Tim A. Koslowski (New Brunswick) gives a talk at the Mini-Workshop on the Foundations of Shape Dynamics (23 June, 2014) titled "Shape Dynamics". Abstract: Based on the introduction to shape dynamics by Sean Gryb, I will discuss the question: "Given that gravity (from the perspective of shape dynamics) is fundamentally the evolution of spatial conformal geometry and not spacetime: How is the arrow of time generated? How is the illusion of a spacetime generated? What are the limitations of the spacetime description? I will give explicit answers to several aspect of these questions and I will explain where the uncharted territory begins.

Shape Dynamics

Detlef Dürr (LMU) gives a talk at the MCMP Colloquium (23 January, 2013) titled "Bohmian Mechanics, speakable quantum physics". Abstract: I introduce Bohmian Mechanics, which is a theory of particles in motion. The law of motion is  not classical, i.e. the particles do not move on Newtonian trajectories. As this is often not appreciated I shall discuss some features which will help to sharpen one's intuition about this theory of nature.

Bohmian Mechanics, speakable quantum physics

Karim Thébault (MCMP/LMU) gives a talk at the MCMP Colloquium (9 January, 2013) titled "Quantisation as a guide to ontic structure". Abstract: The ontic structural realist stance is motivated by a desire to do philosophical justice to the success of science, whilst withstanding the    metaphysical undermining generated by the various species of ontological underdetermination. We are, however, as yet in want of general principles to provide a scaffold for the explicit construction of structural ontologies. Here we will attempt to bridge this gap by utilising the formal procedure of quantisation as a guide to ontic structure of modern physical theory.  The example of non-relativistic particle mechanics will be considered and, for that case, it will be argued that, modulo certain mathematical ambiguities, a consistent candidate structural ontology can be established.

Quantisation as a guide to ontic structure

Igor Khavkine (Utrecht) gives a talk at the MCMP workshop "Quantum Gravity in Perspective" (31 May-1 June, 2013) titled "Gravity. An exercise in quantization". Abstract: The quantization of General Relativity (GR) is an old and chellenging prob- lem that is in many ways still awaiting a satisfactory solution. GR is a partic- ularly complicated field theory in several respects: non-linearity, gauge invari- ance, dynamibal causal structure, renormalization, singularities, infared effects. Fortunately, much progress has been made on each of these fronts. Our under- standing of these problems has evolved greatly over the past century, together with our understandig of quantum field theory (QFT) in general. Today, the state of the art in QFT knows how to address each of these challenges, as they occur in isolation in ohter field theories. There is still an active research program aiming to combine the relevant methods and apply them to GR. But, at the very least, the problem of the quantization of GR can be formulated as a well defined mathematical question. On the other hand, quantum GR also faces a different set of obstacles: timelessness, non-renormalizability, naturality, unification, which reflect, not its technical difficulty, but rather the aesthetic and philosophical preferences of practing theoretical physicists. I will briefly discuss how the technical state of the art and a scientifically conservative philosophical position make these obstacles irrelevant. Time per- mitting, I will also briefly touch on some aspects of the state of technical state of the art that have turned the quantization of GR into a (still challenging) exercise: covariant Poisson structure, BV-BRST treatment of gauge theories, deformation quantization, Epstein-Glaser renormalization.

Gravity. An exercise in quantization

Thomas Pashby (Pittsburgh) gives a talk at the MCMP Colloquium (28 May, 2014) titled "Against Dogma: Locality, Conditionalisation, and Collapse in Relativistic Quantum Mechanics". Abstract: I argue here against the widespread view (due to David Malament) that the non-commutativity of non-instantaneous localisation projections implies the existence of act-outcome correlations in relativistic QM. There are two facets to my argument: first, I claim that the interpretation of collapse as a process brought about by the experimenter is mistaken; second, I contend that a fully relativistic model should not condition on the occurrence of spacelike separated instantaneous events. This leaves the door open to define a relativistically invariant (but non-commuting) system of localization, which I interpret in terms of conditional probabilities for the occurrence of events. In accord with Tumulka (2009), I conclude that non-local correlations of events in a relativistic quantum theory need not imply the sort of action at a distance that worries Malament (1996).

