Talks

We present a short review of the local conformal symmetry and its anomalous violation in curved $4d$ space-time. Furthermore we discuss the ambiguities of conformal anomaly and the anomaly-induced effective actions. Despite the conformal symmetry is always broken at quantum level, it is useful for constructing the best known approximations for investigating quantum corrections to the classical action of gravity. These quantum corrections represent an appropriate basis for a number of applications in cosmology and black hole physics.

Spacelike separated classical interventions make us to rethink what is quantum and what is classical. Quantum Lorentz transformations show that identification of subsystems is a tricky business, ditto entropy, entanglement and thermodynamic quantities. Resolution of information loss problem in black hole physics is tied to a construction of a theory of quantized gravity.

Abstract: Efforts to extrapolate non-relativistic (NR) quantum mechanics to a covariant framework encounter well-known problems, implying that an alternate view of quantum states might be more compatible with relativity. This talk will reverse the usual extrapolation, and examine the NR limit of a real, classical scalar field. A complex scalar \psi that obeys the Schrodinger equation naturally falls out of the analysis. One can also replace the usual operator-based measurement theory with classical measurement theory on the scalar field, and examine the NR limit of this as well. In this limit, the local energy density of the field scales as |\psi|^2, adding credibility to this approach. With the added postulate that "all measurements correspond to boundary conditions that extremize the classical action" (see arXiv:0906.5409), additional quantitative comparisons emerge between this \psi and the standard quantum wavefunction. Uncertainty can then be introduced (along with a "collapse" due to Bayesian updating) by simply giving the classical scalar field two components instead of one, leading to an intriguing \psi-epistemic model.

Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this talk, we show how it is possible to derive the complex nature of the quantum formalism directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, and that the probability of this sequence is a real-valued function of this number pair. By making use of elementary symmetry and consistency conditions, and without assuming that these real number pairs have any other algebraic structure, we show that these pairs must be manipulated according to the rules of complex arithmetic. We demonstrate that these complex numbers combine according to Feynman's sum and product rules, with the modulus-squared yielding the probability of a sequence of outcomes. We then discuss how complementarity --- the key guiding idea in the derivation --- can be understood as a consequence of the intrinsically relational nature of measurement, and discuss the implications of this for our understanding of the status of the quantum state.

I will consider various attempts to derive the quantum probabilities from the HIlbert space formalism within the many-worlds interpretation, and argue that they either fail, or depend on tacit probabilistic assumptions. The main problem with the project is that it is difficult to understand what the state of system X is psi even *means* without already supposing some probabilistic link to definite observed or observable phenomena involving X. I will argue it is better to conceive of quantum states as *representations* of empirically inferred probabilities for quantum processes associated with definite observable phenomena, accepting all the issues this raises concerning what exactly are to count as observable outcomes, and relatedly, what as real, as an unavoidable conundrum but also a potential source of progress in the evolution of physical theory.

I give a review and assessment of relational approaches to quantum theory – that is, approaches that view QM “as an account of the way distinct physical systems affect each other when they interact – and not the way physical systems ‘are’”. I argue that the “relational QM” is a misnomer: the correct way to understand these approaches is in terms of structuralism, whereby the correlations themselves are fundamental. I then argue that the connection to gravitational physics and gauge symmetries has a crucial impact on the attractiveness of such approaches.

It's been suggested that "decoherence explains the emergence of a classical world". That is, if we believe our world is quantum, then decoherence can explain why it LOOKS classical. Logically, this implies that without decoherence, the world would not look classical. But... what on earth WOULD it look like? Human beings seem incapable of directly observing anything "nonclassical". I'll show you how a hypothetical quantum critter could interact with, and learn about, its world. A quantum agent can use coherent measurements to gain quantum knowledge about its surroundings. They can use that quantum knowledge to accomplish tasks. Moreover, clumsy classical critters (like me!) could identify quantum agents (and prove that they are using quantum knowledge), because they outperform all classical agents. I'll explain the remarkable new perspective on quantum states that comes from thinking about quantum knowledge, and I'll argue that it's a useful perspective by showing you two concrete applications derived from it.