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Physical Review Letters

Is CP Invariance Violated?

Dragutin Lalović

Published Dec 9, 1968• 4 citations
Publisher

Abstract

The well-known fact that the existing quantum mechanical formalism is inconsistent with the energy-time uncertainty-relation postulate is shown to play a crucial role in the logical deduction leading to the conclusion that $\mathrm{CP}$ invariance is violated in some neutral kaon decays. It is therefore argued that if one believes in the existence of the energy-time uncertainty relation, then one has to accept that none of the existing experimental facts can unambiguously be interpreted as evidence against the universal validity of $\mathrm{CP}$ invariance.

DOI
10.1103/physrevlett.21.1662

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The well-known fact that the existing quantum mechanical formalism is inconsistent with the energy-time uncertainty-relation postulate is shown to play a crucial role in the logical deduction leading to the conclusion that CP\mathrm{CP}CP invariance is violated in some neutral kaon decays. It is therefore argued that if one believes in the existence of the energy-time uncertainty relation, then one has to accept that none of the existing experimental facts can unambiguously be interpreted as evidence against the universal validity of CP\mathrm{CP}CP invariance.
We point out that decoherence parameters in the correlated two neutral kaon system breaks the transformation invariance of basis and their magnitude are stringently limited by the experimentally measured magnitudes of CP violation and of the strangeness non conserving ΔS=±2ΔS = \pm 2ΔS=±2 transitions.
It is shown that the results of CP and T violation experiments can be interpreted using a very general framework that does not require a Hilbert space of states or linear operators to represent the symmetries or dynamics. Analysis within this general framework brings out the aspects of quantum mechanics that are essential for this interpretation. More importantly, should quantum mechanics be eventually replaced by a new paradigm, this framework could \emph{still} be used to establish violation of CP and T invariance from the already known experimental results. This work arose as a `formal response' to a talk "Three Merry Roads to T-Violation" by Dr. Bryan Roberts [1]. Both talks were given at a "Workshop on Cosmology and Time" held at Penn State in April 2013, which brought together physicists and philosophers of science.
A review of the experimental status of CPT invariance leads to two conclusions: (i) There is no hint of a CPT violation in the data. (ii) CPT invariance has not been probed with a quantitative sensitivity that greatly exceeds that achieved in studies of CP symmetry. I sketch some models where CPT violations could be implemented. Yet it is hard to see how those types of ansatz could generate observable effects in the transitions of neutral K mesons. On the other hand the quite special quantum aspects of the reaction φ → KL KS can be harnessed to probe quantum mechanics in novel ways by analyzing EPR like correlations of a kind that have not been studied before. Some comparisons are made with Weinberg's recent formulation of non-linear (though homogenous) quantum mechanics and with generalizations that can be obtained from Bohm's interpretation of quantum mechanics.
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.