Against Dogma: Locality, Conditionalisation, and Collapse in Relativistic Quantum Mechanics

Sean Gryb (Nijmegen) gives a talk at the Mini-Workshop on the Foundations of Shape Dynamics (23 June, 2014) titled "An Introduction to Shape Dynamics: a New Perspective on Quantum Gravity". Abstract: Shape Dynamics is a theory of gravity where the fundamental ontology is that of evolving conformally invariant spatial geometry. This implements a notion of local spatial scale invariance such that what is seen to be physically meaningful is the information about the local "shapes" (as opposed to size) of a system. Perhaps surprisingly, this theory can be proven to reproduce a vast number of the solutions to the Einstein equations. However, black hole solutions are known to differ from those of GR past the horizon and do not lead to singularities. Shape Dynamics, thus, provides an intriguing new starting point for a theory of quantum gravity. In this introductory chalkboard talk, I will try to give some motivations for Shape Dynamics and will describe the basic structure of the theory, outlining how one can prove equivalence with GR. This will lay the ground work for Tim Koslowski's talk, which will discuss some recent developments of the theory.

An Introduction to Shape Dynamics: a New Perspective on Quantum Gravity

Andreas Barrels (Bonn) gives a talk at the MCMP Colloquium (7 May, 2014) titled "How to Bite the Bullet of Quidditism - Why a Standard Argument against Categoricalism in Physics Fails". Abstract: Categoricalism is the statement that fundamental properties of physics are categorical, i.e., they have their dispositional characters not with metaphysical necessity. According to Black (2000), Bird (2005, 2007), and Esfeld (2009), categoricalism entails quidditism, the possible existence of properties which are not exclusively individuated by their dispositional characters. If quidditism is true, we cannot know, in principle, whether it is property F or its “Doppelgänger” G that shows up by exhibiting a certain set of dispositional characters. Since we cannot accept our metaphysics of properties to condemn us to necessary ignorance of fundamental properties, we must reject quidditism. Therefore, categoricalism fails. I argue that the possible epistemic situation revealed by quidditism is a case of empirical underdetermination of theoretical properties. This type of situation is not conceived, in general, as the occurrence of some necessary limit of knowledge. There are rational procedures to deal with empirical underdetermination in physics, and thus to decide about the properties the existence of which we are committed to accept. Thus, the unacceptability claim against quidditism is not well founded and categoricalism cannot be defeated that way.

How to Bite the Bullet of Quidditism - Why a Standard Argument against Categoricalism in Physics Fails

Michael Stöltzner (South Carolina) gives a talk at the Irvine-Munich Workshop on the Foundations of Classical and Quantum Field Theories (14 December, 2014) titled "Best Possible Worlds and Random Walks: The Principle of Least Action as a Thought Experiment". Abstract: Over the centuries, no other principle of classical physics has to a larger extent nourished exalted hopes of a universal theory, has constantly been plagued by mathematical counterexamples, and has ignited metaphysical controversies than has the principle of least action (PLA). The aim of this paper is first to survey a series of modern approaches, among them the structural realist readings of Planck and Hilbert, a neo-Kantian relativized a priori principle, and more recent discussions about modality within the context of analytic metaphysics. But these considerations seem outrun by the broad applicability of the PLA beyond classical physics. In the case of Feynman’s path integral, the PLA does no longer amount to the distinction of the actual dynamics among the possible ones, but to the definition of a stochastic process to which all possibilities contribute with a certain probability. To reach a unified philosophical picture of all the various applications of the PLA and its kin, I suggest to consider them as a thought experiment about the applicability of mathematics to a physical problems.

Best Possible Worlds and Random Walks: The Principle of Least Action as a Thought Experiment

Carlo Rovelli (Aix-Marseille) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "Physics without Fundamental Time". Abstract: Rivers of ink have flown on the basic conceptual structure of quantum gravity -a theory where we expect the notions of classical spacetime, particles, fields, energy and momentum to require substantial revision-. I discuss a specific solution to these questions and apply concretely it to a physical calculation, the tunneling time of a Hajicek-Kiefer black-to-white hole transition. This is a quantum gravitational effect that might have some chance to be actually observable, or could have even been already observed in the "Fast Radio Bursts" observed by the Arecibo and Parkes radio-telescopes.

