Peter Mittelstaedt

Unsharp particle-wave duality in a photon split-beam experiment

In a quantum mechanical two-slit experiment one can observe a single photon simultaneously as particle (measuring the path) and as wave (measuring the interference pattern) if the path and the interference pattern are measured in the sense of unsharp observables. These theoretical predictions are confirmed experimentally by a photon split-beam experiment using a modified Mach—Zehnder interferometer.

The Constitution of Objects in Kant’s Philosophy and in Modern Physics

From a historical point of view the main goal of Kant’s transcendental deduction in the Critique of Pure Reason was to show that there are well defined limits for the validity of the synthetic judgements a priori. Since objects of experience are constituted by means of certain categories, the general statements which follow from these categories are a priori valid for all objects of experience, but the a priori validity is also restricted to these objects. “Consequently, there can be no a priori knowledge, except of objects of possible experience.”

Relativistic quantum logic

On the basis of the well-known quantum logic and quantum probability a formal language of relativistic quantum physics is developed. This language incorporates quantum logical as well as relativistic restrictions. It is shown that relativity imposes serious restrictions on the validity regions of propositions in space-time. By an additional postulate this relativistic quantum logic can be made consistent. The results of this paper are derived exclusively within the formal quantum language; they are, however, in accordance with well-known facts of relativistic quantum physics in Hilbert space.

Analysis of the Einstein-Podolsky-Rosen Experiment by Relativistic Quantum Logic

The EPR experiment is investigated within the abstract language of relativistic quantum physics (relativistic quantum logic). First we show that the principles of reality (R) and locality (L) contradict the validity principle (Q) of quantum physics. A reformulation of this argument is then given in terms of relativistic quantum logic which is based on the principlesR andQ. It is shown that the principleL must be replaced by a convenient relaxation ¯L, by which the contradiction can be eliminated. On the other hand this weak locality principle ¯L does not contradict Einstein causality and is thus in accordance with special relativity.

Time dependent propositions and quantum logic

ConclusionCompound propositions which can successfully be defended in a quantumdialogue independent of the elementary propositions contained in it, must have this property also independent of the mutual elementary commensur-abilities. On the other hand, formal commensurabilities must be taken into account. Therefore, for propositions which can be proved by P, irrespective of both the elementary propositions and of the elementary commensur-abilities, there exists a formal strategy of success. The totality of propositions with a formal strategy of success in a quantum dialogue form the effective quantum logic. The propositions of the effective quantum logic can be derived from a calculus Qeff which is — on the other hand — equivalent to a lattice Lqi.Propositions about measuring results are above all time dependent propositions A(S;t). In a dialogue, different partial propositions will have in general different time values. If one can (accidentally) win a material dialogue, this dialogue can be related to a single time value. For the propositions of the effective quantum logic there exist formal strategies of success, independent of the elementary propositions contained in it. All partial propositions appearing in the dialogue are formally commensurable. Therefore the propositions of effective quantum logic which can be proved by formal dialogues can always be related to a single time. They present a description of the system S considered in which all partial propositions can be related jointly to the state of S.Therefore in the effective quantum logic we have — in the limit of equal time values — a situation which corresponds conceptually to the description of the system (S; ψ) in Hilbert space. Consequently, one would expect that also the lattice Lqi — except from the tertium non datur8 — agrees with the lattice Lq of subspaces of Hilbert space. It has been shown that these lattices are in fact isomorphic.

The problem of objectification in quantum mechanics

The hypotheses of weak and strong objectification of quantum mechanical observables, as well as theoretical arguments and experimental evidence against these hypotheses, are systematically reviewed.

Constitution of objects in classical mechanics and in quantum mechanics

The constitution of objects is discussed in classical mechanics and in quantum mechanics. The requirement of objectivity and the Galilei invariance of classical and quantum mechanics leads to the postulate of covariance which must be fulfilled by observable quantities. Objects are then considered as carriers of these covariant observables and turn out to be representations of the Galilei group. Individual systems can be defined in classical mechanics by their trajectories in phase space. However, in quantum mechanics the characterization of individuals can only be achieved approximately by means of unsharp observables.

Die Sprache der Physik

Die Sprache der Physik ist eine prazisierte und vollstandig interpretierte Sprache, die einem Begriffssystem entspricht. Sie ermoglicht die Formulierung der physikalischen Theorien und stellt uber die Interpretation der Begriffe den Zusammenhang zwischen Theorie und Experiment her. Diese Sprache der Physik ist zu unterscheiden von der nicht prazisierten und nur unvollkommen gedeuteten Erlauterungssprache, in der ublicherweise die physikalischen Lehrbucher abgefast sind. Zwar sind die meisten Worter aus der Umgangssprache oder einer daraus entwickelten Bildungssprache entnommen, ihre Bedeutung im Kontext der Physik ist aber durch terminologische Fortsetzungen bestimmt, die nur sehr wenig mit den Bedeutungen zu tun haben, die die betreffenden Worter innerhalb der zahlreichen Verwendungsmoglichkeiten einer naturlichen Sprache besitzen. Dazu kommt, das die Sprache der Physik, obwohl sie bisher nicht durchgehend formalisiert wurde, durch die umfangreiche Verwendung mathematischer Kalkule doch wesentliche Zuge einer Formalsprache besitzt. Wir haben es daher mit einer teilweise formalisierten, im ubrigen durch terminologische Festsetzungen prazisierten Wissenschaftssprache zu tun, die zur Formulierung physikalischer Gesetze und Theorien verwendet werden kann.

Leibniz's Principle, Physics, and the Language of Physics

This paper is concerned with the problem of the validity of Leibnizs principle of the identity of indiscernibles in physics. After briefly surveying how the question is currently discussed in recent literature and which is the actual meaning of the principle for what concerns physics, we address the question of the physical validity of Leibnizs principle in terms of the existence of a sufficient number of naming predicates in the formal language of physics. This approach allows us to obtain in a formal way the result that a principle of the identity of indiscernibles can be justified in the domain of classical physics, while this is not the case in the domain of quantum physics.

Chirality as a quasi-classical property of molecular systems

Abstract It is shown that Hunds model of chiral molecules is not invalidated by perturbations caused by a time dependent potential and that the existence of chiral states can be explained within the framework of ordinary quantum mechanics.