Conference at Cambridge: On Symmetry in Physics

On Symmetry in Physics

Saturday 5 March 2011
The Deighton Room, Blue Boar Court, Trinity College, Cambridge

This room is on the first floor at the intersection of Trinity Street and
Green Street, but is hard to find from within the College’s Court (accessed
via Whewell’s Court). Therefore, at 09.50, 11.25 and at 13.50, there will
be a guide whom you can ask, who will be stationed on the cobblestones at
the front of Trinity College’s main entrance, i.e. opposite Heffer’s
bookshop, on Trinity Street.

10.00: Boris Groisman, Cambridge University: Symmetric local toy-model
theories with entanglement as a support for the ontic view of quantum
states

11.00 Coffee

11.30 Nic Teh, Cambridge University:
The Metaphysics of Monopoles

12.30 Lunch

2.00 pm Tony Short, Cambridge University:
The continuum limit of quantum walks

3.00 pm Tea

3.45 pm Harvey Brown, Oxford University:
Ruminations on the significance of Noether’s theorems

4.45 Close

ABSTRACTS

10.00 am: Boris Groisman: Symmetric local toy-model theories with
entanglement as a support for ontic view of quantum states

Recently, Local Toy Model Theories (LTMT), initially proposed by
Hardy (1999) and Spekkens (2007), had attracted considerable
attention. Hardy was motivated by making a case for non-cloning being
logically independent of non-locality. Spekkens used his model to
support the conjecture that quantum states are states of observer’s
incomplete knowledge (epistemic states), rather than real states of
affairs (ontic states).
In this talk, I will make a case for ontic view of quantum states. I
will discuss an alternative local (i.e. local hidden variable)
toy-model, where joint states of correlated individual systems
exhibit entanglement, thereby confirming recent claims that
entanglement is logically independent of non-locality. My main thesis
will be that in the process constructing toy-models we face two
choices. First, we can avoid introducing entangled states by
postulating restrictions on our knowledge of the system state of
affairs. Second, if we allow full knowledge of the system, then
entanglement will be the price to pay. The latter option is a good
indication that quantum states are ontic states.

11.30: Nic Teh: The Metaphysics of Monopoles

Topological solitons are emergent objects that arise generically in the
context of gauge field theory as well as many other areas of physics,
including condensed matter theory, nuclear physics, quantum computing, and
string theory. Nonetheless, despite a recent wave of investigations into
the philosophy (especially the metaphysics) of gauge theory, no
philosophical treatment has so far been given of these objects. This paper
attempts to redress this lack by giving a conceptual analysis of solitons
and drawing attention to the metaphysical puzzles that they raise, some of
which have been noted in passing by S. Coleman and R. Jackiw. For the sake
of simplicity, brevity, and relevance, I will focus on the species of
soliton known as the BPS monopole, although many of the same conceptual
points will hold for instantons and branes. I give an account of their
individuation as well as their part-whole structure, describing both how
the monopoles are constituted by fields, as well as how composite solutions
are composed of elementary monopoles. Since this is a conference on
symmetry, I would also like to focus on several aspects of the role that
symmetry plays in the above, viz. (i) the importance of gauge symmetry for
the existence of interesting solitonic solutions (why should a *redundancy*
of description be essential to their existence?), (ii) the role that
spontaneous symmetry breaking plays in producing emergent topological
structures, and (iii) the homotopy group (i.e. symmetry!) structure that
controls the patching together of solutions. If there is time I may
consider how supersymmetry enters into an account of such objects.

14.00: Tony Short: The continuum limit of quantum walks

Quantum walks correspond to local unitary evolution in discrete space and
time, and are widely studied in quantum computation, where they play an
analogous role to random walks in classical computation. Intriguingly, when
we zoom out from the discrete structure of a quantum walk to its continuum
limit, in some very natural cases we obtain the dynamics of relativistic
particles. We will investigate the idea that nature really is discrete at
some microscopic scale, and explore the possible connections between quantum
walks and particle physics.

15.45: Harvey Brown: Ruminations on the significance of Noether’s theorems

In 1918 Noether published two theorems related to the role of
symmetry principles in Lagrangian dynamics. The first (and better known)
theorem concerns global symmetries and correlates such symmetries with
conservation principles. Some recent studies have questioned the traditional
reading of this theorem. The second theorem deals with local symmetries; an
application in general relativity had been anticipated in 1916 by Einstein,
and it played a significant role in his understanding of the significance of
general covariance in the theory, and his appreciation of Noether’s 1918
work.

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