Quantum elements of time and space

Carl Friedrich von Weizsäcker, Thomas Görnitz, Holger Lyre

Afanasev Sergei Borisovich

The idea of space-time as a combination of shapeless fundamental elements is proposed.The history of the development of ideas about the discrete space-time structure is analyzed.Quantum space-time is considered as a set of quantum states defined on a set of discretizations with an arbitrary shape of the boundaries of regions.The fundamental element of such space-time is described by the totality of its probabilistic characteristics.We consider a concept in which space-time is the only quantum object, and all material particles and interaction carriers are described as excited states of the fundamental elements of this quantum object.

W. M. Stuckey, Michael Silberstein, Timothy J. McDevitt

We propose an adynamical interpretation of quantum theory called Relational Blockworld (RBW) where the fundamental ontological element is a 4D graphical amalgam of space, time and sources called a “spacetimesource element.” These are fundamental elements of space, time and sources, not source elements in space and time. The transition amplitude for a spacetimesource element is computed using a path integral with discrete graphical action. The action for a spacetimesource element is constructed from a difference matrix K and source vector J on the graph, as in lattice gauge theory. K is constructed from graphical field gradients so that it contains a non-trivial null space and J is then restricted to the row space of K, so that it is divergence-free and represents a conserved exchange of energy–momentum. This construct of K and J represents an adynamical global constraint between sources, the spacetime metric and the energy–momentum content of the spacetimesource element, rather than a dynamical law for time-evolved entities. To illustrate this interpretation, we explain the simple EPR-Bell and twin-slit experiments. This interpretation of quantum mechanics constitutes a realist, psi-epistemic model that might underwrite certain information-theoretic accounts of the quantum.

Michele Cini

Joan A. Vaccaro

An asymmetry exists between time and space in the sense that physical systems inevitably evolve over time, whereas there is no corresponding ubiquitous translation over space. The asymmetry, which is presumed to be elemental , is represented by equations of motion and conservation laws that operate differently over time and space. If, however, the asymmetry was found to be due to deeper causes, this conventional view of time evolution would need reworking. Here we show, using a sum-over-paths formalism, that a violation of time reversal (T) symmetry might be such a cause. If T symmetry is obeyed, then the formalism treats time and space symmetrically such that states of matter are localized both in space and in time. In this case, equations of motion and conservation laws are undefined or inapplicable. However, if T symmetry is violated, then the same sum over paths formalism yields states that are localized in space and distributed without bound over time, creating an asymmetry between time and space. Moreover, the states satisfy an equation of motion (the Schrödinger equation) and conservation laws apply. This suggests that the time–space asymmetry is not elemental as currently presumed, and that T violation may have a deep connection with time evolution.