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Volumn 69, Issue 6, 2004, Pages 24-

Neutrino interferometry in curved spacetime

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EID: 2342417640     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.69.063008     Document Type: Article
Times cited : (51)

References (84)
  • 13
    • 85038993627 scopus 로고    scopus 로고
    • Note here that while there is some similarity between GINI and femtolensing effects, there are at least two effects that suggest that neutrino interference might be, at a pragmatic level, intrinsically more observable than femtolensing. (i) The typical length scale for the impact parameter in gravitational lensing is given by the Einstein radius of the lens. It may happen that the source-lens-observer geometry means that the Einstein radius of a lens is actually “inside” the lens body. There will be many situations, then, where the lensing object is optically thick to photons at the Einstein radius but transparent to neutrinos, meaning that interference effects are, in principle, observable in the former situation but not the latter. (ii) Interference effects can only show up when different lensed images are unresolved (i.e., one’s apparatus must not be able to determine which photon—or neutrino—belongs to which image). But, because of the very different, intrinsic angular resolutions of the microscopic processes involved in neutrino and photon detection, a clearly resolved, astrophysical light source may well be an unresolved source as far as neutrinos are concerned
    • Note here that while there is some similarity between GINI and femtolensing effects, there are at least two effects that suggest that neutrino interference might be, at a pragmatic level, intrinsically more observable than femtolensing. (i) The typical length scale for the impact parameter in gravitational lensing is given by the Einstein radius of the lens. It may happen that the source-lens-observer geometry means that the Einstein radius of a lens is actually “inside” the lens body. There will be many situations, then, where the lensing object is optically thick to photons at the Einstein radius but transparent to neutrinos, meaning that interference effects are, in principle, observable in the former situation but not the latter. (ii) Interference effects can only show up when different lensed images are unresolved (i.e., one’s apparatus must not be able to determine which photon—or neutrino—belongs to which image). But, because of the very different, intrinsic angular resolutions of the microscopic processes involved in neutrino and photon detection, a clearly resolved, astrophysical light source may well be an unresolved source as far as neutrinos are concerned.
  • 23
    • 85038980835 scopus 로고    scopus 로고
    • Data from SN 1987A neutrinos have been used to contain other neutrino properties including neutrino mixing and mass hierarchy, neutrino lifetime, and neutrino magnetic moment: see Ref. 18 for a review
    • Data from SN 1987A neutrinos have been used to contain other neutrino properties including neutrino mixing and mass hierarchy, neutrino lifetime, and neutrino magnetic moment: see Ref. 18 for a review.
  • 42
    • 85039032197 scopus 로고    scopus 로고
    • As an example of this, take the contention on p. 1483 of Alsing et al. in Ref. 34 that the phase of photons propagating through a Schwarzschild metric vanishes to lowest order. This applies only to radially propagating photons and even then should really be thought of as a statement about the action along the classical, null-geodesic, rather than as a claim that the phase—and therefore a potentially measurable phase difference—actually is (close to) zero. Likewise, note that while the statement made in Ref. 38 that “(Formula presented)if one compares two experimental setups with and without gravity with the same curved distance in both cases there is no effect” is true, it implicitly assumes that there is only one path from source to detector that need be considered—and this does not hold in general in the presence of gravity
    • As an example of this, take the contention on p. 1483 of Alsing et al. in Ref. 34 that the phase of photons propagating through a Schwarzschild metric vanishes to lowest order. This applies only to radially propagating photons and even then should really be thought of as a statement about the action along the classical, null-geodesic, rather than as a claim that the phase—and therefore a potentially measurable phase difference—actually is (close to) zero. Likewise, note that while the statement made in Ref. 38 that “(Formula presented)if one compares two experimental setups with and without gravity with the same curved distance in both cases there is no effect” is true, it implicitly assumes that there is only one path from source to detector that need be considered—and this does not hold in general in the presence of gravity.
  • 43
    • 85039005616 scopus 로고    scopus 로고
    • Though it should be stressed here that the authors of Ref. 29 and many of the other papers we have mentioned do obtain the correct result for the phase difference between neutrino mass eigenstates traveling along the same macroscopic paths in curved spacetime (i.e., for flat space neutrino oscillations in the presence of a point mass) because, in such cases, any putative (Formula presented) term will vanish in subtracting one phase from the other (this term being the same for both phases)
    • Though it should be stressed here that the authors of Ref. 29 and many of the other papers we have mentioned do obtain the correct result for the phase difference between neutrino mass eigenstates traveling along the same macroscopic paths in curved spacetime (i.e., for flat space neutrino oscillations in the presence of a point mass) because, in such cases, any putative (Formula presented) term will vanish in subtracting one phase from the other (this term being the same for both phases).
  • 48
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    • C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W.H. Freeman, San Francisco, 1973)
    • C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (W.H. Freeman, San Francisco, 1973).
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    • L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Course of Theoretical Physics, Pergamon International Library of Science, Technology, Engineering and Social Studies, 4th rev. ed. (Pergamon Press, Oxford, 1975)
    • L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, Course of Theoretical Physics, Pergamon International Library of Science, Technology, Engineering and Social Studies, 4th rev. ed. (Pergamon Press, Oxford, 1975).
