This is a textbook on quantum mechanics. It is addressed to graduates and advanced undergraduates. The book presents quantum theory as a logically coherent system, placing stronger emphasis on the theory' s probabilistic structure and on the role of symmetries. It makes students aware of foundational problems from the very beginning, but at the same time, it urges them to adopt a pragmatic attitude towards the quantum formalism. The book consists of five parts. Part I is a review of classical (...) physics, including probability theory, and a historical introduction to quantum theory. Part II presents quantum theory in terms of six fundamental principles. The principles are presented together with the necessary mathematical background and with applications to simple systems. Part III analyses the properties of quantum particles. It starts with the description of symmetries, continues to non-relativistic particles, the introduction of spin, and particle statistics. It concludes with a symmetries-based introduction to relativistic quantum systems and with the first steps towards relativistic quantum field theory. Part IV presents techniques adapted to specific problems: the structure and spectra of composite systems, decays and transitions, particle scattering, and open quantum systems. Finally, Part V revisits quantum foundations: quantum measurement theory, the major interpretations of quantum theory, and the frontiers of quantum theory in contemporary research. (shrink)

This survey tries to investigate the truths and deficiencies of prevalent philosophy about Uncertainty Relations (UR) and Quantum Measurements (QMS). The respective philosophy, known as being eclipsed by unfinished controversies, is revealed to be grounded on six basic precepts. But one finds that all the respective precepts are discredited by insurmountable deficiencies. So, in regard to UR, the alluded philosophy discloses oneself to be an unjustified mythology. Then UR appear either as short-lived historical conventions or as simple and limited mathematical (...) formulas, without any essential significance for physics. Such a finding reinforces the Dirac’s prediction that UR “in their present form will not survive in the physics of future”. The noted facets of UR motivate reconsiderations of associated debates on QMS. Mainly one reveals that, properly, UR have not any essential connection with genuine descriptions of QMS. For such descriptions, it is necessary that, mathematically, the quantum observables to be considered as random variables. The measuring scenarios with a single sampling, such are wave function collapse or Schrodinger’s cat thought experiment, are revealed as being useless ¨inventions. We propose to describe QMS as transmission processes for stochastic data. Note that, for existing quantum debates, the above UR–QMS revaluations, offer a few arguments for lucrative parsimony in approaches of matters. The unlucrative aspects of those debates have to be reconsidered too, probably in more or less speculative visions. (shrink)

A potentially new interpretation of quantum mechanics posits the state of the universe as a consistent set of facts that are instantiated in the correlations among entangled objects. A fact (or event) occurs exactly when the number or density of future possibilities decreases, and a quantum superposition exists if and only if the facts of the universe are consistent with the superposition. The interpretation sheds light on both in-principle and real-world predictability of the universe.

For sharp quantum observables the following facts hold: (i) if we have a collection of sharp observables and each pair of them is jointly measurable, then they are jointly measurable all together; (ii) if two sharp observables are jointly measurable, then their joint observable is unique and it gives the greatest lower bound for the effects corresponding to the observables; (iii) if we have two sharp observables and their every possible two outcome partitionings are jointly measurable, then the observables themselves (...) are jointly measurable. We show that, in general, these properties do not hold. Also some possible candidates which would accompany joint measurability and generalize these apparently useful properties are discussed. (shrink)

The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency—or potentiality—of (...) a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way. (shrink)

In the phenomenology of the consciousness of internal time, Edmund Husserl has frequent recourse to sound and melody as illustrations of the processes that give rise to immanent temporal objects. In Husserl’s analysis, there is a philosophically pregnant tension between the geometrical diagrams representing multiple dimensions of immanent time and his intuition that time-points might be no more than fictions leading to absurdities. In this paper, I will address this tension in order to motivate a complementarity approach to temporal objects (...) such as sound and melody that might illuminate the phenomenology of sound-consciousness. (shrink)

We analyze the question whether or not quantum theory should be used to describe single particles. Our final result is that a rational basis for such an ’individuality interpretation’ does not exist. A critical examination of three principles, supporting the individuality interpretation, leads to the result that no one of these principles seems to be realized in nature. The well-known controversy characterized by the names of Einstein, Bohr and Bell is analyzed. EPR proved ’predictive incompleteness’ of quantum theory, which implies (...) that no individuality interpretation exists. Contrary to the common opinion, Bell’s proof of ’metaphysical completeness’ does not invalidate EPR’s proof because two crucially different meanings of ’completeness’ are involved. The failure to distinguish between these two meanings is closely related to a fundamentally deterministic world view, which dominated the thinking of the 19th century and determines our thinking even today. (shrink)

For many among the scientifically informed public, and even among physicists, Heisenberg's uncertainty principle epitomizes quantum mechanics. Nevertheless, more than 86 years after its inception, there is no consensus over the interpretation, scope, and validity of this principle. The aim of this chapter is to offer one such interpretation, the traces of which may be found already in Heisenberg's letters to Pauli from 1926, and in Dirac's anticipation of Heisenberg's uncertainty relations from 1927, that stems form the hypothesis of finite (...) nature. Instead of a mere mathematical theorem of quantum theory, or a manifestation of "wave-particle duality", the uncertainty relations turn out to be a result of a more fundamental premise, namely, the inherent limitation on spatial resolution that follows from the bound on physical resources. The implication of this view are far reaching: it depicts the Hilbert space formalism as a phenomenological, "effective", formalism that approximates an underlying discrete structure; it supports a novel interpretation of probability in statistical physics that sees probabilities as deterministic, dynamical transition probabilities which arise from objective and inherent measurement errors; and it helps to clarify several puzzles in the foundations of statistical physics, such as the status of the "disturbance" view of measurement in quantum theory, or the tension between ontology and epistemology in the attempts to describe nature with physical theories whose formalisms include subjective probabilities. Finally, this view also renders obsolete the entire class of interpretations of quantum theory that adhere to "the reality of the wave function". (shrink)

Time, along with concepts as space and matter, is bound to be a central concept of any physical theory. The chapter first discusses how time is treated similarly in quantum and classical theories. It then provides a few references on time‐reversal. The chapter discusses three chosen authors' (Paul Busch, Jan Hilgevoord and Jos Uffink) clarifications of uncertainty principles in general. Next, the chapter follows Busch in distinguishing three roles for time in quantum physics. They are external time, intrinsic time and (...) observable time. It also provides a brief discussion on time operators, in particular Pauli's influential proof. Finally, the chapter talks about time‐energy uncertainty principles with intrinsic times. (shrink)

In this paper we review some properties of fuzzy observables, mainly as realized by commutative positive operator valued measures. In this context we discuss two representation theorems for commutative positive operator valued measures in terms of projection valued measures and describe, in some detail, the general notion of fuzzification. We also make some related observations on joint measurements.

This is an entry to the Compendium of Quantum Physics, edited by F Weinert, K Hentschel and D Greenberger, to be published by Springer-Verlag.