Symplectic reduction and the problem of time in nonrelativistic mechanics

The deep connection between the interpretation of theories invariant under local symmetry transformations (i.e. gauge theories) and the philosophy of space and time can be illustrated nonrelativistically via the investigation of reparameterisation invariant reformulations of Newtonian mechanics, such as Jacobi's theory. Like general relativity, the canonical formulation of such theories feature Hamiltonian constraints; and like general relativity, the interpretation of these constraints along conventional Dirac lines is highly problematic in that it leads to a nonrelativistic variant of the infamous problem of time. I argue that, nonrelativistically at least, the source of the problem can be found precisely within the symplectic reduction that goes along with strict adherence to the Dirac view. Avoiding reduction, two viable alternative strategies for dealing with Hamiltonian constraints are available. Each is found to lead us to a novel and interesting re-conception of time and change within nonrelativistic mechanics. Both these strategies and the failure of reduction have important implications for the debate concerning the relational or absolute status of time within physical theory

Superpositions of the cosmological constant allow for singularity resolution and unitary evolution in quantum cosmology

A novel approach to quantization is shown to allow for superpositions of the cosmological constant in isotropic and homogeneous mini-superspace models. Generic solutions featuring such superpositions display unitary evolution and resolution of the classical singularity. Physically well-motivated cosmological solutions are constructed. These particular solutions exhibit characteristic features of a cosmic bounce including universal phenomenology that can be rendered insensitive to Planck-scale physics in a natural manner.Comment: Version accepted to Physics Letters B. Minor revisions, clarifications added. 7 pages, 3 figure

Hawking Radiation and Analogue Experiments: A Bayesian Analysis

We present a Bayesian analysis of the epistemology of analogue experiments with particular reference to Hawking radiation. First, we prove that such experiments can be confirmatory in Bayesian terms based upon appeal to 'universality arguments'. Second, we provide a formal model for the scaling behaviour of the confirmation measure for multiple distinct realisations of the analogue system and isolate a generic saturation feature. Finally, we demonstrate that different potential analogue realisations could provide different levels of confirmation. Our results provide a basis both to formalise the epistemic value of analogue experiments that have been conducted and to advise scientists as to the respective epistemic value of future analogue experiments.Comment: 25 pages, 5 figure

The Problem of Time

The `problem of time' is a cluster of interpretational and formal issues in the foundations of general relativity relating to both the representation of time in the classical canonical formalism, and to the quantization of the theory. The purpose of this short chapter is to provide an accessible introduction to the problem

What Can We Learn From Analogue Experiments?

In 1981 Unruh proposed that fluid mechanical experiments could be used to probe key aspects of the quantum phenomenology of black holes. In particular, he claimed that an analogue to Hawking radiation could be created within a fluid mechanical `dumb hole', with the event horizon replaced by a sonic horizon. Since then an entire sub-field of `analogue gravity' has been created. In 2016 Steinhauer reported the experimental observation of quantum Hawking radiation and its entanglement in a Bose-Einstein condensate analogue black hole. What can we learn from such analogue experiments? In particular, in what sense can they provide evidence of novel phenomena such as black hole Hawking radiation

The Problem of Time

The `problem of time' is a cluster of interpretational and formal issues in the foundations of general relativity relating to both the representation of time in the classical canonical formalism, and to the quantization of the theory. The purpose of this short chapter is to provide an accessible introduction to the problem

What Can We Learn From Analogue Experiments?

In 1981 Unruh proposed that fluid mechanical experiments could be used to probe key aspects of the quantum phenomenology of black holes. In particular, he claimed that an analogue to Hawking radiation could be created within a fluid mechanical `dumb hole', with the event horizon replaced by a sonic horizon. Since then an entire sub-field of `analogue gravity' has been created. In 2016 Steinhauer reported the experimental observation of quantum Hawking radiation and its entanglement in a Bose-Einstein condensate analogue black hole. What can we learn from such analogue experiments? In particular, in what sense can they provide evidence of novel phenomena such as black hole Hawking radiation

The Problem of Time

The `problem of time' is a cluster of interpretational and formal issues in the foundations of general relativity relating to both the representation of time in the classical canonical formalism, and to the quantization of the theory. The purpose of this short chapter is to provide an accessible introduction to the problem