Gravitationally Induced Neutrino–Oscillation Phases

In this essay, we introduce a new effect of gravitationally induced quantum mechanical phases in neutrino oscillations. These phases arise from an hitherto unexplored interplay of gravitation and the principle of the linear superposition of quantum mechanics. In the neighborhood of a 1.4 solar–mass neutron star, gravitationally induced quantum mechanical phases are roughly 20% of their kinematical counterparts. When this information is coupled with the mass square differences implied by the existing neutrino–oscillation data we find that the new effect may have profound consequences for type-II supernova evolution. Neutrinos [1,2] play a profound role on almost all length scales. These scales range from the evolution of the nuclei to the evolution of biological structures [3], to the evolution of the stars, the galaxies, and the universe [4,5]. The detection [6] of an ancient neutrino burst on February 23, 1987 provided a dramatic confirmation of the essential elements of the physics of type-II supernovae [7] and placed an upper limit of about 10 eV on the mass of the electron neutrino [8]. The detection of solar neutrinos in terrestrial detectors provides a similarly convincing confirmation of our understanding of the solar evolution [9]. These important observational triumphs mark the beginning of a new era: The era of neutrino astronomy. The observations on the solar neutrinos have already given birth to the more controlled accelerator– and reactor–based neutrino oscillation experiments. 1 E-mail address: [email protected] . 2 E-mail address: [email protected] . Preprint submitted to Elsevier Preprint 1 March 2008 G en . R el . a nd G ra v. 2 8 (1 99 6) 1 16 111 70 For decades the solar neutrino anomaly [10] has indicated that the neutrino flavor eigenstates may be a linear superposition of mass eigenstates [11]. This view has been further strengthened by the data on atmospheric neutrinos [12], and most recently by the observation of excess νe observed at the Liquid Scintillator Neutrino Detector (LSND) Neutrino Oscillation Experiment (NOE) at LAMPF [13]. The excess events observed at LSND NOE have been tentatively interpreted as νμ → νe oscillations [13]. At the present time, (a) the question of neutrino masses [14], (b) the relation of the neutrinos to the spacetime symmetries as manifested in Dirac [15], or Majorana [16–18], or other fundamental constructs appropriate to the neutral particles [19], (c) the question of CP violation in the leptonic sector [21], and (d) other related issues that extend the physics beyond the standard model [22], are being probed with intense theoretical and experimental vigor. Gravitation plays no direct role on neutrino oscillations in the existing literature. 3 In this essay we shall introduce the notion of gravitationally induced quantum mechanical neutrino–oscillation phases and discuss the possibility of their observation for type-II supernova. A bit of history is necessary at this point. In one of the classic experiments of physics, Colella, Overhauser, and Werner (COW) established that quantum mechanics and gravitation, despite the well–known conceptual problems, behave in a manner expected for any other interaction [26]. Given the fact that the experiment involved thermal neutrons (non-relativistic quantum realm) and the Earth’s gravitational field (weak gravity), this may not be too unexpected. Nevertheless, theoretical investigation of this elegant experiment provides a deep understanding of gravitation in the context of quantum mechanics [27]. From a formal point of view the COW experiment studies the effect of gravitation on the quantum mechanical evolution of a single–mass eigenstate. For neutrinos, when we extend the COW–like considerations to the linear superposition of mass eigenstates, a new gravitationally induced quantum mechanical effect emerges. Despite the similarities between the COW effect and the new effect introduced here, there are important conceptual differences between the two effects. These differences shall also be enumerated at the appropriate place in this essay. In a certain sense (to become precise below), the two effects shall be seen to be complementary. Let us assume that in the “creation region,” Rc, located at ~rc, 4 a weak 3 However, see (a) Ref. [23], where Violation of Equivalence Principle (VEP) in the context of neutrino oscillation experiments is considered; (b) the work of Goldman et al. on “Kaons, Quantum Mechanics, and Gravity” in Ref. [24] (Ref. [24] also contains references to many classic works on the subject); and (c) the work of J. Anandan on the gravitational phase operator [25]. 4 The creation region Rc is assumed fixed in the global coordinate system.