Physics without Fundamental Time

Relativity

Donald Salisbury (Austin) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "The Intrinsic Hamilton-Jacobi Dynamics of General Relativity and its Implications for the Semi-Classical Emergence of Time". Abstract: The quantization of the general theory of relativity is notoriously difficult, in particular on account of the underlying general covariance and the consequent appearance of constraints in the classical Hamiltonian theory. The notion of time in the quantum theory is especially troubling since differing ideas of time suggest themselves depending on the quantum rules that are employed and the interpretations given to time in the classical theory itself. I will address the problem of time from a perspective in which constraints are implemented in a Hamilton-Jacobi framework through the use of intrinsic coordinates. The canonical approach is especially suited for this task. The decisive result is that the problem of time is even greater than one might have expected; there are arbitrarily many equally valid and possibly inequivalent time choices that one can introduce in this manner, all involving the use dynamical variables that are invariant under the action of the four-dimensional diffeomorphism-induced group as described in Pons, Salisbury, and Sundermeyer, Phys. Rev. (2009), 084015. I will review a Kuchař-inspired, but fully diffeomorphism covariant, classical Hamiltonian approach to general relativity in which spacetime scalar phase space variables are introduced that can serve as intrinsic coordinates. There corresponds to each choice a constraint which can be converted (as originally proposed by Asher Peres for conventional variables) into an Einstein-Hamilton-Jacobi (EHJ) equation. The choice of intrinsic coordinates is rendered simple in terms of these new variables, as are the choices in the new intrinsic EHJ equation. Indeed, the resulting intrinsic dynamics follows immediately from the EHJ equation. No Lagrangian is obtained, and this might be expected given that spacetime scalars must depend on time derivatives of the metric and their introduction into the Einstein action would result in the appearance higher derivative contributions. To each EHJ equation there corresponds a Wheeler-DeWitt quantum equation with its own emergent time. I will begin to examine possible quantum implications of the existence of distinct emergent intrinsic times.

The Intrinsic Hamilton-Jacobi Dynamics of General Relativity and its Implications for the Semi-Classical Emergence of Time

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

Francesca Vidotto (Radboud) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "Discrete Time in Quantum Gravity". Abstract: We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space. We work in 2+1 dimensions, but these results may be relevant also for the physical 3+1 case.

Discrete Time in Quantum Gravity

Henrique Gomes (Perimeter Institute) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "Timeless Quantum Mechanics in Configuration Space: an Outsider View". Abstract: In this talk, I will explore a timeless interpretation of quantum mechanics of closed systems, solely in terms of path integrals in non-relativistic timeless configuration space. What prompts a fresh look at the foundational problems in this context, is the advent of multiple gravitational models in which Lorentz symmetry is only emergent. In this setting, I propose a new understanding of records as certain relations between two configurations, the recorded one and the record-holding one. These relations are formalized through a factorization of the amplitude kernel, which forbids unwanted 'recoherence' of branches. On this basis, I show that in simple cases the Born rule is consistent with counting the relative density of observers with the same records. Furthermore, unlike what occurs in consistent histories, in this context there is indeed a preferred notion of coarse-grainings: those centered around piece-wise classical paths in configuration space (with a certain radius). Thus, this new understanding claims to resolve aspects of the measurement problem which are still deemed controversial in the standard approaches (but which probably leaves others open...).

Timeless Quantum Mechanics in Configuration Space: an Outsider View

Sean Gryb (Radboud) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "In Favour of a Schrödinger Evolution of the Universe". Abstract: In the canonical formulation of reparametrization invariant systems, time evolution on phase space is generated by a fully constrained Hamiltonian. On the orthodoxy view, the quantum formalism for such systems is constructed through Dirac quantization, which leads to a real, time-independent constraint on the quantum state. The question then remains how to extract a notion of time evolution from this frozen formalism. On one predominant view, the system is to be split in terms of ''partial observables'' -- which may be used as internal clocks -- and a set of ''complete observables'' -- which are understood to evolve in terms of the former. This has led to a controversy around the interpretation of the partial observables within the formalism. In this talk, we will provide a negative argument against the orthodoxy view that clarifies the role that should be played by the partial observables. We then present a proposal for the canonical quantization of reparametrization invariant systems that naturally encodes a genuine notion of time evolution and illustrate how this proposal can be applied to gravity.

