Hermiticity and Self-Adjointness in Quantum Mechanics

Science sets itself apart from other paths to truth by recognizing that even its greate practitioners sometimes err.

The Symmetries of Quantum and Classical Information. The Ressurected “Ether" of Quantum Information

In this work, we present an original formula that proposes the unification of quantum, gravitational, and electromagnetic fields in a four-dimensional spacetime, considering the complex interactions among these fundamental forces. The formula integrates concepts from general relativity, electromagnetism, quantum mechanics, and scalar fields to provide a comprehensive description of the fundamental laws of physics. The equation is derived from a relativistic action incorporating various contributions, such as spacetime curvature, quantum fields, and matter-energy interactions. This model may open new perspectives in the quest for a unified theory of fundamental forces, being applicable to the observation and simulation of both cosmic and microscopic phenomena

In general relativity there is a long-standing problem of defining momentum and angular momentum in a general curved space-time. In this chapter, we describe an application of twistor theory which aims to provide a solution to this problem. As we shall see, this aim is not entirely achieved and the programme has both successes and failures. We recall that in general relativity, all the local matter content is described by the stress–energy tensor T ab . Gravitational energy, whether in gravitational waves or in the form of gravitational potential energy, is notoriously non-local and one cannot expect to characterise it by a local density. Instead, Penrose (1982) has suggested that one should seek a non-local invariant associated to any two-surface S and representing the total momentum–angular momentum flux through that surface. This non-local invariant will be constructed by twistorial techniques tailored to give the right answer for linearised general relativity where there is a clear right answer. We begin by reviewing the definition of momentum and angular momentum in special relativity and in linearised general relativity. A material system in special relativity is defined by its stress–energy tensor T ab which we may suppose for definiteness to have support within a world tube W in Minkowski space, M . (The case of say electromagnetic fields spread throughout M is a simple generalisation.)

The special theory of relativity and quantum mechanics merge in the key principle of quantum field theory, the principle of locality. We review some examples of its “unreasonable effectiveness” in giving rise to most of the conceptual and structural frame of quantum field theory, especially in the absence of massless particles. This effectiveness shows up best in the formulation of quantum field theory in terms of operator algebras of local observables; this formulation is successful in digging out the roots of global gauge invariance, through the analysis of superselection structure and statistics, in the structure of the local observable quantities alone, at least for purely massive theories; but so far it seems unfit to cope with the principle of local gauge invariance. This problem emerges also if one attempts to figure out the fate of the principle of locality in theories describing the gravitational forces between elementary particles as well. An approach based on the need to keep an operational meaning, in terms of localization of events, of the notion of space-time, shows that, in the small, the latter must loose any meaning as a classical pseudo-Riemannian manifold, locally based on Minkowski space, but should acquire a quantum structure at the Planck scale. We review the geometry of a basic model of quantum space-time and some attempts to formulate interaction of quantum fields on quantum space-time. The principle of locality is necessarily lost at the Planck scale, and it is a crucial open problem to unravel a replacement in such theories which is equally mathematically sharp, namely, a principle where the general theory of relativity and quantum mechanics merge, which reduces to the principle of locality at larger scales. Besides exploring its fate, many challenges for the principle of locality remain; among them, the analysis of superselection structure and statistics also in the presence of massless particles, and to give a precise mathematical formulation to the measurement process in local and relativistic terms; for which we outline a qualitative scenario which avoids the Einstein, Podolski, and Rosen paradox.

Ontology is integral to the two most fundamental scientific theories of the twentieth century: quantum theory and the special and general theories of relativity. Issues that drove the development of quantum theory include the reality of quanta, the simultaneous wave- and particle-like nature of matter and energy, determinism, probability and randomness, Schrodinger’s wave equation, and Heisenberg’s uncertainty principle. So did the reality of the predictions about space, time, matter, energy, and the universe itself that were deduced from the special and general theories of relativity. Dirac’s prediction of antimatter based solely on the mathematics of his theory of the electron and Pauli’s prediction of the neutrino based on his belief in quantum mechanics are cases in point. Ontological interpretations of the uncertainty principle, of quantum vacuum energy fields, and of Schrodinger’s probability waves in the form of multiple universe theories further illustrate this point.

The happiest thought of Einstein's life

This chapter introduces the concepts relevant to the special and general theories of relativity. In the theory of special relativity, measured time intervals are, in general, distinct for different observers. In this framework, space and time can be described in the form of a particular four-dimensional space–time. The new expressions for the kinetic energy and the momentum imply that no object can move faster than the speed of light.

