The question of whether the Einstein shift in clock rates has a bearing on the validity of the fourth Heisenberg uncertainty relation is discussed. It is shown that, even if one would accept all the relevant assumptions and conclusions of Bohr and Rosenfeld, this uncertainty relation could not be saved by an Einstein shift in the case of an electrostatic weighing. This means that the Einstein shift does not play any role in determining the validity of the fourth Heisenberg relation.

It is shown that the covariance together with the quantum principle speak for an affinely connected structure which, for distances greater than Planck’s length, goes over in a metrically connected structure of space-time.

It is shown that the covariance together with the quantum principle speak for an affinely connected structure which, for distances greater than Planck’s length, goes over in a metrically connected structure of space-time.

Planck's units define the limits of super GUT and also the possibilities of classical measurements. A “planckion'” is the largest ultrarelativistic elementary particle and also the smallest body that can serve as a classical standard.

Empirical and theoretical evidence show that the astrophysical problem of dark matter might be solved by a theory of Einstein-Mayer type. In this theory, up to global Lorentz rotations, the reference system is determined by the motion of cosmic matter. Thus, one is led to a “Riemannian space with teleparallelism” realizing a geometric version of the Mach-Einstein doctrine. The field equations of this gravitational theory contain hidden matter terms, where the existence of hidden matter is inferred solely from its gravitational (...) effects. It is argued that, in the nonrelativistic mechanical approximation, they provide an inertia-free mechanics, where the inertial mass of a body is induced by the gravitational action of the comic masses. Interpreted from the Newtonian point of view, this mechanics shows that the effective gravitational mass of astrophysical objects depends on r such that one expects the existence of dark matter. (shrink)

The Einstein equations can be written as Fierz-Pauli equations with self-interaction, $W\gamma _{ik} = - G_{ik} + \tfrac{1}{2}g_{ik} g^{mn} G_{mn} - k(T_{ik} - \tfrac{1}{2}g_{ik} g^{mn} T_{mn} )$ together with the covariant Hilbert-gauge condition, $(\gamma _i^h - \tfrac{1}{2}\delta _i^k g^{mn} \gamma _{mn} )_{;k} = 0$ where W denotes the covariant wave operator and G ik the Einstein tensor of the metric g ik collecting all nonlinear terms of Einstein's equations. As is known, there do not, however, exist plane-wave solutions γ ik(z)with (...) g ik Z,i Z,k=0of these equations such that what is essential to the introduction of gravitons is not satisfied in general relativity. This nonexistence corresponds with the uncertainty relation,Δp(Δg*)2(Δx)3≥h hG/ c 3 concerning the total nonlinear gravitational field g *ik =g k +γ k. (shrink)

A discussion of the diffraction and scattering of particles by a grating shows that the experiment discussed by H. Hönl and by L. Rosenfeld in 1965 and again in 1981 does not reveal any contradiction between general relativity and quantum theory. Moreover, these theories, in principle, cannot refute one another because the (weak) principle of equivalence, underlying general relativity theory, entails that gravitation does not alter the laws of microphysics.

We discuss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves. Firstly, we have the problem of the influence of gravitational fields on the de Broglie waves, which influence is in accordance with Eeinstein's weak principle of equivalence and the limitation of measurements given by Heisenberg's uncertainty relations. Secondly, the quantization of the gravitational fields is a “quantization of geometry.” However, classical and quantum gravitation have the same physical meaning according (...) to limitations of measurements given by Einstein's strong principle of equivalence and the Heisenberg uncertainties for the mechanics of test bodies. (shrink)

According to the Einstein-Mayer theory of the Riemanniann space-time with Einstein-Cartan teleparallelism, the local Lorentz invariance is broken by the gravitational field defining Machian reference systems. This breaking of symmetry implies the occurrence of “hidden matter” in the Einstein equations of gravity. The hidden matter is described by the non-Lorentz-invariant energy-momentum tensor $\hat \Theta _{ik}$ satisfying the relation $\hat \Theta _{i;k}^k = 0$ . The tensor $\hat \Theta _{ik}$ is formed from the Einstein-Cartan torsion field given by the anholonomy objects, (...) FAik=2hA[i,k], and appears together with Hilbert’s energy-momentum tensor T* ik and Poincaré’s pressure λgik on the right-hand side of Einstein’s equations so that one has $$R_{ik} - (1/2)g_{ik} R = - \kappa T*_{ik} - \lambda g_{ik} - \hat \Theta _{ik}$$ According to this theory, in the universe and in cosmic systems one must excep “invisible masses” described by the Poincaré and Einstein-Cartan terms to exist. The torsion field FAik makes the space-time a Machian universe; it is of the same nature as the “weak interacting matter” discussed in astrophysics. (shrink)

It is shown that, due to Rosenfeld's inequality relations, there is no possibility of defining states of the Friedmann universe in a physically sensible manner when the world radius becomes equal to or smaller than Planck's length.

