Feynman insisted 'no one understands quantum theory'. Yet, experimentalists tell us quantum theory is the most successful theory in history. Quantum theory cannot be understood as a classical mechanical theory since it arose through the 'interpolation' of two highly successful but complementary classical mechanics: Newtonian particle mechanics and Maxwellian wave mechanics. The two-slit experiment illustrates that what is experienced depends on choice of experimental set-up. Quantum theory is properly understood within the more general framework of engineering thermodynamics. In Part One, I point to four essential characteristics of quantum theory that cannot be understood in any framework defined by the classical mechanical presuppositions of symmetry and conservation. These four characteristics are the participatory, the complementary, the indeterminate and the new non-commutative geometry. In Part Two, articulating engineering thermodynamics, I note there are two histories and two formulations of thermodynamics: Carnot's engineering thermodynamics and the 'rational mechanical' tradition of Clausius-Boltzmann. These four essential characteristics of quantum theory are also characteristics of engineering thermodynamics. In Part Three, I trace the precursors of Lazare Carnot's engineering thermodynamics to earlier insights of Huygens, d'Alembert, Leibniz and the Bernoullis. Leibniz brought these forth in his meta-paradigm shift from Statics to Dynamics. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)'.
Feynman insisted 'no one understands quantum theory'. Yet, experimentalists tell us quantum theory is the most successful theory in history. Quantum theory cannot be understood as a classical mechanical theory since it arose through the 'interpolation' of two highly successful but complementary classical mechanics: Newtonian particle mechanics and Maxwellian wave mechanics. The two-slit experiment illustrates that what is experienced depends on choice of experimental set-up. Quantum theory is properly understood within the more general framework of engineering thermodynamics. In Part One, I point to four essential characteristics of quantum theory that cannot be understood in any framework defined by the classical mechanical presuppositions of symmetry and conservation. These four characteristics are the participatory, the complementary, the indeterminate and the new non-commutative geometry. In Part Two, articulating engineering thermodynamics, I note there are two histories and two formulations of thermodynamics: Carnot's engineering thermodynamics and the 'rational mechanical' tradition of Clausius-Boltzmann. These four essential characteristics of quantum theory are also characteristics of engineering thermodynamics. In Part Three, I trace the precursors of Lazare Carnot's engineering thermodynamics to earlier insights of Huygens, d'Alembert, Leibniz and the Bernoullis. Leibniz brought these forth in his meta-paradigm shift from Statics to Dynamics. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)'.
Formulations of quantum mechanics (QM) can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. A straightforward generalization of classical mechanics to QM is hampered by the inconsistency of quantum properties with classical logic, a circumstance that was noted many years ago by Birkhoff and von Neumann. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call 'compatible quantum theory (CQT)', consists of a 'microscopic' part (MIQM), which applies to a closed quantum system of any size, and a 'macroscopic' part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. Thus, the present formulation, in contrast to earlier ones, derives the Born probability formulas and the consistency (decoherence) conditions for frameworks. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths ('c-truths'), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The completion of the theory requires a macroscopic mechanism for selecting a physical framework, which is part of the macroscopic theory (MAQM). The selection of a physical framework involves the breaking of the microscopic 'framework symmetry', which can proceed either phenomenologically as in the standard quantum measurement theory, or more fundamentally by considering the quantum system under study to be a subsystem of a macroscopic quantum system. The decoherent histories formulation of Gell-Mann and Hartle, as well as that of Omnès, are theories of this fundamental type, where the physical framework is selected by a coarse-graining procedure in which the physical phenomenon of decoherence plays an essential role. Various well-known interpretations of QM are described from the perspective of CQT. Detailed definitions and proofs are presented in the appendices.
