Amit Hagar

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".

Huw Price (1996, 2002, 2003) argues that causal-dynamical theories that aim to explain thermodynamic asymmetry in time are misguided. He points out that in seeking a dynamical factor responsible for the general tendency of entropy to increase, these approaches fail to appreciate the true nature of the problem in the foundations of statistical mechanics (SM). I argue that it is Price who is guilty of misapprehension of the issue at stake. When properly understood, causal-dynamical approaches in the foundations of SM offer a solution for a different problem; a problem that unfortunately receives no attention in Price’s celebrated work.

Quantum computers are hypothetical quantum information processing (QIP) devices that allow one to store, manipulate, and extract information while harnessing quantum physics to solve various computational problems and do so putatively more efficiently than any known classical counterpart. Despite many ‘proofs of concept’ (Aharonov and Ben–Or 1996; Knill and Laflamme 1996; Knill et al. 1996; Knill et al. 1998) the key obstacle in realizing these powerful machines remains their scalability and susceptibility to noise: almost three decades after their conceptions, experimentalists still struggle to maintain useful quantum coherence in QIP devices with more than a pair of qubits (e.g., Blatt and Wineland 2008). This slow progress has prompted debates on the feasibility of quantum computers, yet the quantum information community has dismissed the skepticism as “ideology” (Aaronson 2004), claiming that the obstacles are merely technological (Kaye et al. 2007, 240). In a recent paper (Hagar 2009) I’ve argued that such a skepticism with respect to the feasibility of quantum computers need not be deemed ideological at all, and that the aforementioned ‘proofs of concept’ are physically suspect. Using analogies from the foundations of classical statistical mechanics (SM), I’ve also argued that instead of active error correction, the appropriate framework for debating the feasibility of large–scale, fault–tolerant and computationally superior quantum computers should be the project of error avoidance: rather than trying to constantly ‘cool down’ the QIP device and prevent its thermalization, one should try to locate those regions in the device’s state space which are thermodynamically ‘abnormal’, i.e., those regions in the device’s state space which resist thermalization regardless of external noise. This paper is intended as a further contribution to the debate on the feasibility of large–scale, fault–tolerant and computationally superior quantum computers. Relying again on analogies from the foundations of classical SM, it suggests a skeptical conjecture and frames it in the ‘passive’, error avoidance, context..