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General Physical Uncertainty Relations as a Consequence of the Lorentz Transformation

机译:洛仑兹变换的结果导致一般物理不确定性关系

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The uncertainty relations fall into the ranks of the most important quantum relations. 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, p_x, and the uncertainty relation of the object's observation time, t, and its energy, E. The relations take the form: △p_x△x ≥ H and △E△t ≥ 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 △p_x△x ≥ h and △E△t ≥ h, where h is the Planck constant.
机译:不确定性关系属于最重要的量子关系。人们认为,在宏观世界中并没有观察到动量和坐标的不确定性关系以及能量和时间的不确定性关系。正在进行的工作的目的是证明存在延伸到宏体的一般物理不确定性关系。检查了由配备有一对同步时钟的杆组成的宏观物体和本身执行理想物理时钟功能的宏观物体。对于对象的一维运动(沿X轴),一般的物理关系直接从Lorentz变换得出-对象的x坐标的不确定性关系及其沿X轴的脉冲投影p_x和不确定性对象的观察时间t与能量E的关系。该关系的形式为:△p_x△x≥H和△E△t≥H。关系中的H值具有作用维度,并取决于精度对象时钟的时间和/或物理时钟的属性。尽管不确定性的概念与量子力学中的解释不同,但在极限情况下具有理想物理时钟的关系仍以△p_x△x≥h和△E△t≥h的形式表示,其中h是普朗克持续的。

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