Operational approach to time and clocks in quantum theory

Abstract

Throughout the existence of humankind, people have organised their lives based on the sunrise and sunset, the Moon phases and star movements. Nature has guided our daily routines, as it still does, and it would be hard to imagine what life would look like without the already known cycles imposed by nature. As the humanity progressed, we have realised that a day is not always of the same length, but our sleep cycle most often is, and that it would be extremely useful to have further references for organising our day and habits. So people started calculating time with the Sun clock, sand clock, water clock etc. Since these were all limited in their performance, mechanical and pendulum clocks were introduced later, followed by quartz clocks, and as the ultimate performing ones, in the 20th century the first atomic clocks were constructed. This revolutionised time-keeping, speeded up technology development and made very precise coordination in every-day lives possible. It is now hard to think of spending a day without an accurate watch. But where does this notion of time and clocks physically arise from? And is it valid only in the classical limit that we experience, or is it possible to introduce very precise and well-synchronised quantum clocks as well? This is what we will try to deal with in this thesis. We start from the assumption that the only observable time is the one given by clocks, and hence to learn more about quantum time we need to build good quantum clocks and try to synchronise them. We define clocks as quantum systems that need to provide a time reference, such as a sequence of ticks. Further, we attempt to find limits on their synchronisation, since it is well known that quantum systems interact with their environment thereby getting disturbed. What we find out is that the performance of the quantum clocks we define depends crucially on their dimension (number of the distinguishable states available), and that the quantum clocks of a certain dimension could possibly perform better than the classical ones with the same state space size. The limitations to synchronising local quantum clocks suggest that global time in quantum mechanics might not be a physically grounded notion. We also investigate what limitations would be imposed on the evolution of our Universe, if it itself was/contained a quantum clock providing ticks that we observe as time. Our results show that the theory of inflation is consistent with the time keeping the Universe needed to perform at its early beginning, while the speed of evolution as of today would not be fast enough for the Universe to be able to store its ticks then. Although our argument is still not completely general, and does not exclude other possible theories for the evolution of the Universe, it is a novel approach to combining cosmology with quantum information and it would be very interesting to extend this research further.