A assimetria quântica entre o tempo e o espaço

quinta-feira, agosto 18, 2016

Quantum asymmetry between time and space

Joan A. Vaccaro

Published 20 January 2016. DOI: 10.1098/rspa.2015.0670

Prof. Joan Vaccaro - Source/Fonte: Griffith University


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.

Data accessibility

Electronic supplementary material is available at http://dx.doi.org/10.1098/rspa.2015.0670 or via http://rspa.royalsocietypublishing.org.

Competing interests

I have no competing interests.


I did not receive external funding for the research reported here.


I thank D.T. Pegg, H.M. Wiseman, M.J. Hall and T. Croucher for helpful discussions.

Received September 28, 2015. Accepted December 23, 2015.

© 2016 The Authors.

Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.