By the end of the nineteenth century all the important elements of classical physics were fully mature. Newton's Laws had been applied with success to everything from industrial machines to planetary orbits. Classical thermodynamics had extended energy conservation arguments into thermal processes, and scientists including J. Willard Gibbs and Ludwig Boltzmann had developed the statistical interpretation of entropy. James Clerk Maxwell had explained all electromagnetic phenomena, from AC generators/motors to light, with the four Maxwell's equations and three material-dependent constitutive relations. There was serious discussion that physics was on the verge of being “finished” – becoming a closed system of knowledge like classical geometry with only essentially routine tasks left of determining how the known laws could be applied to engineering problems. Yet by 1930 the foundations of mechanics, electromagnetics, and atomic-scale systems had been shaken to the core by the new revolutions in the Theory of Relativity, the photon picture of light, and quantum physics. We are still reaping the benefits of the application of these new scientific paradigms in our technology today, including semiconductor electronic devices, lasers, and GPS systems. But the description of reality that these theories provide is still deeply anti-intuitive and disturbing. Nevertheless, quantum physics is one of the most extensively experimentally verified theories that we know. Even when quantum theory and common sense seem to diverge, quantum theory gives the right answers when tested by experiment. In the next chapter we will develop the framework of quantum theory that has been so successful when people “shut up and calculate,” as one scientist suggested as the way through the philosophical thicket of quantum physics. But in this chapter, we will spend a brief time considering the historical development and continuing paradoxical implications of quantum theory. The photoelectric effect and photons In 1905, Albert Einstein, who was a key figure in the revolution of modern physics, was working as a clerk in the patent office in Zurich, Switzerland. Einstein had finished his studies in physics, but had not obtained a coveted position as a university professor. He was intensely interested in the latest developments in classical physics and was aware of a few of the remaining loose ends that were resisting explanation in the classical model.
Quantum mechanics is our most successful physical theory. However, it raises conceptual issues that have perplexed physicists and philosophers of science for decades. This 2004 book develops an approach, based on the proposal that quantum theory is not a complete, final theory, but is in fact an emergent phenomenon arising from a deeper level of dynamics. The dynamics at this deeper level are taken to be an extension of classical dynamics to non-commuting matrix variables, with cyclic permutation inside a trace used as the basic calculational tool. With plausible assumptions, quantum theory is shown to emerge as the statistical thermodynamics of this underlying theory, with the canonical commutation/anticommutation relations derived from a generalized equipartition theorem. Brownian motion corrections to this thermodynamics are argued to lead to state vector reduction and to the probabilistic interpretation of quantum theory, making contact with phenomenological proposals for stochastic modifications to Schrödinger dynamics.
In order to solve the problem of which is the real logic of Quantum Mechanics (QM), we suggest to study the mutual relationships between the physical theory (as a whole, that is both its experimental part and its theoretical part), its mathematics and its logic. That results to be a more general problem than what is considered by traditional studies on Quantum Logic (QL). These studies focus attention on the problem of the relationship between the experimental part of the physical theory and only its mathematics, from which logic is then derived. The new approach, that we suggest, generalises the interpretation that one of us (A. D.) successfully tested on the foundations of classical physical theories. The foundations of a theory are interpreted in terms of two options on the kind of mathematics, either classical one or constructive one, and the kind of logic, either classical logic or intuitionistic logic. It is remarkable that each theory making use of intuitionistic logic – i. e. L. Carnot’s classical mechanics, S. Carnot’s thermodynamics, Lobacevskij’s non-Euclidean geometry is organised in order to solve an universal problem (expressed by a double negated sentence), rather than in an entirely deductive way; hence, a non-classical logic does not belong exclusively to QM. From an historical and foundational analysis about QM, we conclude that in QM it is the law of double negation and not modular law (introduced by Birkhoff and von Neumann without giving physical evidence to it) which fails, i. e. which represents the true difference between Classical Logic (CL) and QL. We have looked for previous works on QL supporting our suggestion; in the past