Quantum reference systems and quantum general covariance

Fields: quantum gravity, quantum foundations, quantum field theory

Every measurement is done with respect to some reference frame and every reference frame is associated with a physical reference system, for example some laboratory. It is often for all practical purposes justified to idealize the reference system as a classical non-dynamical entity that is external to the physical scenario of interest and whose objective in life is to define a description of the latter through its associated frame. This is the case in both general relativity and quantum (field) theory.

There are circumstances, however, when such idealizations are no longer appropriate. This is the case with more fundamental descriptions of physics, which take into account that every reference system is a physical system and should thereby ultimately be subjected to the laws of quantum theory. For example, in so-called background independent approaches to quantum gravity, classical reference frames and coordinates are a priori absent and replaced with dynamical quantum reference systems. Treating reference systems fundamentally as quantum systems is also inevitable in the foundations of quantum theory once considering laboratories as physical systems and invoking the universality of quantum theory. Both fields thereby face the question of how to describe physics from the `perspective' of quantum reference systems and how the descriptions relative to different such choices are related.

This question also brings into focus the fate of general covariance in a quantum regime, which, despite its importance in general relativity, has not been sufficiently explored yet. Given the a priori absence of coordinates in quantum gravity, a quantum version of general covariance must bear on the ability to consistently switch between the descriptions of the same physics relative to arbitrary choices of quantum reference systems. Any given description relative to a quantum reference system can be regarded as a quantum frame perspective on the physics.

Some of our research has focused on using quantum reference systems to develop a perspective-neutral approach to quantum general covariance, which exploits gauge symmetries to accommodate all the different quantum frame perspectives in one framework. This approach yields "quantum coordinate transformations" which have the same compositional structure as coordinate transformations on a manifold, except that they map between different Hilbert spaces. These quantum coordinate transformations give rise to a quantum version of the relativity of various physical properties; for example, quantum correlations, superpositions, clock synchronizations, classicality, temporal locality, measurements and many other properties depend on the quantum frame perspective. One of the aims of this perspective-neutral program is to contribute to 'operationalizing' research in background independent quantum gravity by providing a platform for linking different quantum frame perspectives in a diffeomorphism invariant context.


Schematic representation of "quantum coordinate changes", i.e. changing from the description of physics relative to quantum reference system A to the description relative to quantum reference system B.

 


Classical analog of changing quantum reference system perspective at the level of the constraint surface in phase space.

 

Further reading:

  • P. A. Höhn, A. Smith and M. Lock 2020, "Equivalence of approaches to relational quantum dynamics
    in relativistic settings", Preprint arXiv:2007.00580 https://arxiv.org/abs/2007.00580
  • P. A. Höhn, A. Smith and M. Lock 2019, "The trinity of relational quantum dynamics", Preprint
    arXiv:1912.00033 https://arxiv.org/abs/1912.00033
  • A. Vanrietvelde, P. A. Höhn, F. Giacomini, E. Castro-Ruiz 2020, "A change of perspective: switching quantum reference frames via a perspective-neutral framework", Quantum 4 225, https://doi.org/10.22331/q-2020-01-27-225 (Preprint arXiv:1809.00556)
  • P. A. Höhn 2019, "Switching internal times and a new perspective on the wave function of the Universe", Universe 5(5) 116, https://doi.org/10.3390/universe5050116
    (Universe Cover Story, https://www.mdpi.com/2218-1997/5/5, Preprint arXiv:1811.00611)
  • P. A. Höhn and A. Vanrietvelde 2018, "How to switch between relational quantum clocks", Preprint
    arXiv:1810.04153 https://arxiv.org/abs/1810.04153
  • A. Vanrietvelde, P. A. Höhn and F. Giacomini 2018, "Switching quantum reference frames in the
    N-body problem and the absence of global relational perspectives", Preprint arXiv:1809.05093 https://arxiv.org/abs/1809.05093
  • P. A. Höhn 2017, "Reflections on the information paradigm in quantum and gravitational physics", J. Phys. Conf. Ser. 880 012014, https://doi.org/10.1088/1742-6596/880/1/012014 (invited contribution to DICE Proceedings, Ed. H.-T. Elze, Preprint arXiv:1706.06882)
  • P. A. Höhn, E. Kubalova and A. Tsobanjan 2012, "Effective relational dynamics of a nonintegrable cosmological model", Phys. Rev. D 86 065014, https://doi.org/10.1103/PhysRevD.86.065014 (Preprint arXiv:1111.5193)
  • M. Bojowald, P. A. Höhn and A. Tsobanjan 2011, "Effective approach to the problem of time: general features and examples", Phys. Rev. D 83 125023, https://doi.org/10.1103/PhysRevD.83.125023 (Preprint arXiv:1011.3040)
  • M. Bojowald, P. A. Höhn and A. Tsobanjan 2011, "An effective approach to the problem of time", Class. Quant. Grav. 28 035006, https://doi.org/10.1088/0264-9381/28/3/035006 (Preprint arXiv:1009.5953)