Do Gedankenexperiments compel quantization of gravity?

TL;DR

This paper argues that Gedankenexperiments involving gravity do not necessarily require gravity to be quantized, as previous paradoxes can be resolved without quantum gravity considerations, challenging common assumptions.

Contribution

It demonstrates that the necessity for a quantum field theory of gravity is not supported by existing Gedankenexperiments, using only the Planck length as a resolution limit.

Findings

The paradox can be resolved without gravitational radiation quantization.

Effects are governed by the mass octopole, not quadrupole.

No Gedankenexperiment so far compels quantum gravity.

Abstract

Whether gravity is quantized remains an open question. To shed light on this problem, various Gedankenexperiments have been proposed. One popular example is an interference experiment with a massive system that interacts gravitationally with another distant system, where an apparent paradox arises: even for space-like separation the outcome of the interference experiment depends on actions on the distant system, leading to a violation of either complementarity or no-signalling. A recent resolution shows that the paradox is avoided when quantizing gravitational radiation and including quantum fluctuations of the gravitational field. Here we show that the paradox in question can also be resolved without considering gravitational radiation, relying only on the Planck length as a limit on spatial resolution. Therefore, in contrast to conclusions previously drawn, we find that the necessity for a quantum field theory of gravity does not follow from so far considered Gedankenexperiments of this type. In addition, we point out that in the common realization of the setup the effects are governed by the mass octopole rather than the quadrupole. Our results highlight that no Gedankenexperiment to date compels a quantum field theory of gravity, in contrast to the electromagnetic case.