Setna rocznica sformułowania przez Alberta Einsteina ogólnej teorii względności jest doskonałą okazją do ponownego postawienia pytań o wpływ wspomnianej teorii na filozofię. Interesującą perspektywę oferują badania z zakresu historii nauki i historii filozofii, które pozwalają dokładniej przyjrzeć się procesowi recepcji wspomnianej teorii. Proces ten jest waż- nym źródłem wiedzy o kształtowaniu się relacji nauk przyrodniczych i filozofii, gdyż poprzez analizę wskazywanych trudności i kontrowersji pozwala zidentyfikować wiele ukrytych założeń o charakterze filozoficznym, które trudno dostrzec na innych etapach rozwoju nauki. Dzięki temu analiza procesu recepcji nowych teorii naukowych staje się wyróżnionym przedmiotem analiz relacji matematyki, nauk przyrodniczych i filozofii. Z tych względów warto przyjrzeć się interesują- cym dyskusjom i polemikom, które miały miejsce w obrębie nauki polskiej.Szczególnie interesujące polemiki i dyskusje wokół teorii względności rozegrały się w Krakowie i we Lwowie przed rokiem 1925. Wspomniane ośrodki zostały wybrane również z tego względu, że w początkach XX wieku, wykorzystując możliwości polityczno-kulturalne powstałe w związku z istnieniem stosunkowo szerokiego zakresu autonomii Galicji, stały się one najważniejszymi centrami rozwoju nauki polskiej. Sytuacja ta zadecydowała również o połączeniu wymienionych ośrodków stosunkowo silną siecią powiązań, widocznych szczególnie na gruncie fizyki. W obu miastach powstała również specyficzna (choć z zachowaniem pewnych lokalnych odrębności) odmiana refleksji nad nauką, którą dogodnie jest określić przy pomocy pojęcia „filozofii w nauce” stworzonego przez M. Hellera.Opracowanie rozpoczyna się od krótkiego przybliżenia historii recepcji szczególnej teorii względności w Krakowie. W procesie tym najistotniejszą rolę odegrał August Witkowski, który już w 1905 roku docenił znaczenie pierwszych prac Einsteina. Kolejne punkty zwrotne w procesie recepcji teorii Einsteina wyznaczyły dwa kolejne Zjazdy Lekarzy i Przyrodników Polskich, które odbyły się kolejno we Lwowie w 1907 r. i w Krakowie w 1911 r. Pierwszy z nich zadecydował o popularyzacji idei relatywistycznych pośród przyrodników polskich, a kolejny – o popularyzacji ich wśród filozofów. Dla zrozumienia lokalnej specyfiki filozoficznych rozważań prowadzonych w ośrodku lwowskim odwołamy się do rozwoju recepcji wokół podstaw mechaniki. Zagadnienie to szczególnie mocno interesowało lwowskich uczonych z tej racji, że Lwów był do 1915 roku jedynym polskim ośrodkiem akademickim rozwijającym nauki techniczne i koncentrował w naturalny sposób większość polskich uczonych zajmujących się nauką mechaniki. To właśnie środowiska związane z lwowską Szkołą Politechniczną odegrały ważną rolę w późniejszych dyskusjach wokół szczególnej i ogólnej teorii względności.W dalszej kolejności szkicowo zaprezentowana zostanie lwowska polemika wokół teorii względności i dla kontrastu ukazana zostanie o wiele krótsza polemika rozgrywająca się w Krakowie. Szczególna uwaga zostanie poświęcona dorobkowi Zygmunta Zawirskiego, który w swej działalności podjął problematykę poruszoną w obu ośrodkach i przedstawił najbardziej interesujące rozważania ukazujące nowoczesną wizję filozofii uprawianej w ścisłym kontakcie z naukami przyrodniczymi.Prezentowany styl filozofii w nauce rozwijany w Krakowie i Lwowie został również skrótowo skonfrontowany z konkurencyjnymi filozoficznymi reakcjami na teorie Einsteina: z refleksją rozwijaną w obrębie Szkoły Lwowsko-Warszawskiej (Kazimierz Ajdukiewicz) i z wybraną refleksją neoscholastyczną (Feliks Hortyński SJ, Ludwik Wrzoł SJ, Jan Stepa). Na tym tle lepiej można dostrzec specyfikę filozofii analizowanej w tym studium przypadku – najważniejsze uwagi na ten temat zostały zawarte w zakończeniu niniejszej pracy.Niniejszy artykuł ukazuje fakt, że szczególna i ogólna teoria względności Einsteina znacząco wpłynęły na rozwój refleksji filozoficznej w Polsce. Warto również zaznaczyć, że refleksja filozoficzna stała się w opisywanym okresie ważnym uzupełnieniem pracy naukowej przyrodników, co decyduje również o specyfice rozwoju ówczesnej nauki.

