Philosophy of Physics Seminar (Thursday - Week 6, MT23)

The Leggett-Garg (LG) inequalities were introduced, as a temporal parallel of the Bell inequalities, to test macroscopic realism (MR) -- the world view that a macroscopic system evolving in time possesses definite properties which can be determined without disturbing the future or past state. If violated, such tests indicate the presence of superposition states for macroscopic systems.

In this talk I give an overview of developments in this area over the last few years. This includes the following:

1. The development  of necessary and sufficient conditions for macrorealism and their generalization to multi-time measurements, many variable systems and data sets with higher order correlators.
2. Modifications of the usual non-invasive measurement protocols required in LG tests which provide improved checks that the measurements really are non-invasive.
3. Recently discussed LG-type tests which involve only single time measurements (e.g. the Tsirelson inequality).
4. LG tests for interferometric experiments and for measurements of sign(x) in the harmonic oscillator and other continuous variable systems, which provides a useful setting for genuinely macroscopic tests. The physical origin of the LG violations in the SHO case links to the phenomenon of diffraction in time first highlighted by Moshinsky and is conveniently illustrated using Bohm trajectories.

Some relevant papers:

 [1] J.J. Halliwell Phys. Rev. A 93, 022123 (2016) The Leggett-Garg inequalities and no-signaling in time: a quasi-probability approach

[2] J. J. Halliwell Phys. Rev. A 96, 012121 (2017) Comparing conditions for macrorealism: Leggett-Garg inequalities vs no-signaling in time

[3] S. Majidy et al Phys. Rev. A 100, 042325 (2019) Exploration of an augmented set of Leggett-Garg inequalities using a noninvasive continuous-in-time velocity measurement

[4] J. J. Halliwell and C. Mawby Phys. Rev. A 100, 042103 (2019) Fine's Theorem for Leggett-Garg tests with an arbitrary number of measurement times

[5] J.J. Halliwell, Phys. Rev. A 99, 022119 (2019) Leggett-Garg tests of macrorealism: checks for non-invasiveness and generalizations to higher-order correlators

[6] J.J. Halliwell and C. Mawby Phys. Rev. A 102, 012209 (2020) Conditions for macrorealism for systems described by many-valued variables

[7] S. Majidy et al Phys. Rev. A 103, 062212 (2021) Detecting violations of macrorealism when the Leggett-Garg inequalities are satisfied

[8] J. J. Halliwell Phys. Rev. A 94, 052114 (2016) Leggett-Garg correlation functions from a non-invasive velocity measurement continuous in time

[9] J.J. Halliwell et al Phys. Rev. A 103, 032218 (2021) Leggett-Garg tests for macrorealism: interference experiments and the simple harmonic oscillator

[10] C. Mawby and J. J. Halliwell, Phys. Rev. A 105, 022221 (2022) Leggett-Garg tests for macrorealism in the quantum harmonic oscillator and more general bound systems

[11] C. Mawby and J. J. Halliwell, Phys. Rev. A 107, 032216 (2023) Leggett-Garg violations for continuous variable systems with gaussian states

[12] J. J. Halliwell, H. Beck, B. K. B. Lee, and S. O'Brien, Phys. Rev. A 99, 012124 (2019) A quasi-probability for the arrival time problem with links to backflow and the Leggett-Garg inequalities

With speaker’s consent, talks will be recorded and published on YouTube. Our channel is:

https://www.youtube.com/c/OxfordPhilosophyofPhysics/videos

If you wish to join the dinner following the talk, please email Oliver Pooley: oliver.pooley@philosophy.ox.ac.uk.