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http://arxiv.org/abs/quant-ph/0505064

Quantum limits to the measurement of spacetime geometry

Seth Lloyd

11 pages

"This letter analyzes the limits that quantum mechanics imposes on the accuracy to which spacetime geometry can be measured. By applying the physics of computation to ensembles of clocks, as in GPS, we present a covariant version of the quantum geometric limit, which states that the total number of ticks of clocks and clicks of detectors that can be contained in a four volume of spacetime of radius r and temporal extent t is less than or equal to

rt/(pi x_{P}t_{P}),

where x_{P}, t_{P}are the Planck length and time. The quantum geometric bound limits the number of events or `ops' that can take place in a four-volume of spacetime and is consistent with and complementary to the holographic bound which limits the number of bits that can exist within a three-volume of spacetime."

[tex]\frac{rt}{\pi x_P t_P}[/tex]

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# A new Seth Lloyd paper

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