Salecker-Wigner-Karolyhazy Gedankenexperiment in light of the self-gravity

TL;DR

This paper revisits the Salecker-Wigner-Karolyhazy thought experiment, incorporating self-gravity effects, and concludes that these effects limit length measurement uncertainty to the Planck length.

Contribution

It introduces the role of self-gravity in the thought experiment, refining the fundamental limits of space-time measurement.

Findings

Uncertainty in length measurement is bounded by the Planck length.

Self-gravity effects reduce measurement uncertainty.

Combines quantum mechanics, special relativity, and general relativity insights.

Abstract

In Gedankenexperiment mentioned in the title, the imprecision in space-time measurement is related to the spreading of clock's wave-function with the passage of time required for the measurement. Special relativity puts a bound on the measurement time, it cannot be reduced arbitrarily as the signal used for the measurement cannot propagate with speed greater than that of light. In view of this reasoning, one is led to conclude that the clock should be heavy enough to slow down its wave-function from spreading with time. However, the general relativity puts an upper bound on clock's mass, since its size must remain greater then the Schwarzschild radius associated to it. This way one reaches a limit in length measurement. However, as is discussed below, an additional insight into the question comes by taking into account self-gravitational effects. As a result, the uncertainty in length measurement is reduced to the Planck length.