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    • S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972)
    • S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York, 1972).
  • 54
    • 85038977884 scopus 로고    scopus 로고
    • Note that the (Formula presented) case of this equation can be rederived by, again, considering Fig. 11 while noting, in particular, that the Schwarzschild lens satisfies Eq. (13) for the two classical paths
    • Note that the (Formula presented) case of this equation can be rederived by, again, considering Fig. 11 while noting, in particular, that the Schwarzschild lens satisfies Eq. (13) for the two classical paths.
  • 55
    • 85039030949 scopus 로고    scopus 로고
    • R. M. Crocker and D. Mortlock (unpublished)
    • R. M. Crocker and D. Mortlock (unpublished).
  • 56
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    • P. Schneider, J. Ehlers, and E. E. Falco, Gravitational Lenses (Springer-Verlag, Berlin, 1992), Vol. XIV. (Also Astronomy and Astrophysics Library, 1992.)
    • P. Schneider, J. Ehlers, and E. E. Falco, Gravitational Lenses (Springer-Verlag, Berlin, 1992), Vol. XIV. (Also Astronomy and Astrophysics Library, 1992.)
  • 57
    • 85039013388 scopus 로고    scopus 로고
    • Note that we will assume separability of the phase difference is satisfied in the following discussion
    • Note that we will assume separability of the phase difference is satisfied in the following discussion.
  • 58
    • 85038983401 scopus 로고    scopus 로고
    • This is analogous to the requirement that, for the “usual” equation (obtained in the geometrical optics limit) describing the intensity on a screen in Young’s slit type experiment to be correct, the wavelength of the interfering radiation must not be larger than the slit separation. Otherwise, the equation suggests a (nonphysical) violation of conservation of total intensity in the form of an interference maximum over the whole screen
    • This is analogous to the requirement that, for the “usual” equation (obtained in the geometrical optics limit) describing the intensity on a screen in Young’s slit type experiment to be correct, the wavelength of the interfering radiation must not be larger than the slit separation. Otherwise, the equation suggests a (nonphysical) violation of conservation of total intensity in the form of an interference maximum over the whole screen.
  • 59
    • 85039026081 scopus 로고    scopus 로고
    • See the Appendix of Ref. 32 for a treatment of the direct analog of the coherence length of neutrino oscillations in flat space for curved spacetime, though note that the treatment presented here does not apply for multiple, macroscopic paths
    • See the Appendix of Ref. 32 for a treatment of the direct analog of the coherence length of neutrino oscillations in flat space for curved spacetime, though note that the treatment presented here does not apply for multiple, macroscopic paths.
  • 61
    • 85039024394 scopus 로고    scopus 로고
    • C. W. Kim and A. Pevsner, Neutrinos in Physics and Astrophysics, Contemporary Concepts in Physics, Vol. 8 (Harwood, Chur, Switzerland, 1993)
    • C. W. Kim and A. Pevsner, Neutrinos in Physics and Astrophysics, Contemporary Concepts in Physics, Vol. 8 (Harwood, Chur, Switzerland, 1993).
  • 62
    • 85039012306 scopus 로고    scopus 로고
    • Note that we ignore here the contribution of the detection process to the effective wave packet size that can, in principle, act to restore coherence via broadening the effective wave packet width through accurate energy/momentum measurement: see Ref. 84 for more details and also Ref. 46 for a rigorous, quantum-field-theoretic treatment of neutrino coherence length
    • Note that we ignore here the contribution of the detection process to the effective wave packet size that can, in principle, act to restore coherence via broadening the effective wave packet width through accurate energy/momentum measurement: see Ref. 84 for more details and also Ref. 46 for a rigorous, quantum-field-theoretic treatment of neutrino coherence length.
  • 66
    • 85039028326 scopus 로고    scopus 로고
    • et al., presented at the XXth Int. Conf. on Neutrino Physics and Astrophysics, Munich (2002)
    • Super-Kamiokande Collaboration, T. Nakaya et al., presented at the XXth Int. Conf. on Neutrino Physics and Astrophysics, Munich (2002).
  • 70
    • 85038984558 scopus 로고    scopus 로고
    • We take the largest possible value for this quantity by assuming the scale of the smallest experimentally determined (Formula presented) i.e., the solar mass splitting at (Formula presented)
    • We take the largest possible value for this quantity by assuming the scale of the smallest experimentally determined (Formula presented) i.e., the solar mass splitting at (Formula presented)
  • 71
    • 85038977496 scopus 로고    scopus 로고
    • Certainly, in their numerical study of femtolensing with a disk source, Peterson and Falk 6 found that, allowing for a realistic deviation from smoothness in the source function—which describes the intensity across the disk of the source—interference effects were visible with a source size significantly larger than the Einstein ring. We have not allowed for this (potential) effect for a supernova neutrino source
    • Certainly, in their numerical study of femtolensing with a disk source, Peterson and Falk 6 found that, allowing for a realistic deviation from smoothness in the source function—which describes the intensity across the disk of the source—interference effects were visible with a source size significantly larger than the Einstein ring. We have not allowed for this (potential) effect for a supernova neutrino source.
  • 76
    • 85038981587 scopus 로고    scopus 로고
    • An experimental analog of interference in such a situation would be Young’s double slit apparatus where one beam of light is reflected in a mirror. This produces, of course, a central minimum
    • An experimental analog of interference in such a situation would be Young’s double slit apparatus where one beam of light is reflected in a mirror. This produces, of course, a central minimum.
  • 83
    • 85038996687 scopus 로고    scopus 로고
    • Note that here we are ignoring the energy dependence of the velocities of the different plane wave components of each wave packet so that our calculation makes no account of dispersive effects which, in general, extend the coherence length; see 61
    • Note that here we are ignoring the energy dependence of the velocities of the different plane wave components of each wave packet so that our calculation makes no account of dispersive effects which, in general, extend the coherence length; see 61.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.