TY - JOUR

T1 - Time in the quantum theory and the uncertainty relation for time and energy

AU - Aharonov, Y.

AU - Bohm, D.

PY - 1961

Y1 - 1961

N2 - Because time does not appear in Schrödinger'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, Δt, there must be a minimum uncertainty in the transfer of energy to the observed system, given by Δ(E′-E)>~hΔt. 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.

AB - Because time does not appear in Schrödinger'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, Δt, there must be a minimum uncertainty in the transfer of energy to the observed system, given by Δ(E′-E)>~hΔt. 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.

UR - http://www.scopus.com/inward/record.url?scp=36149020850&partnerID=8YFLogxK

U2 - 10.1103/PhysRev.122.1649

DO - 10.1103/PhysRev.122.1649

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AN - SCOPUS:36149020850

SN - 0031-899X

VL - 122

SP - 1649

EP - 1658

JO - Physical Review

JF - Physical Review

IS - 5

ER -