Heisenberg Uncertainty Relation (Indeterminacy Relations)

H. Chris Ransford

S. Srivastava

The differential and integral forms of Indeterminacy principle or Heisenberg Uncertainty principle have been described in this paper. The uncertainty in the measurement of ∆E is not only due to the measurement of ∆t and h but is also due to quantization factor Q. We have discussed Order-Disorder Transformation, Differential and Integral forms of Indeterminacy principle (Quantum Theory of Uncertainty principle), Quantum Representation and Action Quantization Process in details. We have used the Order- Disorder concept and established that the Heisenberg Uncertainty principle may be evaluated from Order- Disorder Transformation, i.e., Heisenberg Uncertainty principle is the special case of Order- Disorder Transformation. It may be pointed out that our modification of Uncertainty relation is consistent with the results in the range of variables where the modified relationship is valid.

Paul Busch, Brigitte Falkenburg

S. P. Boughn, Marcel Reginatto

Abstract Heisenberg introduced his famous uncertainty relations in a seminal 1927 paper entitled The Physical Content of Quantum Kinematics and Mechanics . He motivated his arguments with a gedanken experiment, a gamma ray microscope to measure the position of a particle. A primary result was that, due to the quantum nature of light, there is an inherent uncertainty in the determinations of the particle’s position and momentum dictated by an indeterminacy relation, δ q δ p ∼ h . Heisenberg offered this demonstration as ‘a direct physical interpretation of the [quantum mechanical] equation pq − qp = − i ℏ ’ but considered the indeterminacy relation to be much more than this. He also argued that it implies limitations on the very meanings of position and momentum and emphasised that these limitations are the source of the statistical character of quantum mechanics. In addition, Heisenberg hoped but was unable to demonstrate that the laws of quantum mechanics could be derived directly from the uncertainty relation. In this paper, we revisit Heisenberg’s microscope and argue that the Schrödinger equation for a free particle does indeed follow from the indeterminacy relation together with reasonable statistical assumptions.

Людвиг Дмитриевич Фаддеев, O. Yakubovskiĭ

R. Shankar