Foundations of Quantum Mechanics

Jauch, Joseph M.; Morrow, R.

doi:10.1119/1.1975143

Cited by 306 publications

(435 citation statements)

References 0 publications

Supporting

Mentioning

423

Contrasting

Unclassified

Order By: Relevance

“…In the sixties and seventies, new formalisms were being investigated by many research groups. In Geneva, the school of Josef Maria Jauch was developing an axiomatic formulation of quantum mechanics [20], and Constantin Piron gave the proof of a fundamental representation theorem for the axiomatic structure [21]. Gunther Ludwig's group in Marburg [22] developed the convex ensemble theory, and in Amherst, Massachusetts, the group of Charles Randall and David Foulis [23,24] was elaborating an operational approach.…”

Section: Magic With Neutronsmentioning

confidence: 99%

The Stuff the World is Made of: Physics and Reality

Aerts¹

1999

Einstein Meets Magritte: An Interdisciplinary Reflection

137

View full text Add to dashboard Cite

Taking into account the results that we have been obtained during the last decade in the foundations of quantum mechanic we put forward a view on reality that we call the 'creation discovery view'. In this view it is made explicit that a measurement is an act of a macroscopic physical entity on a microphysical entity that entails the creation of new elements of reality as well as the detection of existing elements of reality. Within this view most of the quantum mechanical paradoxes are due to structural shortcomings of the standard quantum theory, which means that our analysis agrees with the claim made in the Einstein Podolsky Rosen paper, namely that standards quantum mechanics is an incomplete theory. This incompleteness is however not due to the absence of hidden variables but to the impossibility for standard quantum mechanics to describe separated quantum entities. Nonlocality appears as a genuine property of nature in our view and makes it necessary to reconsider the role of space in reality. Our proposal for a new interpretation for space makes it possible to put forward an new hypothesis for why it has not been possible to unify quantum mechanics and relativity theory.Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Absolute, true, and mathematical time, of itself, and from its own nature, flows equally without relation to anything external.Isaac Newton, 1642 -1726. * Published as: Aerts, D., 1999, "The stuff the world is made of: physics and reality", in Einstein meets Magritte: an interdisciplinary reflection, eds. Aerts, D., Broekaert, J. and Mathijs, E., Kluwer Academic, Dordrecht.

show abstract

Section: Magic With Neutronsmentioning

confidence: 99%

The Stuff the World is Made of: Physics and Reality

Aerts¹

1999

Einstein Meets Magritte: An Interdisciplinary Reflection

137

View full text Add to dashboard Cite

show abstract

“…As regards the main requirements of a satisfactory theory of the measurement process, it is clear from the works of Bohr [8], Jauch [9] and Van Kampen [2] that such a theory demands both a characterisation of the macroscopicality of the observables M and an amplification property of the S − I coupling whereby different microstates of S give rise to macroscopically different states of I. Evidently, this implies that the initial state in which I is prepared must be unstable against microscopic changes in the state of S. On the other hand, as emphasised by Whitten-Wolfe and Emch [10,11], the correspondence between the microstate of S and the eventual observed macrostate of I must be stable against macroscopically small changes in the initial state of this instrument, of the kind that are inevitable in experimental procedures. Thus, the initial state of I must be metastable by virtue of this combination of stability and instability properties.…”

Section: Introductory Discussionmentioning

confidence: 99%

“…Our treatment of this model is designed to obtain conditions on the S − I coupling that lead to both the reduction of the wave-packet and the required correspondence between the reading of the instrument's pointer and the resultant state of S. As in the works [2] , [8][9][10][11] and [14], we avoid the assumption of Von Neumann [1] and Wigner [19] that the observation of the pointer of I requires another measuring instrument, I 2 , which in turn requires yet another instrument, and so on, in such a way that the whole process involves an infinite regression ending up in the observer's brain! Instead, we assume that the measurement process ends with the reading of the pointers that evaluate the macrovariables M of I.…”

