Final Activity Report Summary - GEOMETRY QUANTUM (Quantum probability, geometry and gravity)
The project's aim was the theoretical study of probabilities in quantum theory, their relation to geometry and possible application in developing general quantisation techniques. The most important result of the research so far has been a detailed study of the probabilities associated to sequential quantum measurements. The mathematical description of these probabilities is very different from those of standard probability theory and possess many counter-intuitive features, as for example a very strong dependence on even tiny details of the measurement device.
The reason is that the procedure of constructing these probabilities is not naturally obtained from the standard formalism of quantum theory--there are additional physical assumptions involved, which can in principle be experimentally tested.
This work is related to the study of the so-called time-of-flight probabilities in quantum theory, namely the construction of a probability density for the time that a specific event took place, for example the detection of a particle. This is an old that is caused by the difficulty to include time as a physical observable in quantum theory. We show that the probabilities for the time of arrival are related to the probabilities of sequential measurements, a fact allowing us to construct an algorithm for the determination of the time-of-arrival probabilities for very general quantum systems.
Other work within this project includes the use of geometrical methods (that appear naturally in the description of quantum 'measurements' at more than one moment of time) in the construction of the quantum mechanical description for a class of systems relevant to gravity (known as parameterised systems). We have elaborated in particular on the case of models relevant to cosmology.
The reason is that the procedure of constructing these probabilities is not naturally obtained from the standard formalism of quantum theory--there are additional physical assumptions involved, which can in principle be experimentally tested.
This work is related to the study of the so-called time-of-flight probabilities in quantum theory, namely the construction of a probability density for the time that a specific event took place, for example the detection of a particle. This is an old that is caused by the difficulty to include time as a physical observable in quantum theory. We show that the probabilities for the time of arrival are related to the probabilities of sequential measurements, a fact allowing us to construct an algorithm for the determination of the time-of-arrival probabilities for very general quantum systems.
Other work within this project includes the use of geometrical methods (that appear naturally in the description of quantum 'measurements' at more than one moment of time) in the construction of the quantum mechanical description for a class of systems relevant to gravity (known as parameterised systems). We have elaborated in particular on the case of models relevant to cosmology.