Starting from Planck's thesis concerning the aims and methods of theoretical physics as stated in his famous lecture (Leiden, 1908) onDie Einheit des physikalischen Weltbildes and his lectures in the next year at Columbia University, we discuss some aspects of physics and mathematics in our time. We compare relativity theory, quantum mechanics, and atomic physics at their inception with the situation today in field theories, elementary particle physics, and mathematical physics.

The present authors have given a mathematical model of Mach's principle and of the Mach–Einstein doctrine about the complete induction of the inertial masses by the gravitation of the universe. The analytical formulation of the Mach–Einstein doctrine is based on Riemann's generalization of the Lagrangian analytical mechanics (with a generalization of the Galilean transformation) on Mach's definition of the inertial mass and on Einstein's principle of equivalence. All local and cosmological effects—which are postulated as consequences of Mach's principle by C. (...) Neumann, Mach, Friedländer and Einstein—result from the Riemannian dynamics with the Mach–Einstein doctrine. In celestial mechanics it follows, in addition, Einstein's formula for the perihelion motion. In cosmology, the Riemannian mechanics yields two models of an evolutionary universe with the expansion lows R ~ t or R ~ t2. In this paper, secular consequences of the Mach–Einstein doctrine are examined concerning palaeogeophysics and celestial mechanics. The research predicted secular decrease of the Earth's flattening and secular acceleration of the motion of the Moon and of the planets. The numerical values of this secular effect agree very well with the empirical facts. In all cases, the secular variation $\dot{\alpha}$ of the parameter α is the order of magnitude $\dot{\alpha}=-H_0 \alpha$ , where H0 is the instantaneous value of the Hubble constant: $H_0 =\left({\dot{R}/R} \right)_0 \approx \left( {0.5-1.0} \right) \times 10^{-10}a^{-1}$ . The relation of the secular consequences of the Mach–Einstein doctrine to those of Dirac's hypothesis on the expanding Earth, and to Darwin's theory of tidal friction are also discussed. (shrink)

The analysis of the measurement of gravitational fields leads to the Rosenfeld inequalities. They say that, as an implication of the equivalence of the inertial and passive gravitational masses of the test body, the metric cannot be attributed to an operator that is defined in the frame of a local canonical quantum field theory. This is true for any theory containing a metric, independently of the geometric framework under consideration and the way one introduces the metric in it. Thus, to (...) establish a local quantum field theory of gravity one has to transit to non-Riemann geometry that contains (beside or instead of the metric) other geometric quantities. From this view, we discuss a Riemann–Cartan and an affine model of gravity and show them to be promising candidates of a theory of canonical quantum gravity. (shrink)

The analysis of the measurement of gravitational fields leads to the Rosenfeld inequalities. They say that, as an implication of the equivalence of the inertial and passive gravitational masses of the test body, the metric cannot be attributed to an operator that is defined in the frame of a local canonical quantum field theory. This is true for any theory containing a metric, independently of the geometric framework under consideration and the way one introduces the metric in it. Thus, to (...) establish a local quantum field theory of gravity one has to transit to non-Riemann geometry that contains (beside or instead of the metric) other geometric quantities. From this view, we discuss a Riemann–Cartan and an affine model of gravity and show them to be promising candidates of a theory of canonical quantum gravity. (shrink)

We give picture-covariant formulations of the equations of motion for observables and states such that the Hamiltonian operator is transformed asH-0304;=U(t)HU † (t) under a time-dependent unitary transformationU(t). Next, we consider the explicit and implicit covariance of Heisenberg's equations of motion for observables with respect to general transformations of coordinate operators. Most of our representation is spread out over a number of textbooks and articles, where the subject has been considered with greater or lesser clarity from different points of view.

As an example of a historical case study, some aspects of the post-Newtonian corrections in the Earth–Moon dynamics are described and discussed.

It is argued that, under the assumption that the strong principle of equivalence holds, the theoretical realization of the Mach principle (in the version of the Mach-Einstein doctrine) and of the principle of general relativity are alternative programs. That means only the former or the latter can be realized—at least as long as only field equations of second order are considered. To demonstrate this we discuss two sufficiently wide classes of theories (Einstein-Grossmann and Einstein-Mayer theories, respectively) both embracing Einstein's theory (...) of general relativity (GRT). GRT is shown to be just that “degenerate case” of the two classes which satisfies the principle of general relativity but not the Mach-Einstein doctrine; in all the other cases one finds an opposite situation.These considerations lead to an interesting “complementarity” between general relativity and Mach-Einstein doctine. In GRT, via Einstein's equations, the covariant and Lorentz-invariant Riemann-Einstein structure of the space-time defines the dynamics of matter: The symmetric matter tensor Ttk is given by variation of the Lorentz-invariant scalar densityL mat, and the dynamical equations satisfied by Tik result as a consequence of the Bianchi identities valid for the left-hand side of Einstein's equations. Otherwise, in all other cases, i.e., for the “Mach-Einstein theories” here under consideration, the matter determines the coordinate or reference systems via gravity. In Einstein-Grossmann theories using a holonomic representation of the space-time structure, the coordinates are determined up to affine (i.e. linear) transformations, and in Einstein-Mayer theories based on an anholonomic representation the reference systems (the tetrads) are specified up to global Lorentz transformations. The corresponding conditions on the coordinate and reference systems result from the postulate that the gravitational field is compatible with the strong equivalence of inertial and gravitational masses. (shrink)

