Foundations of Quantum Theory
From Classical Concepts to Operator Algebras
Page
%P
-
Article
Open AccessPenrose’s 1965 singularity theorem: from geodesic incompleteness to cosmic censorship
Supplementing earlier literature by e.g. Tipler et al. (1980), Israel (1987), Thorne (1994), Earman (1999), Senovilla and Garfinkle (2015), Curiel (2019) and Landsman (2021), I provide a historical and concept...
-
Article
Open AccessBohmian Mechanics is Not Deterministic
I argue that Bohmian mechanics (or any similar pilot-wave theory) cannot reasonably be claimed to be a deterministic theory. If one assumes the “quantum equilibrium distribution” provided by the wave function ...
-
Article
Open AccessSingularities, Black Holes, and Cosmic Censorship: A Tribute to Roger Penrose
In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose’s work on general relativity. His 1965 singularity theorem (for w...
-
Chapter
Indeterminism and Undecidability
The aim of this paper is to argue that the (alleged) indeterminism of quantum mechanics, claimed by adherents of the Copenhagen interpretation since Born [8], can be proved from Chaitin’s follow-up to Gödel’s (fi...
-
Article
Open AccessRandomness? What Randomness?
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compre...
-
Article
Editorial
-
Chapter and Conference Paper
Symmetries in Exact Bohrification
The ‘Bohrification” program in the foundations of quantum mechanics implements Bohr’s doctrine of classical concepts through an interplay between commutative and non-commutative operator algebras. Following a ...
-
Article
Does physics make us free?
-
Book
-
Chapter
The measurement problem
The measurement problem of quantum mechanics was probably born in 1926: ‘Thus Schrödinger’s quantum mechanics gives a very definite answer to the question of the outcome of a collision; however, this does not ...
-
Chapter
Classical physics on a finite phase space
Throughout this chapter, X is a finite set, playing the role of the configuration space of some physical system, or, equivalently (as we shall see), of its pure state space (in the continuous case, X will be the ...
-
Chapter
Classical physics on a general phase space
Passing from finite phase spaces X to infinite ones yields many fascinating new phenomena, some of which even seem genuinely “emergent” in not having any finite dimensional shadow, approximate or otherwise. Nonet...
-
Chapter
Symmetry in quantum mechanics
Roughly speaking, a symmetry of some mathematical object is an invertible transformation that leaves all relevant structure as it is. Thus a symmetry of a set is just a bijection (as sets have no further structur...
-
Chapter
Limits: Small \(\hbar \)
Limits are essential to the asymptotic Bohrification program. It was recognized at an early stage in the development of quantum mechanics that the limit
-
Chapter
Symmetry in algebraic quantum theory
In §3.9 we defined symmetries of classical physics as symmetries of either Poisson manifolds or Poisson algebras; these notions are equivalent.
-
Chapter
Spontaneous Symmetry Breaking
As we shall see, the undeniable natural phenomenon of spontaneous symmetry breaking (SSB) seems to indicate a serious mismatch between theory and reality. This mismatch is well expressed by what is sometimes c...
-
Chapter
Topos theory and quantum logic
The topos-theoretic approach to quantum mechanics (also known as quantum toposophy) has the same origin as the quantum logic programme initiated by Birkhoff and von Neumann, namely the feeling that classical logi...
-
Chapter
Quantum mechanics on a finite-dimensional Hilbert space
The quantum analogue of a finite set X (in its role as a configuration space in classical mechanics) is the finite-dimensional Hilbert space ...
-
Chapter
Quantum physics on a general Hilbert space
In this chapter we generalize the results of Chapter 2 to infinite-dimensional Hilbert spaces. So let H be a Hilbert space and let B(H) be the set of all bounded operators on H. Here a notable point is that linea...
-
Chapter
Classical models of quantum mechanics
This chapter gives an introduction to a chain of results attempting to exclude deeper layers underneath quantum mechanics that restore some form of classical physics: ‘[Such results] more or less illustrate th...
