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I will rehearse and try to sharpen some of the perennial worries about making sense of probabilities in Everettian interpretations of quantum mechanics, with particular attention to the recent Decision-Theoretic proposals of Deutsch and others

I will review the current state of the probability problem. My main focus will be on the attempts by David Deutsch and myself to provide a proof of the Born Rule starting from Everettian assumptions, but I will also attempt to locate these attempts within the more general framework of the probability problem.

Everett explained “collapse of the wavepacket” by noting that observer will perceive the state of the measured quantum system relative to the state of his own records. Two elements (missing in this simple and compelling explanation of effective collapse) are required to complete relative state interpretation: (i) A preferred basis for states of at least some systems in the wholly quantum Universe must be identified, so that apparatus pointers and other recording devices can persist over time. This implies breaking of the unitary symmetry in the original (more egalitarian) relative state interpretation, so that it can successfully account for classicality of macroscopic objects in accord with Bohr’s view of the role of measuring apparatus, and with our everyday experience. It is now widely accepted that decoherence (caused by the monitoring of systems by their environments) leads to einselection of pointer states, accounting for the emergence of preferred states. However, tools used by decoherence rely on the second missing link between quantum substrate and reality; (ii) A prescription that connects probabilities of outcomes with amplitudes of quantum states – such as Born’s rule is still needed. Born’s rule could be in principle postulated, but as Everett noted fifty years ago this should not be necessary. I show that both (i) einselection and (ii) Born’s rule follow from symmetries of entangled quantum states. Entanglement represents information transfer between the to-be-classical quantum systems and their environments. Information transfer in course of decoherence produces multiple copies of the state of the system: its redundant imprints in the environment. This multiplicity of records can account for the objective existence of preferred pointer states: (iii) Quantum Darwinism singles out the “fittest observable” of the system (the observable that produces the most information-theoretic “offspring” of its state, i.e. the most copies in the environment). These fittest observables exist objectively: information about them can be found out indirectly, from the environment, without perturbing the underlying state of the system. The objective existence of pointer states is the foundation of the existential interpretation. The existential interpretation recognizes with Everett the relative nature of quantum states, but accounts for the effectively classical states (which unlike quantum states of isolated systems – can be found out without getting disrupted in the process) through quantum Darwinism

I shall present an overview of quantum mechanics in the Everett interpretation, that emphasises its structural characteristics, as a theory of what exists. In this respect it shares common ground with other fundamental theories in physics. As such its appeal is conservative; it makes do with the purely unitary equations of quantum mechanics as exceptionless and universal. It also makes do with standard methods for extracting \'high level\' or \'emergent\' ontology, the furniture of macroscopic worlds, from largish molecules on up. It would appeal all the more if it made do with standard epistemological principles too - for example, in the context of inductive statistical confirmation, with standard Bayesian epistemology. But this links to the question of the interpretation of probability in the Everett interpretation, and here the theory seems anything but conservative. It is a common complaint that the approach leaves no room at all for talk of uncertainty. I shall argue, again on conservative interpretative practises, that this claim is incorrect. Chance events are, indeed, revealed in a surprising light - as quantum branchings - but they are the more perspicuous, and their properties and quantitative measure better explained, in light of that.

In 3d quantum gravity, Planck's constant, the Planck length and the cosmological constant control the lack of (co)-commutativity of quantities like angular momenta, momenta and postion coordinates. I will explain this statement, using the quantum groups which arise in the 3d quantum gravity but avoiding technical details. The non-commutative structures in 3d quantum gravity are quite different from those in the deformed version of special relativity desribed by the kappa-Poincare group, but can be related to the latter by an operation called semi-dualisation. I will explain this operation, and make comments on its possible physical significance. The talk is based on joint work with Shahn Majid.

Quantum field theory in curved spacetime (QFTCS) is the theory of quantum fields propagating in a classical curved spacetime, as described by general relativity. QFTCS has been applied to describe such important and interesting phenomena as particle creation by black holes and perturbations in the early universe associated with inflation. However, by the mid-1970\'s, it became clear from phenomena such as the Unruh effect that \'particles\' cannot be a fundamental notion in QFTCS. By the mid-1980\'s it was understood how to give a mathematically rigorous formulation of the theory of a free quantum field in curved spacetime. During the past decade, major progress has been made in providing a completely mathematically satisfactory formulation of renormalization in interacting QFTCS, thereby overcoming the difficulties caused by the absence of Poincare symmetry as well as the lack of a preferred vacuum state and a fundamental notion of \'particles\'. This talk will describe these developments and some of the insights that have thereby been attained.

The non-Gaussianity of the primordial cosmological perturbations will be strongly constrained by future observations like Planck. It will provide us with important information about the early universe and will be used to discriminate among models. I will review how different models of the early universe can generate different amount and shapes of non-Gaussianity.

I will discuss a solution generating technique that allows to generate stationary axisymmetric solutions of five-dimensional gravity, starting from static ones. This technique can be used to add angular momentum to static configurations. It can also be used to add KK-monopole charge to asymptotically flat five-dimensional solutions, thus generating geometries that interpolate between five-dimensional and four-dimensional solutions.

The k-essence theories admit the superluminal propagation of the perturbations on classical nontrivial backgrounds. In this talk I will review our arguments from arXiv:0708.0561v1 and show that in spite of the superluminal propagation the causal paradoxes do not arise in these theories and in this respect they are not less safe than General Relativity.