## Uncertainty Relations as Consequence of the Lorentz Transformations

**Authors:** V.N. Matveev, O.V. Matveev

It is believed that the uncertainty relation of momentum and coordinates, as well as the uncertainty relation of energy and time in practice are not observed in the macrocosm. The objective of the work at hand was to demonstrate the existence of general physical uncertainty relations that extend to macrobodies.
A macroscopic object consisting of a rod equipped with a pair of synchronized clocks and a macroscopic object in and of itself performing the function of an ideal physical clock are examined. General physical relations are directly derived from Lorentz transformations for the case of the object's one-dimensional motion (along the X axis) – the uncertainty relation of the object's x coordinate and the projection of its impulse along the X axis, px, and the uncertainty relation of the object's observation time, t, and its energy, E. The relations take the form: ΔpxΔx ≥ H and ΔEΔt ≥ H. The H value in the relation has action dimensions and is dependent upon the precision of the object's clocks and/or upon the properties of the physical clock. Despite the interpretation of the concept of uncertainty being different from that in quantum mechanics, the relations derived in the limiting case with ideal physical clock take the form of ΔpxΔx ≥ h and ΔEΔt ≥ h, where h is the Planck constant.

**Comments:** 11 Pages.

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### Submission history

[v1] 2011-12-11 05:22:24

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