On the Salecker-Wigner limit and the use of interferometers in space-time-foam studies

TL;DR

This paper defends the Salecker-Wigner limit against recent criticism, clarifies its relevance to quantum space-time studies, and discusses how interferometers can probe space-time foam models independently of this limit.

Contribution

The paper refutes recent claims that the Salecker-Wigner limit is flawed and clarifies its role in quantum space-time research and interferometry-based tests.

Findings

The criticism of the Salecker-Wigner limit is based on incorrect assumptions.

Quantum uncertainties in distance measurements cannot be fully eliminated.

Interferometers can probe space-time foam models independently of the Salecker-Wigner limit.

Abstract

The recent paper gr-qc/9909017 criticizes the limit on the measurability of distances that was derived by Salecker and Wigner in the 1950s. If justified, this criticism would have important implications for all the recent studies that have used in various ways the celebrated Salecker-Wigner result, but I show here that the analysis reported in gr-qc/9909017 is incorrect. Whereas Salecker and Wigner sought an operative definition of distances suitable for the Planck regime, the analysis in gr-qc/9909017 relies on several assumptions that appear to be natural in the context of most present-day experiments but are not even meaningful in the Planck regime. Moreover, contrary to the claim made in gr-qc/9909017, a relevant quantum uncertainty which is used in the Salecker-Wigner derivation cannot be truly eliminated; unsurprisingly, it can only be traded for another comparable contribution to the total uncertainty in the measurement. I also comment on the role played by the Salecker-Wigner limit in my recent proposal of interferometry-based tests of quantum properties of space-time, which was incorrectly described in gr-qc/9909017. In particular, I emphasize that, as discussed in detail in gr-qc/9903080, only some of the quantum-gravity ideas that can be probed with modern interferometers are motivated by the Salecker-Wigner limit. The bulk of the insight we can expect from such interferometric studies concerns the properties of "foamy" models of space-time, which are intrinsically interesting independently of the Salecker-Wigner limit.