent on a scientific project correlates with the project output. Our results are based on data from the high energy physics laboratory Fermilab. They point out that there is an epistemic saturation point in experimenting, after which the likelihood of obtaining major results drops. With time the number of less significant publications does increase, but highly cited ones do not get published. Since many projects continue to run after the epistemic saturation point, it becomes clearer that decisions made about continuing them are not always rational

Alterations of Sleep and Sleep Oscillations in the Hemiparkinsonian Rat

Our previous studies in the rat model of Parkinson’s disease (PD) cholinopathy demonstrated the sleep-related alterations in electroencephalographic (EEG) oscillations at the cortical and hippocampal levels, cortical drives, and sleep spindles (SSs) as the earliest functional biomarkers preceding hypokinesia. Our aim in this study was to follow the impact of a unilateral substantia nigra pars compacta (SNpc) lesion in rat on the cortical and hippocampal sleep architectures and their EEG microstructures, as well as the cortico-hippocampal synchronizations of EEG oscillations, and the SS and high voltage sleep spindle (HVS) dynamics during NREM and REM sleep. We performed unilateral SNpc lesions using two different concentrations/volumes of 6-hydroxydopamine (6-OHDA; 12 μg/1 μl or 12 μg/2 μl). Whereas the unilateral dopaminergic neuronal loss >50% throughout the overall SNpc rostro-caudal dimension prolonged the Wake state, with no change in the NREM or REM duration, there was a long-lasting theta amplitude augmentation across all sleep states in the motor cortex (MCx), but also in the CA1 hippocampus (Hipp) during both Wake and REM sleep. We demonstrate that SS are the hallmarks of NREM sleep, but that they also occur during REM sleep in the MCx and Hipp of the control rats. Whereas SS are always longer in REM vs. NREM sleep in both structures, they are consistently slower in the Hipp. The dopaminergic neuronal loss increased the density of SS in both structures and shortened them in the MCx during NREM sleep, without changing the intrinsic frequency. Conversely, HVS are the hallmarks of REM sleep in the control rats, slower in the Hipp vs. MCx, and the dopaminergic neuronal loss increased their density in the MCx, but shortened them more consistently in the Hipp during REM sleep. In addition, there was an altered synchronization of the EEG oscillations between the MCx and Hipp in different sleep states, particularly the theta and sigma coherences during REM sleep. We provide novel evidence for the importance of the SNpc dopaminergic innervation in sleep regulation, theta rhythm generation, and SS/HVS dynamics control. We suggest the importance of the underlying REM sleep regulatory substrate to HVS generation and duration and to the cortico-hippocampal synchronizations of EEG oscillations in hemiparkinsonian rats

Predicted enhanced human propensity of current avian-like H1N1 swine influenza virus from China

Influenza A virus (IAV) subtypes against which little or no pre-existing immunity exists in humans represent a serious threat to global public health. Monitoring of IAV in animal hosts is essential for early and rapid detection of potential pandemic IAV strains to prevent their spread. Recently, the increased pandemic potential of the avian-like swine H1N1 IAV A/swine/Guangdong/104/2013 has been suggested. The virus is infectious in humans and the general population seems to lack neutralizing antibodies against this virus. Here we present an in silico analysis that shows a strong human propensity of this swine virus further confirming its pandemic potential. We suggest mutations which would further enhance its human propensity. We also propose conserved antigenic determinants which could serve as a component of a prepandemic vaccine. The bioinformatics tool, which can be used to further monitor the evolution of swine influenza viruses towards a pandemic virus, are described here and are made publically available (http://www.vin.bg.ac.rs/180/tools/iav-mon.php; http://www.biomedprotection.com/iav-mon.php)