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

Planet Signatures in Collisionally Active Debris Discs: scattered light images

Planet perturbations are often invoked as a potential explanation for many spatial structures that have been imaged in debris discs. So far this issue has been mostly investigated with collisionless N-body numerical models. We numerically investigate how the coupled effect of collisions and radiation pressure can affect the formation and survival of radial and azimutal structures in a disc perturbed by a planet. We consider two set-ups: a planet embedded within an extended disc and a planet exterior to an inner debris ring. We use the DyCoSS code of Thebault(2012) and derive synthetic images of the system in scattered light. The planet's mass and orbit, as well as the disc's collisional activity are explored as free parameters. We find that collisions always significantly damp planet-induced structures. For the case of an embedded planet, the planet's signature, mostly a density gap around its radial position, should remain detectable in head-on images if M_planet > M_Saturn. If the system is seen edge-on, however, inferring the presence of the planet is much more difficult, although some planet-induced signatures might be observable under favourable conditions. For the inner-ring/external-planet case, planetary perturbations cannot prevent collision-produced small fragments from populating the regions beyond the ring: The radial luminosity profile exterior to the ring is close to the one it should have in the absence of the planet. However, a Jovian planet on a circular orbit leaves precessing azimutal structures that can be used to indirectly infer its presence. For a planet on an eccentric orbit, the ring is elliptic and the pericentre glow effect is visible despite of collisions and radiation pressure, but detecting such features in real discs is not an unambiguous indicator of the presence of an outer planet.Comment: Accepted for Publication in A&A (NOTE: Abridged abstract and (very)LowRes Figures. Better version, with High Res figures and full abstract can be found at http://lesia.obspm.fr/perso/philippe-thebault/planpapph.pdf

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

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