Destouches-Fevrier (1948), Fine (1974), Bell-Hallett (1981), Gauthier (1983), Adelman-Corbett (1995) already defended this thesis on the relevance of double negation law for QL. Under this light, QL results to have the same logic of a classical theory organised in a problematic manner. Hence, QM has to be referred to intuitionistic logic, in the same way every theory which is developed around a fundamental problem, expressed by a double negated sentence, does. In particular, by following the founder of intuitionism, Brouwer, we reject the identification of intuitionistic logic with an entirely deductive system; rather, the logical system of QL, as a theory, is organised in such a way to put a crucial problem to be solved. In agreement with this kind of organisation, among the several QM formulations we choose Heisenberg’s formulation, which was ignored by previous authors on QL. This formulation is aimed to solve the problem of quantum measurement, that originates the uncertainty methodological principle. Moreover, it is remarkable that it makes use of an operational mathematics (discrete matrices only). We interpret its characteristic arguing about its principal problem through double negated sentences; it results to be a moving from arguments belonging to non-classical logic expressed by a double negated sentence to the recognition of a suitable mathematics for QM formulation. In sum, QL shows how it is possible to state the relationship between QM and mathematics. This point has been almost ignored by the most traditional approaches to QL, which rather drew it from an a priori mathematics of QM (commonly, Hilbert space). As a verification of our approach, we show that even both Lobachevskij’s geometry and S. Carnot’s thermodynamics argued in order to achieve mathematical formulas expressing the content of the basic double negated sentences of respective theory. In the same way the recent book on QM by T. F. Jordan formalised his matrix mechanics. 1. Logic in classical physics and in Quantum Mechanics An historical analysis of Quantum Mechanics (QM) shows that there were at the origin of the theory two distinct formulations: Matrix Mechanics (Heisenberg, 1925) and Wave Mechanics (Schroedinger, 1926). Although Dirac subsumed these two formulations in a comprehensive mathematical framework (Hilbert space), we think that the organisation of the principles is different in Matrix Mechanics from that in Wave Mechanics, and this difference implies different logics. So we think that in order to characterise the logic of QM it is necessary to distinguish between this two formulations. In Matrix Mechanics, Heisenberg’s basic idea was to explain atomic spectra not in terms of atomic orbits (as Old Quantum Theory tried to make), but only by means of the study of experimental data; i. e., frequencies and intensities of light both emitted and absorbed by matter. Through a
www.philipgoyal.org Quantum theory is an extraordinarily successful physical theory. But what does it mean? What implications does it have for the mechanical conception of Nature that underlies classical physics? Remarkably, some eighty years after the creation of quantum theory, we still lack clear answers to these questions. In this paper, we discuss the nature of the obstacles that stand in our way, and describe recent work to overcome them by attempting to reconstruct the mathematics of quantum theory from a small number of simple physical ideas.
This paper outlines a highly respectful, complementary, and local-realist framework designed to bridge the elegant mathematical predictions of standard quantum mechanics with the physical, load-bearing principles of continuum mechanics and fluid dynamics. We focus specifically on the celebrated Feynman path integral formulation, which postulates that a quantum particle simultaneously traverses all possible trajectories between two points. By re-modeling the spatial manifold as a continuous, pre-stressed, and compressible hydrodynamic medium—the Universal Lattice (Bv approx 10^113 Pa)—we demonstrate that a "particle" is not a dimensionless 0D point-mass making probabilistic choices, but a highly pressurized, localized standing-wave droplet (acoustic soliton) possessing 3D volumetric geometry. Within this framework, the "sum over histories" is physically reinterpreted as the natural, deterministic propagation of a fluid wave-front physically exploring and meshing the available spatial geometry. We show that Feynman's Action (S) represents literal thermodynamic work scaled by the natural frequency of the spatial lattice (S=Uv/ν). Furthermore, we demonstrate that wave-function "collapse" is a strictly deterministic return to hydrostatic equilibrium along the path of least mechanical resistance. Finally, we establish that the conversion of volumetric strain energy into surface tension at the yield boundary is a physical manifestation of the Divergence Theorem, and that the optimization of this pathway is mathematically isomorphic to artificial neural network gradient descent. This approach unites standard quantum mathematics with applied engineering, providing a unified, load-bearing foundation for both.