Online research in philosophy

The central part of Everett's formulation of quantum mechanics is a quantum mechanical model of memory and of observation as the recording of information in a memory. To use this model as an answer to the measurement problem, Everett has to assume that a conscious observer can be in a superposition of such memory states and be unaware of it. This assumption has puzzled generations of readers. The fundamental aim of this dissertation is to find a set of simpler assumptions which are sufficient to show that Everett's model is empirically adequate. I argue that Everett's model needs three assumptions to account for the process of observation: an assumption of decoherence of observers as quantum mechanical systems; an assumption of supervenience of mental states (qualities) over quantum mechanical properties; and an assumption about the interpretation of quantum mechanical states in general: quantum mechanical states describe ensembles of states of affairs coexisting in the same system. I argue that the only plausible understanding of such ensembles is as ensembles of possibilities, and that all standard no-collapse interpretations agree in this reading of quantum mechanical states. Their differences can be understood as different theories about what marks the real state within this ensemble, and Everett's theory as the claim that no additional 'mark of reality' is necessary. Using the three assumptions, I argue that introspection cannot determine the objective quantum mechanical state of an observer. Rather, the introspective qualities of a quantum mechanical state can be represented by a (classical) statistical ensemble of subjective states. An analysis of these subjective states and their dynamics leads to the conclusion that they suffice to give empirically correct predictions. The argument for the empirical adequacy of the subjective state entails that knowledge of the objective quantum mechanical state is impossible in principle. Empirical reality for a conscious observer is not described by the objective state, but by a Everettian relative state conditional on the subjective state, and no theoretical 'mark of reality' is necessary for this concept of reality. I compare the resulting concept of reality to Kant's distinction between empirical and transcendental reality.

A remarkable theorem by Clifton, Bub and Halvorson (2003) (CBH) characterizes quantum theory in terms of information--theoretic principles. According to Bub (2004, 2005) the philosophical significance of the theorem is that quantum theory should be regarded as a ``principle'' theory about (quantum) information rather than a ``constructive'' theory about the dynamics of quantum systems. Here we criticize Bub's principle approach arguing that if the mathematical formalism of quantum mechanics remains intact then there is no escape route from solving the measurement problem by constructive theories. We further propose a (Wigner--type) thought experiment that we argue demonstrates that quantum mechanics on the information--theoretic approach is incomplete.

This paper is concerned with the description of the process of measurement within the context of a quantum theory of the physical world. It is noted that quantum mechanics permits a quasi-classical description (classical in the limited sense implied by the correspondence principle of Bohr) of those macroscopic phenomena in terms of which the observer forms his perceptions. Thus, the process of measurement in quantum mechanics can be understood on the quasi-classical level by transcribing from the strictly classical observables of Newtonian physics to their quasi-classical counterparts the known rules for the measurement of the former. The remaining physical problem is the delineation of the circumstances in which the correlation of a peculiarly quantum mechanical observable A with a classically measurable observable B can result in a significant measurement of A. This is undertaken within the context of quantum theory. The resulting clarification of the process of measurement has important implications relative to the philosophic interpretation of quantum mechanics.

The paper presents an argument for the incompleteness in principle of quantum mechanics. I introduce four principles (P0–P3) concerning the interpretation of probability, in general and in quantum mechanics, and argue that the defender of completeness must reject either P0 or all of P1–P3, which options both seem unacceptable. The problem is shown to be more fundamental than the measurement problem and to have implications for our understanding of quantum-mechanical contextuality.

This paper attempts an interpretation of Everett's relative state formulation of quantum mechanics that avoids the commitment to new metaphysical entities like ‘worlds’ or ‘minds’. Starting from Everett's quantum mechanical model of an observer, it is argued that an observer's belief to be in an eigenstate of the measurement (corresponding to the observation of a well-defined measurement outcome) is consistent with the fact that she objectively is in a superposition of such states. Subjective states corresponding to such beliefs are constructed. From an analysis of these subjective states and their dynamics it is argued that Everett's pure wave mechanics is subjectively consistent with von Neumann's classical formulation of quantum mechanics. It follows from the argument that the objective state of a system is in principle unobservable. Nevertheless, an adequate concept of empirical reality can be constructed.

We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance, the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles. These include the uncertainty principle and the violation of Bell's inequality among others. Quantum gambles are closely related to quantum logic and provide a new semantics for it. We conclude with a philosophical discussion on the interpretation of quantum mechanics.

The fallacy that the many worlds interpretation (MWI) of quantum mechanics implies certain survival in quantum-Russian-roulette-like situations (the ‘Quantum Suicide’ (QS) thought experiment) has become common enough that it is now necessary to publicly debunk this belief despite the risk of further publicizing it. ‘Quantum Immortality’ (QI) is an extension of the QS Fallacy (QSF) with some additional unlikely assumptions. The QS/QI ideas are examined here and shown to be false.

An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented which are based upon different decision theories and upon Gleason's Theorem. It is argued that decision theory gives Everettians most or all of what they need from `probability'. Contact is made with Lewis's Principal Principle linking subjective credence with objective chance: an Everettian Principal Principle is formulated, and shown to be at least as defensible as the usual Principle. Some consequences of (Everettian) quantum mechanics for decision theory itself are also discussed.

[NB: this this long (70 pages) and occasionally rambling online-only paper has been almost entirely superseded by material in subsequent; if something is not included in them it usually means that I have had second thoughts. I include it for completeness only.

A quantum particle moving in a gravitational field may penetrate the classically forbidden region of the gravitational potential. This raises the question of whether the time of flight of a quantum particle in a gravitational field might deviate systematically from that of a classical particle due to tunnelling delay, representing a violation of the weak equivalence principle. I investigate this using a model quantum clock to measure the time of flight of a quantum particle in a uniform gravitational field, and show that a violation of the equivalence principle does not occur when the measurement is made far from the turning point of the classical trajectory. The results are then confirmed using the so-called dwell time definition of quantum tunnelling. I conclude with some remarks about the strong equivalence principle in quantum mechanics.

The experimental setup of the self-referential quantum measurement, jovially known as the "quantum suicide" or the "quantum Russian roulette" is analyzed from the point of view of the Principal Principle of David Lewis. It is shown that the apparent violation of this principle---relating objective probabilities and subjective chance---in this type of thought experiment is just an illusion due to the usage of some terms and concepts ill-defined in the quantum context. We conclude that even in the case that Everett's (or some other "no-collapse") theory is a correct description of reality, we can coherently believe in equating subjective credence with objective chance in quantum-mechanical experiments. This is in agreement with results of the research on personal identity in the quantum context by Parfit and Tappenden.