Mathematisches Oberseminar: Quantenmechanische Vielteilchensysteme und relativistische Quantentheorie

We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability distribution arises from the Born rule and which has a clear physical interpretation. The same procedure can be employed to measure the "time at which some event happens" for arbitrary events (and not just specifically for the arrival time of a particle).

I show that the three-particle E = P = L = 0 Newtonian universe can be evolved through the points of triple collision – the Big Bang of the three-particle E = P = L = 0 Newtonian universe. The result is essentially based on a description of the system’s dynamics on shape phase space, the relational phase space of the system. Explicitly, I show that the shape, i.e. angular, degrees of freedom can be evolved uniquely through the points of total collision. This holds for almost all collision solutions. One such solution on shape phase space corresponds to two solutions on absolute phase space, one which ends at and one which begins at a total collision, ‘glued together’ via the unique evolution of the shape degrees of freedom. That way, the Newtonian singularity is passed. Eventually, I sketch the eternal evolution of a three-particle E = P = L = 0 Newtonian universe with a Big Bang: there is a triple collision, i.e. a Big Bang, at the mid-point of that evolution while the particles separate, typically into a Kepler pair and a single particle, and fly off in both time directions away from that point.

In some collapse models, like the Ghirardi-Rimini-Weber model, there are real objective quantum jumps. These spontaneous jumps have empirical consequences, making such models deviate from quantum mechanics. I will argue that the predictions of collapse models in general are not specific enough to deviate from quantum mechanics taken as a general approach, but only from its instantiation in the Standard Model. I will discuss one example I find particularly surprising: a collapse model in which the jumps are so violent that they can be heard. It seems that in this context, one can know for sure that there are genuine stochastic jumps, at odds with the sort of general indistinguishably I seem to claim exists in general. But it's not the case. And I think understanding what goes on is a good way to grasp much better the role played (and not played) by decoherence in the resolution of the measurement problem.