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Uncertainty Principle

The Uncertainty Principle is derived from three elements: the wave-particle duality, the indivisibility of energy and momentum transfers,
Uncertainty and the lack of complete determinism. It states that for a pair of conjugate variables such as position / momentum and time/energy (including the rest mass energy mc2), it is impossible to have a precisely determined value of each member of the pair at the same time. This statement is illustrated with a schematic diagram in Figure 12-02. The corresponding formula is: xpx > , where denotes the uncertainty, x is the position of the point mass m along the x-axis,
px = m vx is the momentum along the x-axis, vx is the velocity along the x-axis, and = h/2 = 1.054x10-27 erg-sec. A similar relation exists for the uncertainty of the time t and energy E, e.g.,

Figure 12-02 Uncertainty Principle [view large image]

t E . In case of heavy mass (such as a macroscopic object), the uncertainties and thus the quantum effect becomes very small, classical physics is applicable once more.
See "A Derivation of the Uncertainty Principle" for more detail.

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