Section: Introductory Discussionmentioning

confidence: 99%

See 1 more Smart Citation

On the mathematical structure of quantum measurement theory

Sewell

2005

Reports on Mathematical Physics

View full text Add to dashboard Cite

We show that the key problems of quantum measurement theory, namely the reduction of the wave-packet of a microsystem and the specification of its quantum state by a macroscopic measuring instrument, may be rigorously resolved within the traditional framework of the quantum mechanics of finite conservative systems. The argument is centred on the generic model of a microsystem, S, coupled to a finite macroscopic measuring instrument I, which itself is an N -particle quantum system. The pointer positions of I correspond to the macrostates of this instrument, as represented by orthogonal subspaces of the Hilbert space of its pure states. These subspaces, or 'phase cells', are the simultaneous eigenspaces of a set of coarse grained intercommuting macro-observables, M , and, crucially, are of astronomically large dimensionalities, which increase exponentially with N . We formulate conditions on the conservative dynamics of the composite (S + I) under which it yields both a reduction of the wave packet describing the state of S and a one-toone correspondence, following a measurement, between the observed pointer position of I and the resultant eigenstate of S; and we show that these conditions are fulfilled by the finite version of the Coleman-Hepp model.Key Words: Schroedinger dynamics of microsystem-cum-measuring instrument; macroscopic phase cells as pointer positions; macroscopic decoherence; reduction of wave packet of microsystem. *

show abstract

“…This has been the case, most prominently, in [29,39,40] and also in an important state-of-the-art book [4]. Quantum logical assumptions are simple enough to be accessible for direct comprehension, in contrast to Mackey's mathematically formulated axioms, but they tend to be linguistic rather than physical.…”

Section: M9mentioning

confidence: 99%

Reconstruction of Quantum Theory

Grinbaum

2007

The British Journal for the Philosophy of Science

View full text Add to dashboard Cite

What belongs to quantum theory is no more than what is needed for its derivation. Keeping to this maxim, we record a paradigmatic shift in the foundations of quantum mechanics, where the focus has recently from interpreting to reconstructing quantum theory. Several historic and contemporary reconstructions are analyzed, including the ones due to Hardy, Rovelli, and Clifton, Bub and Halvorson. We conclude by discussing the importance of a novel concept of intentionally incomplete reconstruction.1 What is wrong with interpreting quantum mechanics?Ever since the first days of quantum mechanics physicists as well as philosophers tried to interpret it, understanding this task as a problem of giving to the new physical theory a clear meaning. One of the principal reasons why one has always felt the need for interpretations has to do with the puzzling aspect of the formalism of quantum mechanics, usually referred to as the measurement problem. Reversible unitary evolution of the wave function, according to standard quantum mechanics, at the moment of measurement is replaced by an irreversible transformation known as wavefunction collapse. First and foremost, interpretations of quantum mechanics aimed at making sense of this surprising change in the theory's dynamics, sometimes taking the collapse at face value and claiming its fundamental irreducible role, or sometimes going to another extreme and denying the collapse altogether. However, looking globally, the enterprize of interpreting quantum mechanics failed: today we still have no consensus on what the meaning of quantum theory is. None of the proposed answers has won overall acceptance. Perhaps the most remarkable manifestation of the failure to interpret quantum mechanics is the attitude taught to most young physicists in 1 lecture rooms and research laboratories in the last half century, "Shut up and calculate!" [37] Why did attempts at a univocal interpretation fail? Many answers are possible, and among them we favor two, both showing that there is an intrinsic deficiency in the idea of interpreting a physical theory with the help of philosophical instruments only.The first answer is that to a physical theory one would naturally like to give a physical meaning in the Greek sense of ϕύσις, i.e. we-as part of the physicists' audience-expect to be told a true story about nature. This is because we casually tend to apply physical theory to the phenomenal world to learn something about the latter, and not the world to physical theory in order to invent a meaning of the theory. Physical theory is above all a tool for predicting the yet unobserved phenomena; so employing existing knowledge and experience of the world to interpret physics runs counter to its basic function as a scientific theory. However, notwithstanding such an against-the-grain direction in which a philosophical interpretation operates, the former does not necessarily lead to formal contradiction that would invalidate the interpretation program logically; more modestly but perhaps no less irr...

show abstract

Foundations of Quantum Mechanics

Cited by 306 publications

References 0 publications

The Stuff the World is Made of: Physics and Reality

The Stuff the World is Made of: Physics and Reality

On the mathematical structure of quantum measurement theory

Reconstruction of Quantum Theory

Contact Info

Product

Resources

About