Uncertainty in Measurements of Distance

Abstract

Ng and van Dam have argued that quantum theory and general relativity give a lower bound of L^{1/3} L_P^{2/3} on the uncertainty of any distance, where L is the distance to be measured and L_P is the Planck length. Their idea is roughly that to minimize the position uncertainty of a freely falling measuring device one must increase its mass, but if its mass becomes too large it will collapse to form a black hole. Here we show that one can go below the Ng-van Dam bound by attaching the measuring device to a massive elastic rod. Relativistic limitations on the rod's rigidity, together with the constraint that its length exceeds its Schwarzschild radius, imply that zero-point fluctuations of the rod give an uncertainty greater than or equal to L_P.

5 pages LaTeX

References in corpus (1)

• Quantum theory's last challenge

Cited by in corpus (13)

• Modern tests of Lorentz invariance
• Minimum Length from Quantum Mechanics and Classical General Relativity
• Fundamental decoherence from quantum gravity: a pedagogical review
• Relational physics with real rods and clocks and the measurement problem of quantum mechanics
• Length Uncertainty in a Gravity's Rainbow Formalism
• Deformed Density Matrix and Quantum Entropy of the Black Hole
• Assessing the Montevideo Interpretation of Quantum Mechanics
• Comment on "Uncertainty in measurements of distance"
• Time Uncertainty in Quantum Gravitational Systems
• A single-world consistent interpretation of quantum mechanics from fundamental time and length uncertainties
• Information, information processing and gravity
• Fundamental Limit on Angular Measurements and Rotations from Quantum Mechanics and General Relativity
• Salecker-Wigner-Karolyhazy Gedankenexperiment in light of the self-gravity