Speaker: Erik Aurell

Title: "On the necessity to quantize the gravitational field"

Is it necessary to quantize the gravitational field? The analogous question for the electrodynamic field was considered settled in a famous paper by Bohr and Rosenfeld, now almost 90 years ago. The answer is yes, as otherwise there would be a a way to bypass the Heisenberg uncertainty relations for a body obeying quantum mechanics and interacting with the field. Bronstein in the 1930ies and Dyson in 2013 pointed out that the Bohr-Rosenfeld argument does not generalize to the gravitational field because the argument assumes compensatory bodies of opposite charge; there is no opposite charge for the gravitational field.

The Bohr and Rosenfeld paper, although famous, is also famously difficult to understand. I will therefore start by describing another argument also due to Bohr, and which arrives at the same result; the argument was first published by Baym and Ozawa in 2009 [reference below]. A gravitational version of this second argument can be found in outline in the beginning of Feynman's lectures on gravitation, and in the summary of the 1957 Chapel Hill conference. At the end of their paper Baym & Ozawa discuss this gravitational argument more quantitatively, and arrive at the conclusion that it does not establish a necessity to quantize that field, unless one assumes that length scales smaller than the Planck length can be resolved.

I will discuss another Gedankenexperiment proposed by Belenchia and collaborators, and show that a putative paradox presented therein can be resolved in the same manner as in Baym & Ozawa, also in this case without the necessity to quantize the gravitational field. 

I will end by discussing what these results might mean, apart from establishing the lack of a valid logical implication. The talk is based on joint recent work with Erik Rydving and Igor Pikovski.

References

1.  G. Baym and T. Ozawa, Proc. Natl. Acad. Sci. U.S.A. 106, 3035 (2009)
2.  A. Belenchia, R. M. Wald, F. Giacomini, E. Castro-Ruiz, Č. Brukner, and M. Aspelmeyer,  Phys. Rev. D 98, 126009 (2018)
3.  E. Rydving, E. Aurell, I. Pikovski, Physical Review D 104 (8), 086024 (2021)