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arXiv:0907.3554 · Physical Review C

Why a splitting in the final state cannot explain the “GSI oscillations” measured at the GSI Experimental Storage Ring

Alexander Merle

Published Nov 30, 2009• 22 citations
arXivHTMLPDF

Abstract

In this article, I provide a pedagogical discussion of the GSI anomaly. Using two different formulations, namely the intuitive quantum-field-theory language of the second quantized picture as well as the language of amplitudes, I clear up the analogies and differences between the GSI anomaly and other processes (the double-slit experiment using photons, ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ scattering, and charged-pion decay). In both formulations, the conclusion is reached that the decay rate measured at GSI cannot oscillate if only standard model physics is involved and the initial hydrogen-like ion is no coherent superposition of more than one state (in case there is no new, yet unknown, mechanism at work). Furthermore, a discussion of the quantum beat phenomenon will be given, which is often assumed to be able to cause the observed oscillations. This is, however, not possible for a splitting in the final state only.

DOI
10.1103/physrevc.80.054616

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In this article, I provide a pedagogical discussion of the GSI anomaly. Using two different formulations, namely the intuitive quantum-field-theory language of the second quantized picture as well as the language of amplitudes, I clear up the analogies and differences between the GSI anomaly and other processes (the double-slit experiment using photons, e+e\ensuremath−\ensuremath→\ensuremathμ+\ensuremathμ\ensuremath−{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}e+e\ensuremath−\ensuremath→\ensuremathμ+\ensuremathμ\ensuremath− scattering, and charged-pion decay). In both formulations, the conclusion is reached that the decay rate measured at GSI cannot oscillate if only standard model physics is involved and the initial hydrogen-like ion is no coherent superposition of more than one state (in case there is no new, yet unknown, mechanism at work). Furthermore, a discussion of the quantum beat phenomenon will be given, which is often assumed to be able to cause the observed oscillations. This is, however, not possible for a splitting in the final state only.
The wave-particle duality mystery, present in the language of quantum physics since its historical origins 100 years ago, has no real correspondence with the actual behaviour of nature when it is observed. The dilemma of the so-called “single particle interference” experiments is not between particles versus waves: the interference in quantum physics is between probability amplitudes for different untagged alternatives in a definite transition between states. This article shows that the same conceptual basis is involved in a plethora of “two-state systems” as a consequence of the linear superposition principle, no matter whether the observables refer to either spatial or internal properties. Several examples, from the Young double-slit interference experiments to neutrino flavour oscillation experiments, are discussed in a common interpretation language.
Darmstadt ννν oscillations in decay of radioactive ion can only come from initial state wave function. Causality forbids any influence on transition probability by detection of ννν or final state interference after decay. Energy-time uncertainty allows two initial state components with different energies to decay into combination of two orthogonal states with same energy, different momenta and different ννν masses. Final amplitudes completely separated at long times have broadened energy spectra overlapping at short times. Their interference produces oscillations between Dicke superradiant and subradiant states having different transition probabilities. Repeated monitoring by interactions with laboratory environment at regular time intervals and same space point in laboratory collapses wave function and destroys entanglement. First-order time dependent perturbation theory gives probability for initial state decay during small interval between two monitoring events. Experiment measures momentum difference between two contributing coherent initial states and obtains information about ννν masses without detecting ννν. Simple model relates observed oscillation to squared ννν mass difference and gives value differing by less than factor of three from values calculated from KAMLAND experiment. Monitoring simply expressed in laboratory frame not easily transformed to other frames and missed in Lorentz-covariant descriptions based on relativistic quantum field theory.
We discuss deviations from the exponential decay law which occur when going beyond the Breit-Wigner distribution for an unstable state.In particular, we concentrate on an oscillating behavior, remisiscent of the Rabi-oscillations, in the short-time region.We propose that these oscillations can explain the socalled GSI anomaly, which measured superimposed oscillations on top of the exponential law for hydrogen-like nuclides decaying via electron-capture.Moreover, we discuss the possibility that the deviations from the Breit-Wigner in the case of the GSI anomaly are (predominantely) caused by the interaction of the unstable state with the measurement apparatus.The consequences of this scenario, such as the non-observation of oscillations in an analogous experiment perfromed at Berkley, are investigated.
The history of the double-slit experiment (DSE) is more than two centuries old. Its results played a significant role in the discovery of the wave nature of light, and then formed the basis for important provisions of quantum mechanics. However, the results are still difficult to interpret unequivocally. In particular, they have been treated recently even outside the framework of the universally accepted, experimentally verifiable science. For example, the results were tried to connect with the influence on the experiment of the experimenter’s consciousness or with the influence of worlds which exist parallel to our world. At the same time, indeed, the interpretation of the results is extremely difficult and the situation with the understanding of these results, especially in light of recent researches, is becoming more and more complicated. The purpose of our study is to analyze the results of several recent experiments and to introduce a new understanding of them taking into account the possibility of resonant (synchronous) interaction of all physical fields that influence the process of the experiment. We believe that it is necessary to take into account the nonlinear nature of the interacting fields where extreme particle-waves can exist.
We study the deviations from the usual exponential decay law for quantum mechanical systems. We show that simple and physically motivated deviations from the Breit-Wigner energy distribution of the unstable state are sufficient to generate peculiar deviations from the exponential decay law. Denoting with p(t)p(t)p(t) the survival probability, its derivative h(t)h(t)h(t) shows typically an oscillating behavior on top of the usual exponential function. We argue that this can be a viable explanation of the observed experimental results at GSI Darmstadt, where the function h(t)h(t)h(t) has been experimentally measured for electron capture decays of Hydrogen-like ions. Moreover, if our interpretation is correct, we predict that by measuring h(t)h(t)h(t) at times close to the initial one, the number of decays per second rapidly drops to zero.