In Favour of a Schrödinger Evolution of the Universe

Bianca Dittrich (Perimeter Institute) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "The Consistent Boundary Formulation". Abstract: I will introduce the consistent boundary formulation which allows to express renormalization flow in a background independent context. I will discuss consequences of this formulation for the Hamiltonian framework and explore in which sense Hamiltonian constraints do actually exists in this context and how this influences the notion of time.

The Consistent Boundary Formulation

Dirac Observables

Philipp Hoehn (Perimeter Institute) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "Constraints, Dirac Observables and Chaos". Abstract: I will discuss fundamental challenges to the standard relational paradigm arising from chaotic dynamics.

Constraints, Dirac Observables and Chaos

J. Brian Pitts (Cambridge) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "Changing Observables in Canonical General Relativity from Hamiltonian-Lagrangian Equivalence". Abstract: Is change missing in classical canonical General Relativity? If one insists on Hamiltonian-Lagrangian equivalence, then there is Hamiltonian change just when there is no time-like Killing vector field. Change has seemed missing partly due to Dirac’s belief that a first-class constraint, especially a primary, generates a gauge transformation. Pons showed that Dirac’s argument stops too soon: working to second order in time brings in first-class secondaries and hence the gauge generator G, a tuned sum of first-class constraints used by Anderson and Bergmann (1951) and recovered by Mukunda, Castellani et al. from the 1980s. I observe that trouble happens immediately: a first-class primary constraint generates an illegal change of initial data in GR, Maxwell and Yang-Mills. Dirac’s subtractive derivation misses it by cancellation; confusion between the electric field E(dA) and canonical momenta p (auxiliary fields in the canonical action \int dt (p \dot{q}-H) also obscures the problem. Dirac’s conjecture that a first-class secondary constraint generates a gauge transformation rests on a false assumption. Looking for gauge symmetries of the canonical action, one finds that the gauge generator G changes the action by at most a boundary term, but an isolated first-class constraint does not. The gauge generator G generates spatio-temporal coordinate transformations (not just spatial ones) for the space-time metric (not just the spatial metric). But are there locally varying _observables_ in canonical General Relativity? Hamiltonian-Lagrangian equivalence guarantees that Hamiltonian observables are equivalent on-shell to Lagrangian observables. (Historically, Lagrangian-inequivalent observables may have arisen within Bergmann’s school due to novel postulation in Bergmann-Schiller 1953.) With first-class constraints exposed as not generating gauge transformations, observables’ Poisson brackets should be taken with the gauge generator G, as noted by Pons, Salisbury and Sundermeyer. Heeding Einstein’s point-coincidence argument excludes primitive point individuation and thus active diffeomorphisms in favor of (4-d) tensor calculus. Kuchař’s unsystematic waiver of the vanishing Poisson brackets condition to permit change has a more principled extension: observables should be internally gauge _invariant_ (0 Poisson bracket with G for Maxwell, Yang-Mills, etc.) but externally gauge _covariant_. Hence the Poisson bracket with the coordinate-changing G should be the Lie derivative, indeed the Lie derivative of a geometric object (on-shell). For GR with no matter gauge group, observables are (on-shell) space-time geometric objects (components in coordinates with a transformation law). Hence the space-time metric and its concomitants (connection, curvature, etc.) are locally varying observables. Questions regarding Legendre projectability when an internal gauge group is also present and regarding the mixed supergravity transformations are noted. Velocity-dependent gauge transformations call for phase space extended by time---“phase space-time”; GR’s Lie derivative is an example. Vacuum GR’s phase space-time has 20 infinity^3 + 1 dimensions and 8 infinity^3 first-class constraints; one should not have expected a reduced phase _space_ description of a theory with many-fingered time. Classical clarity might be of some use in quantization.

