8/11/2023 0 Comments Heisenberg principle atom locationThis implies that even at rest the particle is in a state of change. Derivation Elaborating the Origin of Lower Limit in Uncertainty Principleįor this construction, we shall consider the uncertainty principle for the pair of position and momentum observable, If x (position) and p (momentum) are supposed to be a pair of complementary variables and if and are uncertainties associated with this pair, then Heisenberg's uncertainty principle states įor a particle at rest, a frequency (f) is associated that depends on mass (m): Hence, the position of a particle in vibration can be expressed in the form of a 1-dimensional complex vector space ℂ 1 = ℂ (this can be viewed as a ℝ 2 with the Cartesian unit j generating an imaginary line), which can be called an imaginary line. This complex plane gives us information of the coordinate in a curved space with the real line giving the coordinate in a normal 1-dimensional space. To resolve this problem we can consider the curved path is in an complex plane. 2.Īs already mentioned, the particle is in a 1-dimensional space, but plotting coordinates only in terms of one parameter in curved space is not possible. Consider then the same particle in a particular state of vibration as depicted in Fig. 1 is not appropriate because it presupposes a representation in a flat 1-dimensional space. However, we know that matter/particles are always in state of vibrations, hence Fig. 1, we can easily plot coordinates in terms of a 1-dimension line. 1 the red bar represents the particle of width. Let us consider a particle of finite extent in a 1-dimensional space as illustrated in Fig. The aim of this paper is to explain the physical origin of Heisenberg's uncertainty principle and also why there is a lower limit of precision for any complementary pair. Certain quantities, such as position, energy and time, are unknown as per Heisenberg’s uncertainty principle, except by probabilities, probabilities gives us most probable value for these quantities but physical origin of these probabilities are not known. Questions such as why there is a lower limit of uncertainty for the two complementary variables have not been answered. If A and B are presumed to be a pair of complementary variables, such as position and momentum, and if and are the uncertainties associated with this pair, then Heisenberg's uncertainty principle states Īlthough the mathematical origin of Heisenberg’s uncertainty principle is known and the principle has been experimentally verified, its physical origin is not known.
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