This chapter reconstructs Kuhn’s philosophy of measurement and data, paying special attention to what he calls the “fifth law of thermodynamics.” According to this law, there will always be discrepancies between experimental results and scientists’ prior expectations. The history of experiments to determine the values of the fundamental constants offers a striking illustration of Kuhn’s fifth law of thermodynamics, with no experiment giving quite the expected result. The chapter highlights the synergy between Kuhn’s view and the systematic project of iteratively determining the value of physical constants, initiated by spectroscopist Raymond Birge, which was ongoing when Kuhn joined Berkeley in 1956. The analysis sheds light on various underappreciated aspects of Kuhn’s thought, especially his notion of progress as improvement in measurement accuracy.

Recently there has emerged an exciting and rapidly growing field of research known as quantum information theory. This interdisciplinary field is unified by the following two goals: first, the possibility of harnessing the principles and laws of quantum mechanics to aid in the acquisition, transmission, and processing of information; and second, the potential that these new technologies have for deepening our understanding of the foundations of quantum mechanics and computation. Many of the new technologies and discoveries emerging from quantum information theory are challenging the adequacy of our old concepts of entanglement, non-locality, and information. This research suggests that the time is ripe for a reconsideration of the foundations – and philosophical implications – of quantum information theory.

Historically, apart from a small group of physicists working on foundational issues, it was philosophers of physics who recognized the importance of the concepts of entanglement and non-locality long before the mainstream physics community. Prior to the 1980s, discussions of the infamous “EPR” paper and John Bell's seminal papers on quantum non-locality were carried out more often by such philosophers than by ordinary physicists. In the 1990s that situation rapidly changed, once the larger community of physicists had begun to realize that entanglement and non-locality were not just quirky features of quantum mechanics, but physical resources that could be harnessed for the performance of various practical tasks. Since then, a large body of literature has emerged in physics, revealing many new dimensions to our concepts of entanglement and non-locality, particularly in relation to information. Regrettably, however, only a few philosophers have followed these more recent developments, and many philosophical discussions still end with Bell's work.

Entanglement can be understood as an extraordinary degree of correlation between states of quantum systems – a correlation that cannot be given an explanation in terms of something like a common cause. Entanglement can occur between two or more quantum systems, and the most interesting case is when these correlations occur between systems that are space-like separated, meaning that changes made to one system are immediately correlated with changes in a distant system even though there is no time for a signal to travel between them. In this case one says that quantum entanglement leads to non-local correlations, or non-locality.

More precisely, entanglement can be defined in the following way. Consider two particles, A and B, whose (pure) states can be represented by the state vectors ψA and ψB. Instead of representing the state of each particle individually, one can represent the composite two-particle system by another wavefunction, ΨAB. If the two particles are unentangled, then the composite state is just the tensor product of the states of the components: ΨAB = ψA ⊗ ψB; the state is then said to be factorable (or separable). If the particles are entangled, however, then the state of the composite system cannot be written as such a product of a definite state for A and a definite state for B. This is how an entangled state is defined for pure states: a state is entangled if and only if it cannot be factored: ΨAB ≠ ψA ⊗ ψB.

The challenge of semiclassical mechanics: Reassessing the views

Semiclassical mechanics significantly broadens our understanding of the relationship between classical and quantum mechanics. It reveals that there is much more to the relation between these theories than simply showing that classical behavior can be recovered from quantum systems in the limit of large actions (ħ → 0) or large quantum numbers (n → ∞). Although these limits are an important piece of the puzzle, the usual reductionist account of the quantum–classical relation in terms of these limits alone does not tell the whole story.

More specifically, research in semiclassical mechanics has uncovered a number of surprising theoretical and experimental correspondences. Indeed the program of semiclassical research can be broadly understood as the theoretical and experimental task of uncovering these correspondences and extending them in new ways. On the theoretical side, semiclassical methods such as EBK quantization, Gutzwiller's trace formula, and closed orbit theory show how classical structures can be used to construct quantum quantities. These semiclassical methods have proven to be not just useful calculational tools, but also important investigative tools, in that they are often able to provide physical insight into the structure of the quantum dynamics, and hence lead to new discoveries.

The rise and fall of the old quantum theory

The principles of the old quantum theory were first articulated by Niels Bohr in 1913 in a three-part paper titled “On the Constitution of Atoms and Molecules.” Bohr had adopted Ernest Rutherford's model of the atom, according to which the mass of the atom is concentrated in a small central nucleus, while the electrons orbit the nucleus in planetary trajectories. The key challenge facing Rutherford's model was that it was unstable: according to classical electrodynamics, the electron, which is a moving charged body, should radiate energy and so eventually collapse into the nucleus. Bohr's solution was to incorporate Max Planck's theory of radiation, according to which “the energy radiation from an atomic system does not take place in the continuous way assumed in ordinary electrodynamics, but that it, on the contrary, takes place in distinctly separated emissions” (Bohr 1913, p. 4; BCW 2, p. 164). In this early paper, and most subsequent accounts, Bohr summarized his quantum theory by means of two assumptions or postulates. According to the first postulate, electrons cannot travel in any path they like around the nucleus, rather atomic systems can only exist in a series of discrete “stationary states,” in which the electron is in a particular allowed stable periodic orbit and is not emitting radiation.