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.