Changing Observables in Canonical General Relativity from Hamiltonian-Lagrangian Equivalence

Oliver Pooley (Oxford) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "First-Class Constraints, Gauge, and the Wheeler-DeWitt Equation". Abstract: Recently, Pitts (2014) has argued that the claim that first-class constraints generate gauge transformations (hereafter “orthodoxy”) fails even in electromagnetism, which is standardly taken to illustrate its correctness. Independently, Barbour and Foster (2008) have argued that a key presupposition of the primary argument for orthodoxy (due to Dirac, 1964) is not satisfied in the important case of reparameterization-invariant theories. In assessing these claims, one needs to distinguish between, (i) transformations that relate points of phase space that represent the same instantaneous state and (ii) transformations that map curves on phase space to curves that represent the same history. Pitts shows that arbitrary first-class constraints fail to generate transformations of type (ii), but leaves untouched the orthodox position concerning (i). Barbour and Foster show that we have no reason to regard transformations generated by Hamiltonian constraints as type (i), but that leaves open that they may be regarded as transformations of type (ii). I will discuss whether the latter possibility allows one to reconcile applying Dirac’s constrained quantization procedure to the Hamiltonian constraint and interpreting the Wheeler–DeWitt wavefunction as representing genuine change.

First-Class Constraints, Gauge, and the Wheeler-DeWitt Equation

Tim A. Koslowski (Brunswick) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "The Gravitational Arrow of Time". Abstract: The arrow of time appears to always to point in one direction (i.e. we can clearly tell whether a movie is played forward or backward) although the underlying physics is time-reversal symmetric. The most widely accepted explanation for this is that the experienced arrow is the thermodynamic arrow of time (i.e. the direction of entropy growth). This scenario requires the past hypothesis, i.e. an atypical initial condition. We propose an alternative mechanism: The arrow of time is the direction in which the complexity of the universe grows. Gravity generates this arrow of time and creates subsystems with low entropy initial conditions spontaneously. I show this in detail in the Newtonian limit and discuss the extension to cosmological models in GR.

The Gravitational Arrow of Time

Kurt Sundermeyer (FU Berlin/MPIWG) gives a talk at the Workshop on the Problem of Time in Perspective (3-4 July, 2015) titled "Facets of Time in Physics". Abstract: In an attempt to understand slogans such as "The End Of Time", "Forget About Time", "Time Reborn", "Time Remains", I started to write an essay about the various notions of time in physics (with a glimpse to philosophy) from classical mechanics to quantum gravity. By this curiosity-driven motivation I realized that there are not only various notions of time, but that there are diverse problems with time and problems of time. In my talk I will present the structure and inputs of this still unfinished treatise, and I expect to receive valuable feedback from the competent participants of this workshop.

Facets of Time in Physics

Miklós Rédei (LSE) gives a talk at the MCMP Colloquium (13 May, 2015) titled "A Categorial Approach to Relativistic Locality". Abstract: In the talk relativistic locality of a probabilistic physical theory is interpreted as an interconnected web of properties which express compatibility of the theory with the underlying causal structure of spacetime. Four components of this web are distinguished:  spatiotemporal locality, causal locality-Independence, causal locality-Dependence, and causal locality-Dynamic. These four conditions will be specified in terms of concepts from the categorical approach to quantum field theory and results are recalled indicating the extent to which an algebraic quantum field theory satisfying the Haag–Kastler axioms is causally local.

A Categorial Approach to Relativistic Locality

Mathematical Philosophy - the application of logical and mathematical methods in philosophy - is about to experience a tremendous boom in various areas of philosophy. At the new Munich Center for Mathematical Philosophy, which is funded mostly by the German Alexander von Humboldt Foundation, philosophical research will be carried out mathematically, that is, by means of methods that are very close to those used by the scientists.<br>The purpose of doing philosophy in this way is not to reduce philosophy to mathematics or to natural science in any sense; rather mathematics is applied in order to derive philosophical conclusions from philosophical assumptions, just as in physics mathematical methods are used to derive physical predictions from physical laws.<br>Nor is the idea of mathematical philosophy to dismiss any of the ancient questions of philosophy as irrelevant or senseless: although modern mathematical philosophy owes a lot to the heritage of the Vienna and Berlin Circles of Logical Empiricism, unlike the Logical Empiricists most mathematical philosophers today are driven by the same traditional questions about truth, knowledge, rationality, the nature of objects, morality, and the like, which were driving the classical philosophers, and no area of traditional philosophy is taken to be intrinsically misguided or confused anymore. It is just that some of the traditional questions of philosophy can be made much clearer and much more precise in logical-mathematical terms, for some of these questions answers can be given by means of mathematical proofs or models, and on this basis new and more concrete philosophical questions emerge. This may then lead to philosophical progress, and ultimately that is the goal of the Center.

MCMP – Philosophy of Physics

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