Space-time localisation with quantum fields

Maike Klüppel, Holger Neumann

Marc-Thierry Jaekel, Serge Reynaud

The description of relativistic effects requires a preliminary definition of events localised in space-time while the clocks used for time definition and the fields used in synchronisation or localisation procedures are necessarily quantum systems. We outline an algebraic framework where basic requirements of quantum theory and relativity are consistently dealt with. This approach which may be termed as a `quantum relativity' is built on the algebra of symmetries. It contains the definition of quantum observables associated with Einstein localisation in space-time as well as the evaluation of their commutation relations including the energy-time relation. These commutators also describe the relativistic shifts undergone under frame transformations, not only for inertial frames but also for uniformly accelerated frames. The quantum redshift laws differ from their classical counterparts while still obeying universal metric properties. The paper presents this approach in terms closely connected to the seminal Einstein conception of localisation in space-time and refers to already published papers for more technical developments.

Jean Reignier

Space and Time are essential ways by which humans think about their environment. The mathematical parameters associated with these concepts appear nearly in the same way in the formulation of both the classical and the quantum theories, but cer tainly not any more at the level of our intuitive understanding of their results. This paper aims to explain why it can be so, starting from an analysis of the way some basic principles are introduced in these theories. These principles are: localisation in space, isolation of a system, state of an isolated system, and causality. The problem of quantum non-locality is analysed again. It is shown that localising a microscopic entity can depend on the kind of localising experiment one performs. I give an example of an entity which will be considered as localised or alternatively as non-localised, depending on the localising experiment. I also discuss the ideas of time and of duration in quantum physics. I show that if duration can be properly defined for a statistical set of particles, it is not so for the individuals.

Tim Maudlin

R. Grobe

Tejinder P. Singh

Abstract The Ghirardi-Rimini-Weber theory of spontaneous collapse offers a possible resolution of the quantum measurement problem. In this theory, the wave function of a particle spontaneously and repeatedly localises to one or the other random position in space, as a consequence of the hypothesised quantum jumps. In between jumps, the wave function undergoes the usual Schrödinger evolution. In the present paper, we suggest that these jumps take place in Hilbert space, with no reference to physical space and a physical three-dimensional space arises as a consequence of localisation of macroscopic objects in the universe. That is, collapse of the wave-function is responsible for the origin of space. We then suggest that similar jumps take place for a hypothetical time operator in Hilbert space and classical time, as we know it emerges from localisation of this time operator, for macroscopic objects. More generally, the jumps are suggested to take place in an operator space-time in Hilbert space, leading to an emergent classical space-time.