As is well known, the law of parity conservation does not hold in weak interactions. This type of asymmetry created a number of theoretical problems which were solved, first of all, by a new understanding of the features of neutrinos and their role in weak interactions. These solutions were based, however, essentially on the handedness (chirality) of neutrinos which is closely related to their vanishing rest mass. The thesis of neutrinos with nonvanishing rest mass, newly considered in the literature, therefore (...) requires a rediscussion of the early arguments concerning the relation between the neutrino theory and some weak interaction essentials. When one does this, as in the present paper, it is noted that neutrinos with rest mass lead to some difficulties, in particular to a violation of T invariance. (shrink)

A classic exposition of Kant's ethical thought.

The present volume contains the lectures and papers given at the 1994 international conference on hermeneutics in Halle (Germany). The conference aimed at a state of the art in the light of recent developments in science and humanities. The place in which the conference was held is renowned for its centuries-old tradition in hermeneutics and among the lectures there are indeed some devoted to this history. For the most part, however, the papers concentrate on present-day problems in fields as different (...) as comparative literature, religious studies, bible exegesis, esthetics, social sciences, intercultural dialogue. The theme of the conference, "strangeness and familiarity", reflects the tension in which any interpretation process is situated and that any theory of interpretation has to account for. The contributions to the volume are in German and French. (shrink)

CHAPTER INTRODUCTION At first sight Plotinus' philosophy is full of contradictions. The same entity will appear with different characteristics in different ...

Originally published: London: Allen & Unwin, 1936.

This old difficulty has recently received a new explanation from the pen of Dr. E. G. Hardy . Dr. Hardy believes—and his view has met with some acceptance—that the disability, under which these Gallic candidates for admission to the Senate laboured, was the want of a municipalis origo. Up to this time, he contends, only Romans who were members of a town of Roman or Latin rights were eligible for admission to the Senate. Now in the Tres Galliae there were (...) practically no such towns: these Gallic chiefs possessed the ciuitas individually by special grant and not as members of any municipality. Hence the door of the curia was closed to them while it was open to Romans from Lugdunum or Vienna. (shrink)

In the Classical Quarterly of April, 1914, I ventured to call in question the explanation of this well-known difficulty put forward by Dr. E G. Hardy in his Roman Laws and Charters. Dr. Hardy has done me the honour of replying to my article in the October Quarterly, but his lengthy argument entirely fails to convince me.

This old difficulty has recently received a new explanation from the pen of Dr. E. G. Hardy. Dr. Hardy believes—and his view has met with some acceptance—that the disability, under which these Gallic candidates for admission to the Senate laboured, was the want of a municipalis origo. Up to this time, he contends, only Romans who were members of a town of Roman or Latin rights were eligible for admission to the Senate. Now in the Tres Galliae there were practically (...) no such towns: these Gallic chiefs possessed the ciuitas individually by special grant and not as members of any municipality. Hence the door of the curia was closed to them while it was open to Romans from Lugdunum or Vienna. (shrink)

This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

Introduction: why the De anima commentaries? This book will concentrate on interpretations of the De anima in late antiquity, and what we can learn from ...

The long-term persistence of neurotic symptoms, such as anxiety, poses difficult problems for any psychological theory. An attempt is made to revive the Watson-Mowrer conditioning theory and to avoid the many criticisms directed against it in the past. It is suggested that recent research has produced changes in learning theory that can be used to render this possible. In the first place, the doctrine of equipotentiality has been shown to be wrong, and some such concept as Seligman's “preparedness” is required, (...) that is the notion that certain CS are biologically prepared to be more readily connected with anxiety responses than others. In the second place, the law of extinction has to be amended, and the law of incubation or enhancement added, according to which the exposure of the CS-only may, under certain specified conditions, have the effect of increasing the strength of the CR, rather than reducing it. The major conditions favouring incubation are Pavlovian B conditioning, that is a type of conditioning in which the CR is a drive; a strong UCS, and short exposure of the CS-only. (shrink)

The relative neglect of Greek commentary by modern Aristotelian scholarship could be justified, if only the neglectors had sufficient knowledge of the material they disdain. The curt dismissal of ancient views on the active intellect by W. D. Ross is perhaps a paradigm case of misplaced condemnation, for he evidently failed to take account of what their authors were about. It would be open to those who wish to discount these commentators to argue that they were, to a greater or (...) lesser extent, influenced by their Neoplatonism, and that this impairs their judgment on Aristotelian problems. But that would not be sufficient ground for total neglect: it merely indicates the need for careful utilization. One might go so far as to ask whether it is not perfectly possible for a commentator who happened to be a Neoplatonist to offer straightforward and reasonably unbiased commentary on Aristotle. Even if the answer to that question were negative, is it not likely that such Neoplatonic views as he read into Aristotle would at least be slanted towards Aristotelianism? (shrink)