Comment on "Uncertainty in measurements of distance"

TL;DR

This paper defends a fundamental quantum-gravity bound on distance measurement uncertainty, refutes a recent claim that it can be surpassed, and emphasizes the connection with black hole physics and the holographic principle.

Contribution

It clarifies and supports the lower bound on measurement uncertainty derived from quantum mechanics and general relativity, countering recent claims to surpass it, and discusses its relation to black hole physics.

Findings

The bound elta l pprox l^{1/3} l_P^{2/3} is robust against proposed modifications.

Recent attempts to go below this bound are refuted.

The bound is consistent with black hole physics and the holographic principle.

Abstract

We have argued that quantum mechanics and general relativity give a lower bound $\delta l \gtrsim l^{1/3} l_P^{2/3}$ on the measurement uncertainty of any distance $l$ much greater than the Planck length $l_P$. Recently Baez and Olson have claimed that one can go below this bound by attaching the measuring device to a massive elastic rod. Here we refute their claim. We also reiterate (and invite our critics to ponder on) the intimate relationship and consistency between black hole physics (including the holographic principle) and our bound on distance measurements.