Quantum Foundations

This series consists of talks in the area of Foundations of Quantum Theory. Seminar and group meetings will alternate.

Seminar Series Events/Videos

Currently there are no upcoming talks in this series.

 

Tuesday Sep 15, 2009
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We present a first-principles implementation of {\em spatial} scale invariance as a local gauge symmetry in geometry dynamics using the method of best matching. In addition to the 3-metric, the proposed scale invariant theory also contains a 3-vector potential A_k as a dynamical variable. Although some of the mathematics is similar to Weyl's ingenious, but physically questionable, theory, the equations of motion of this new theory are second order in time-derivatives. It is tempting to try to interpret the vector potential A_k as the electromagnetic field.

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Tuesday Sep 08, 2009

Betting (or gambling) is a useful tool for studying decision-making in the face of [classical] uncertainty. We would like to understand how a quantum "agent" would act when faced with uncertainty about its [quantum] environment. I will present a preliminary construction of a theory of quantum gambling, motivated by roulette and quantum optics. I'll begin by reviewing classical gambling and the Kelly Criterion for optimal betting. Then I'll demonstrate a quantum optical version of roulette, and discuss some of the challenges and pitfalls in designing such analogues.

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Tuesday Aug 04, 2009
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Violation of local realism can be probed by theory–independent tests, such as Bell’s inequality experiments. There, a common assumption is the existence of perfect, classical, reference frames, which allow for the specification of measurement settings with arbitrary precision. However, if the reference frames are ``bounded'', only limited precision can be attained. We expect then that the finiteness of the reference frames limits the observability of genuine quantum features.

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Tuesday Jun 16, 2009
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Although most realistic approaches to quantum theory are based on classical particles, QFT reveals that classical fields are a much closer analog. And unlike quantum fields, classical fields can be extrapolated to curved spacetime without conceptual difficulty. These facts make it tempting to reconsider whether quantum theory might be reformulated on an underlying classical field structure.

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Tuesday May 05, 2009
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Researchers in quantum foundations claim (D'Ariano, Fuchs, ...):

Quantum = probability theory + x

and hence:

x = Quantum - probability theory

Guided by the metaphorical analogy:

probability theory / x = flesh / bones

we introduce a notion of quantum measurement within x, which, when flesing it with Hilbert spaces, provides orthodox quantum mechanical probability calculus.

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Tuesday Mar 31, 2009
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We know the mathematical laws of quantum mechanics, but as yet we are not so sure why those laws should be inevitable. In the simpler but related environment of classical inference, we also know the laws (of probability). With better understanding of quantum mechanics as the eventual goal, Kevin Knuth and I have been probing the foundations of inference. The world we wish to infer is a partially-ordered set ('poset') of states, which may as often supposed be exclusive, but need not be (e.g. A might be a requirement for B).

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Thursday Mar 12, 2009
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Eugene Wigner and Hermann Weyl led the way in applying the theory of group representations to the newly formulated theory of quantum mechanics starting in 1927. My talk will focus, first, on two aspects of this early work. Physicists had long exploited symmetries as a way of simplifying problems within classical physics.

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Tuesday Mar 10, 2009
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Quantum foundations in the light of gauge theories We will present the conjecture according to which the fact that q and p cannot be both ``observables'' of the same quantum system indicates that there is a remnant universal symmetry acting on classical states. In order to unpack this claim we will generalize to unconstrained systems the gauge correspondence between properties defined by first-class constraints and gauge symmetries generated by these constraints.

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Tuesday Mar 03, 2009
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Quantum mechanics is a non-classical probability theory, but hardly the most general one imaginable: any compact convex set can serve as the state space for an abstract probabilistic model (classical models corresponding to simplices). From this altitude, one sees that many phenomena commonly regarded as ``characteristically quantum' are in fact generically ``non-classical'. In this talk, I'll show that almost any non-classical probabilistic theory shares with quantum mechanics a notion of entanglement and, with this, a version of the so-called measurement problem.

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Tuesday Feb 10, 2009
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A standard canonical quantization of general relativity yields a time-independent Schroedinger equation whose solutions are static wavefunctions on configuration space. Naively this is in contradiction with the real world where things do change. Broadly speaking, the problem how to reconcile a theory which contains no concept of time with a changing world is called 'the problem of time'.

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