Journal of Guangxi University for Nationalities

The Discussion of the Uncertain Relations of △t·△E≥/2

Luo Li

Published Jan 1, 2000• 0 citations

Abstract

From the four uncertain relations of the present typical time energy we analyse △t、△E and △t·△E≥2 , including △t△E≈h . Then we have the conclusion that △t·△E≥2 or △t△E≈h should not be regarded as the uncertain relations of the coordinated quantum mechanics of △x·△P x≥2 or △x·△P x≈h . In the end, we suggest some resolutions.

Related papers

The general discussion of uncertain relation in quantum mechanics

Zhang Yun-sheng

The paper gives some concrete discussions of uncertainly relation and relevant examples that concern.

Journal of Dezhou UniversityJan 1, 20040 citations

The Simple Method of Deducing Uncertain Relation

Youchang Jiang

In the paper,the three common types of deducing model on uncertain relation are pointed out and then the author deduces the uncertain relation on the basis of the basic hypothesis of quantum mechanics.

Sichuan University of Arts and Science JournalJan 1, 20070 citations

Critical Look at the Time--Energy Uncertainty Relations

K. Urbanowski

The Heisenberg and Mandelstam-Tamm time-energy uncertainty relations are analyzed. The conlusion resulting from this analysis is that within the Quantum Mechanics of Schrödinger and von Neumann, the status of these relations can not be considered as the same as the status of the position-momentum uncertainty relations, which are rigorous. The conclusion is that the time--energy uncertainty relations can not be considered as universally valid.

arXiv:1908.05273Acta Physica Polonica BDec 19, 20192 citations

Time in the Quantum Theory and the Uncertainty Relation for Time and Energy

Yakir Aharonov, David Böhm

Because time does not appear in Schr\"odinger's equation as an operator but only as a parameter, the time-energy uncertainty relation must be formulated in a special way. This problem has in fact been studied by many authors and we give a summary of their treatments. We then criticize the main conclusion of these treatments; viz., that in a measurement of energy carried out in a time interval, $\ensuremath{\Delta}t$, there must be a minimum uncertainty in the transfer of energy to the observed system, given by $\ensuremath{\Delta}({E}^{\ensuremath{'}}\ensuremath{-}E)>~\frac{h}{\ensuremath{\Delta}t}$. We show that this conclusion is erroneous in two respects. First, it is not consistent with the general principles of the quantum theory, which require that all uncertainty relations be expressible in terms of the mathematical formalism, i.e., by means of operators, wave functions, etc. Secondly, the examples of measurement processes that were used to derive the above uncertainty relation are not general enough. We then develop a systematic presentation of our own point of view, with regard to the role of time in the quantum theory, and give a concrete example of a measurement process not satisfying the above uncertainty relation.

Physical ReviewJun 1, 1961481 citations

Exploring the implications of the uncertainty relationships in quantum mechanics

Huai‐Yu Wang

Heisenberg guessed, after he established the matrix quantum mechanics, that the non-commutativity of the matrices of position and momentum implied that the position and momentum of a particle could not be precisely simultaneously determined. He consequently conjectured that time and energy should also have a similar relationship. Soon after, Robertson derived an inequality concerning the space coordinate and momentum, which was thought to be the mathematical expression of the uncertainty relation guessed by Heisenberg. Since then, people have tried various devices to prove the correctness of these two relations. However, no one conducted a careful analysis of Heisenberg’s primary paper. In this work, we point out some serious problems in Heisenberg’s paper and the literature talking about the uncertainty relationships: the physical concepts involved in the uncertainty relations are not clear; one physical concept had more than one explanation, i.e., switching concepts; there has never been measurement experiment to support the relations. The conclusions are that the so-called coordinate–momentum uncertainty relation has never been related to actual measurement and there does not exist a time–energy uncertainty relation.

Frontiers in PhysicsDec 8, 20223 citations

Self-Locating Uncertainty, Subjective Probability and the Everett Interpretation

Fraser, Keith

This paper analyses an attempt to reintroduce the probabilistic predictions of quantum mechanics into the Everett interpretation. An overview of the measurement problem and the Everett interpretation are first given, with particular attention paid to the issue of probability within a deterministic theory. An argument is put forth that observers in an Everettian multiverse generically experience a period of post-measurement uncertainty in regards to their location. It is further argued that this uncertainty allows pre-measurement to observers to act as if they are uncertain about future outcomes. This is then the justification for attaching probabilities to the squared moduli of the wave function. It is also noted that there is an assumption of typicality present in discussions of probability within Everett and some arguments to justify this assumption are considered.

Jan 1, 20140 citations