String dualities and empirical equivalence

String dualities establish empirical equivalence between theories that often look entirely different with respect to their basic ontology and physical structure. Therefore, they represent a particularly interesting example of empirical equivalence in physics. However, the status of duality relations in string physics differs substantially from the traditional understanding of the role played by empirical equivalence. The paper specifies three important differences and argues that they are related to a substantially altered view on the underdetermination of theory building.     

Dualities of fields and strings

Duality, the equivalence between seemingly distinct quantum systems, is a curious property that has been known for at least three quarters of a century. In the past two decades it has played a central role in mapping out the structure of theoretical physics. I discuss the unexpected connections that have been revealed among quantum field theories and string theories. Written for a special issue of Studies in History and Philosophy of Modern Physics.     

Decision theory and information propagation in quantum physics

In recent papers, Zurek [(2005). Probabilities from entanglement, Born's rule p_k=|ψ_k|² from entanglement. Physical Review A, 71, 052105] has objected to the decision-theoretic approach of Deutsch [(1999) Quantum theory of probability and decisions. Proceedings of the Royal Society of London A, 455, 3129–3137] and Wallace [(2003). Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation. Studies in History and Philosophy of Modern Physics, 34, 415–438] to deriving the Born rule for quantum probabilities on the grounds that it courts circularity. Deutsch and Wallace assume that the many worlds theory is true and that decoherence gives rise to a preferred basis. However, decoherence arguments use the reduced density matrix, which relies upon the partial trace and hence upon the Born rule for its validity. Using the Heisenberg picture and quantum Darwinism—the notion that classical information is quantum information that can proliferate in the environment pioneered in Ollivier et al. [(2004). Objective properties from subjective quantum states: Environment as a witness. Physical Review Letters, 93, 220401 and (2005). Environment as a witness: Selective proliferation of information and emergence of objectivity in a quantum universe. Physical Review A, 72, 042113]—I show that measurement interactions between two systems only create correlations between a specific set of commuting observables of system 1 and a specific set of commuting observables of system 2. This argument picks out a unique basis in which information flows in the correlations between those sets of commuting observables. I then derive the Born rule for both pure and mixed states and answer some other criticisms of the decision theoretic approach to quantum probability.     

The role of a posteriori mathematics in physics

The calculus that co-evolved with classical mechanics relied on definitions of functions and differentials that accommodated physical intuitions. In the early nineteenth century mathematicians began the rigorous reformulation of calculus and eventually succeeded in putting almost all of mathematics on a set-theoretic foundation. Physicists traditionally ignore this rigorous mathematics. Physicists often rely on a posteriori math, a practice of using physical considerations to determine mathematical formulations. This is illustrated by examples from classical and quantum physics. A justification of such practice stems from a consideration of the role of phenomenological theories in classical physics and effective theories in contemporary physics. This relates to the larger question of how physical theories should be interpreted.     

Reduction and emergence in the fractional quantum Hall state

We present the fractional quantum Hall (FQH) effect as a candidate emergent phenomenon. Unlike some other putative cases of condensed matter emergence (such as thermal phase transitions), the FQH effect is not based on symmetry breaking. Instead FQH states are part of a distinct class of ordered matter that is defined topologically. Topologically ordered states result from complex long-ranged correlations between their constituent parts, such that the system displays strongly irreducible, qualitatively novel properties.     

Constraints and divergent assessments of fertility in non-empirical physics in the history of the string theory controversy

This paper examines historic appraisals of string theory to develop a less abstract understanding of the string theory controversy and assessment in non-empirical physics. This historical approach reveals several points of conflict in the controversy, each centring on a constraint. By proceeding stepwise through these constraints, I reveal the role that constraints played in determining divergent assessments of string theory. Rather than disagreement between two competing methods, a level of agreement is found amongst those critical and supportive of string theory as to the commitment to the relevant constraints, but disagreement as to the sufficiency of consistency, the path to background independence and a non-perturbative formulation, and how to interpret the significance of applications. Furthermore, the string theory community itself is shown to be divided in its commitment to the necessity of uniqueness and the legitimacy of anthropic reasoning. These varied assessments, guided by considerations of constraints, have informed divergent claims as to the past and future fertility of string theory. These are claims as to the value of string theory in guiding research in quantum gravity: claims as to whether string theory has and will be valuable as a means rather than an end.     

Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II: The search of the interface between QFT and QG

The main topics of this second part of a two-part essay are some consequences of the phenomenon of vacuum polarization as the most important physical manifestation of modular localization. Besides philosophically unexpected consequences, it has led to a new constructive “outside-inwards approach” in which the pointlike fields and the compactly localized operator algebras which they generate only appear from intersecting much simpler algebras localized in noncompact wedge regions whose generators have extremely mild almost free field behavior.Another consequence of vacuum polarization presented in this essay is the localization entropy near a causal horizon which follows a logarithmically modified area law in which a dimensionless area (the area divided by the square of dR where dR is the thickness of a light-sheet) appears. There are arguments that this logarithmically modified area law corresponds to the volume law of the standard heat bath thermal behavior. We also explain the symmetry enhancing effect of holographic projections onto the causal horizon of a region and show that the resulting infinite dimensional symmetry groups contain the Bondi–Metzner–Sachs group. This essay is the second part of a partitioned longer paper.     

String theory,Einstein, and the identity of physics: Theory assessment in absence of the empirical

String theorists are certain that they are practicing physicists. Yet, some of their recent critics deny this. This paper argues that this conflict is really about who holds authority in making rational judgment in theoretical physics. At bottom, the conflict centers on the question: who is a proper physicist? To illustrate and understand the differing opinions about proper practice and identity, we discuss different appreciations of epistemic virtues and explanation among string theorists and their critics, and how these have been sourced in accounts of Einstein's biography. Just as Einstein is claimed by both sides, historiography offers examples of both successful and unsuccessful non-empirical science. History of science also teaches that times of conflict are often times of innovation, in which novel scholarly identities may come into being. At the same time, since the contributions of Thomas Kuhn historians have developed a critical attitude towards formal attempts and methodological recipes for epistemic demarcation and justification of scientific practice. These are now, however, being considered in the debate on non-empirical physics.