What We Can Say about the Uncertainty Relation in Quantum Measurement

Seth Lloyd, Vittorio Giovannetti, Lorenzo Maccone

Durgadas Datta.

Because the particles follow a wave pattern of probability prescribed by schrodinger equation and we are guided by uncertainty principles, we often wrongly interpret the nature of reality. Heisenberg only prescribes the measurement problems of very small due to limitations of wave length of the observing beam and that is the natural limitation but wrongly we say that nature is acting indeterministi. Thus we wrongly understand uncertainty principles connecting t to saying that nature can never be precisely defined in momentum and position.In the same way we measure time in relativity theory confusing the very notion of time.

Paul Busch

John Ashmead

Abstract Does the Heisenberg uncertainty principle (HUP) apply along the time dimension in the same way it applies along the three space dimensions? Relativity says it should; current practice says no. With recent advances in measurement at the attosecond scale it is now possible to decide this question experimentally. The most direct test is to measure the time-of-arrival of a quantum particle: if the HUP applies in time, then the dispersion in the time-of-arrival will be measurably increased. We develop an appropriate metric of time-of-arrival in the standard case; extend this to include the case where there is uncertainty in time; then compare. There is – as expected – increased uncertainty in the time-of-arrival if the HUP applies along the time axis. The results are fully constrained by Lorentz covariance, therefore uniquely defined, therefore falsifiable. So we have an experimental question on our hands. Any definite resolution would have significant implications with respect to the role of time in quantum mechanics and relativity. A positive result would also have significant practical applications in the areas of quantum communication, attosecond physics (e.g. protein folding), and quantum computing.

Yu Watanabe

S. Rajasekar, R. Velusamy

One of the most striking deviations of quantum mechanics from classical mechanics is that any measurement of a microscopic system involves the interaction with the measuring instruments. The interaction cannot be neglected and in fact leads to uncontrollable disturbance on the system. In 1927, Werner Karl Heisenberg in his celebrated paper established the quantitative expression for unavoidable momentum disturbance caused by any position measurement. The crucial word here is simultaneously. The uncertainty relation gives the lower bound on the product of the uncertainties of two pairs of variables. But it says nothing about the accuracy with which individual observables can be measured. The physical meaning of energy-time uncertainty is different from that of x-px uncertainty. Position and momentum are observables to which Hermitian operators are assigned and which are measured at a particular time. An important implication of the uncertainty principle is that quantum systems do follow classical trajectories which conflict with our everyday experience.