The special theory of relativity (STR) is operationally expanded onto orthogonal accelerations: normal and binormal that complement the instantaneous tangential speed and thus can be structurally extended into operationally complete 4D spacetime without defying the STR. Thus the former classic Lorentz factor, which defines proper time differential can be expanded onto within a trihedron moving in the Frenet frame (T,N,B). Since the tangential speed which was formerly assumed as being always constant, expands onto effective normal and binormal speeds ensuing from the normal and binormal accelerations, the expanded formula conforms to the former Lorentz factor. The obvious though previously overlooked fact that in order to change an initial speed one must apply accelerations (or decelerations, which are reverse accelerations), made the Einstein’s STR incomplete for it did not apply to nongravitational selfpropelled motion. Like a toy car lacking accelerator pedal, the STR could drive nowhere. Yet some scientists were teaching for over 115 years that the incomplete STR is just fine by pretending that gravity should take care of the absent accelerator. But gravity could not drive cars along even surface of earth. Gravity could only pull the car down along with the physics that peddled the nonsense while suppressing attempts at its rectification. The expanded formula neither defies the STR nor the general theory of relativity (GTR) which is just radial theory of gravitation. In fact, the expanded formula complements the STR and thus it supplements the GTR too. The famous Hafele-Keating experiments virtually confirmed the validity of the expanded formula proposed here.

Based on special relativity, we introduce a way to develop a new field theory from (1) the relativistic property of the particle coupling coefficient with the field, and (2) the field due to a static point source. As an example, we discuss a theory of electromagnetic and gravitational fields. The results of this special relativistic gravitational theory for the redshift and the deflection of light are the same as those deduced from general relativity. The results of experiments on the planetary perihelion procession shift and on an additional “short-range gravity” are more favorable to the special relativistic gravitational theory than to general relativity. We put forward a new idea to test experimentally whether the equivalence principle of general relativity is correct.

Klein-Weyl's program and the ontology of gauge and quantum systems

The Lorentz-Poincaré interpretation of special relativity (SR) keeps the classical concepts of separated space and time, at the price of postulating an indetectable preferred inertial frame or “ether”. But SR does not contain gravity. The presence of gravity could make the ether detectable. This is one idea behind the “scalar ether theory of gravitation” (SET), which coincides with SR if the gravity field vanishes, and passes a number of tests. However, the coupling of SET with the Maxwell electromagnetic (EM) field needs to use the theory’s dynamical equation for the energy tensor in a non-trivial way. It cannot be assumed that the energy tensors of the charged matter and the EM field add to give the total energy tensor, source of the gravitational field. Thus, an additional, “interaction” energy tensor T inter has to be postulated. Asking that T inter is Lorentz-invariant in the situation of SR, fixes its form. It depends only on a scalar field p. T inter is an exotic kind of matter and is distributed in the whole space, hence it could contribute to dark matter. For a weak gravitational field, p obeys a first-order partial differential equation (PDE) involving the EM field and the Newtonian potential. However, the EM field varies on the scale of the wavelength, which is extremely small. To get the field p in a galaxy, some averaging has to be done. After several attempts based on the homogenization theory, a simpler way has been found recently: If the macro-averages of p and the EM field vary smoothly, it can be shown that the PDE for p remains valid in the same form with spacetime-averaged fields. The current stage of calculations will also been shown.

This paper is about some of the ways in which the study of Cosmology has been key, both in initially developing, and in probing retroactively into, the foundations of modern physics. The past role of cosmological observations in triggering the development of mathematical physics, and modern science in general, is well known. But the present role of cosmological observations in possibly triggering a review of some never-challenged assumptions is playing out only presently, and so is not completely known yet. The cosmological observations cited in this paper concern the apparently universal pattern displayed by barred spiral galaxies. The typical barred spiral galaxy follows a common ‘body plan’ consisting of two spiral arms, acutely curved, and a central bar, not exactly straight. The arm curvature seems about the same for all such galaxies, and the bar wandering, if it is visible, is similar in initial slope to the arms. The several issues in physical theory that this so-common pattern invites us to acknowledge and investigate first arose in Electrodynamics. They then propagated into Quantum Mechanics and into Special Relativity Theory, and then into General Relativity Theory. Quantum Mechanics and Relativity Theory are the main pillars of twentieth century physics. So better clarifying the issues in Electrodynamics is important. If that elucidation comes to pass, Cosmology will have driven modern science, yet again, to a new level of understanding.

The report considers the interaction of scalar particles, photons and fermions with the gravitational and electromagnetic Schwarzschild, Reissner-Nordstrom, Kerr and Kerr-Newman fields. The behavior of effective potentials in the relativistic Schrodinger-type second-order equations is analyzed. It was found that the quantum theory is incompatible with the hypothesis of the existence of classical black holes with event horizons of zero thickness that were predicted based on solutions of the general relativity (GR) with zero and non-zero cosmological constant $\Lambda$. The alternative may be presented by compound systems, i.e., collapsars with fermions in stationary bound states.