**Adam Caulton**

**University of Cambridge**

*Adventures off the mass-shell*

What is the correct possibility space for a given particle of a quantum field? The firm orthodoxy, initiated by Wigner in 1939, is that we should look to the irreducible representations of the Poincaré group. I argue that the justifications for this are murky, and offer two rational reconstructions. According to one, the justification is that the Poincaré group comprises all the actions that can be performed on a simple system; but this is false, made particularly relevant in the case of interactions. According to another, conflicting reconstruction, Poincaré invariance is a reality condition; but this applies only to the entire system of fields, not to individual particles. Therefore it ought not constrain the possibility spaces of individual particles.

Consequently, I argue, we have reason to consider “larger” state spaces than are normally considered. The elements of these state spaces represent entire four-dimensional histories rather than instantaneous states, most of which are “off mass-shell”, in that the relativistic mass condition is violated. I conclude by arguing that off-mass-shell particles, far from being mere formal inventions for the sake of S-matrix calculations, are just as “real” as their free counterparts—indeed, they are to be found as much in classical relativistic theories as in quantum relativistic theories.

**Fay Dowker**

**Imperial College London**

*Towards a Quantum Analogue of the Fine Trio*

There is a trio of equivalent conditions on a set of experimental probabilities: (i) the existence of a locally causal model, (ii) the existence of a joint probability measure on all the experimental outcomes that returns the experimental probabilities as marginals and (iii) the relevant collection of Bell inequalities. I will refer to these conditions as (i) “Bell causality”, (ii) “Non-contextuality” and (iii) “Bounds” and will describe an attempt to find quantum analogues of this trio of conditions. Viewing quantum theory as a species of generalised measure theory, a la Sorkin, immediately provides an quantum “Noncontextuality” condition: the existence of a joint *quantum* measure. This quantum measure implies Bounds on the probabilities that can be located within the Navasues-Pironio-Acin hierarchy and that include the Tsirelson inequalities. I will touch on the knotty issues involved in the search for a “quantum Bell causality” condition and briefly explain why it could be important for quantum gravity.

**Doreen Fraser**

**University of Waterloo**

*How Wick rotation relates relativistic quantum field theory to non-relativistic theories*

One way to analyze the relationship between special relativity and quantum theory is to contrast non-relativistic quantum mechanics with relativistic quantum field theory (RQFT). I will focus on another thread which is woven through the history of RQFT and which relates the theory to non-relativistic counterparts: analytic continuation (aka Wick rotation). Wick rotation has been invoked to induce correspondences between RQFT on Minkowski spacetime and various real and specially-constructed theories on Euclidean space and spacetime. Wick rotating is a purely formal mathematical manipulation; nevertheless, it has proven to be a fruitful technique for solving problems in RQFT. I will consider the light that these formal correspondences between RQFT and theories on Euclidean space(time) shed on which features of RQFT can be regarded as distinctively relativistic.

**Leah Henderson**

**Carnegie Mellon University**

*Reformulating quantum theory: is special relativity an example to follow?*

There is a research programme in the foundations of quantum mechanics to reaxiomatise the theory in terms of simple, physically motivated postulates, which might, for example, be of an information-theoretic nature. In this area, Einstein’s postulates for special relativity are often held up as an exemplar of what is wanted. Yet it has been argued that ‘special relativity should not be a template for a fundamental reformulation of quantum mechanics’ (Brown & Timpson 2006). In this talk, I will analyse some different ways in which the case of special relativity might be regarded as an example to emulate in the quantum domain. I will argue that although some of the appeals to special relativity are suspect, there are still several senses in which the case of special relativity is a highly appropriate motivating example for the quantum reaxiomatisation programme.

**Miklós Rédei**

**London School of Economics & Political Science**

*Facets of relativistic locality*

The talk interprets relativistic locality as a set of interconnected features that express harmony of a physical theory with the causal structure of spacetime. Three groups of relativistic locality features will be distinguished: spatio-temporal, static-causal and kinematic-causal. Spatio-temporal locality conditions require that physical systems are conceived of explicitly as pertaining to regions in spacetime; static-causal locality conditions express independence of physical systems localized in causally disjoint spacetime regions and require the possibility of explaining correlations between independent systems in a causality-conform manner; kinematic-causal conditions require the dynamic of the theory to be compatible with the causal structure of spacetime. The nature and interrelation of these relativistic locality concepts will be discussed in general terms and some formulations and properties of these conditions in specific frameworks of relativistic quantum field theory will be discussed.

**Chris Smeenk**

**University of Western Ontario**

*Reflections on the Cosmological Constant*

There is widespread agreement within the physics community that the cosmological constant problem is a crisis in theoretical physics. My aim is to clarify the nature of the problem. The disastrous prediction follows from treating treating the vacuum energy density of quantum fields as a source of the gravitational field. Two aspects of this inference are troubling. First, the connection between vacuum energy density and the successful predictions of quantum field theory is tenuous — the Casimir effect, Lamb shift, and so on fail to establish that the zero-point energies of quantum fields contribute to the vacuum energy density. Second, the vacuum energy density contributes to Einstein’s field equations for general relativity as an effective cosmological constant term. This way of coupling the vacuum energy density is not mandatory, and there are also questions about the nature of a vacuum state in a general curved spacetime. In effect, I will treat the cosmological problem is an instance of a general methodological problem that arises in combining theories: the need to identify surplus structure that can be eliminated in the new theory.

**Giovanni Valente**

**University of Pittsburgh**

*Entanglement, Relativistic Causality and Independence between Quantum Field Systems*

Entanglement between distant quantum systems poses two main problems in philosophy of quantum mechanics. First, it undermines the possibility of achieving a division of the microscopic world into independent subsystems. Second, the non-local character of entangled correlations seems to entail a conflict with relativistic causality, namely the requirement that no causal process can propagate faster than light, thereby raising a threat of inconsistency with Einstein’s theory of Special Relativity. In this talk, I will discuss these problems within the framework of relativistic quantum field theory, that is our most successful theory about the microscopic world. First, I will show how the notion of local operations assures the compatibility of quantum entanglement with relativistic causality. Then, I will address the question whether a quantum field system can be isolated from its entanglement with other spacelike separated systems by acting on it by means of a local operation.

**David Wallace**

**University of Oxford, Balliol**

*Thoughts on the gauge principle*

Gauge symmetry occupies a paradoxical position in contemporary physics. How can one and the same thing be (a) the third pillar of relativistic quantum field theory, alongside special relativity and quantum mechanics, and (b) a mere descriptive redundancy, indicating that we have overdescribed the theory’s degrees of freedom? Working mostly in classical field theory but motivated by its application in quantum field theory, I will attempt to get some clarity on what we are really saying about a theory conceptually and metaphysically when we say that it has gauge symmetry. Along the way I hope to shed some light on the vexed question of in what sense general relativity is also a gauge theory.

**Jakob Yngvason**

**University of Vienna**

*Localization and entanglement in relativistic quantum physics*

The synthesis of quantum mechanics and special relativity leads naturally to systems with an infinite number of degrees of freedom and mathematical structures that differ from those appropriate for systems with a finite number of particles. This has some consequences for the definition of concepts like ‘localization’ and ‘entanglement’.