Limitation to quantum measurements of space-time distances

Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the folklore, the minimum error in the measurement of a length is shown to be proportional to the one-third power of the length itself. This uncertainty in space-time measurements implies an uncertainty of the space-time metric and yields quantum decoherence for particles heavier than the Planck mass. There is also a corresponding minimum error in energy-momentum measurements.

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Quantum limitations of the measurement of space-time distances

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(
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)
,
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(
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)

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•
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(
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)
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(
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)

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(
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(
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