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Free fall in KvN mechanics and Einstein's principle of equivalence. / Sen, Abhijit; Dhasmana, Shailesh; Silagadze, Zurab K.
в: Annals of Physics, Том 422, 168302, 01.11.2020.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Free fall in KvN mechanics and Einstein's principle of equivalence
AU - Sen, Abhijit
AU - Dhasmana, Shailesh
AU - Silagadze, Zurab K.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - The implementation of Einstein's principle of equivalence in Koopman–von Neumann (KvN) mechanics is discussed. The implementation is very similar to the implementation of this principle in quantum mechanics. This is not surprising, because KvN mechanics provides a Hilbert space formulation of classical mechanics that is very similar to the quantum mechanical formalism. Both in KvN mechanics and quantum mechanics, a propagator in a homogeneous gravitational field is simply related with a free propagator. As a result, the wave function in a homogeneous gravitational field in a freely falling reference frame differs from the free wave function only in phase. Fisher information, which quantifies our ability to estimate mass from coordinate measurements, does not depend on the magnitude of the homogeneous gravitational field, and this fact constitutes the formulation of Einstein's principle of equivalence, which is valid both in quantum mechanics and KvN mechanics.
AB - The implementation of Einstein's principle of equivalence in Koopman–von Neumann (KvN) mechanics is discussed. The implementation is very similar to the implementation of this principle in quantum mechanics. This is not surprising, because KvN mechanics provides a Hilbert space formulation of classical mechanics that is very similar to the quantum mechanical formalism. Both in KvN mechanics and quantum mechanics, a propagator in a homogeneous gravitational field is simply related with a free propagator. As a result, the wave function in a homogeneous gravitational field in a freely falling reference frame differs from the free wave function only in phase. Fisher information, which quantifies our ability to estimate mass from coordinate measurements, does not depend on the magnitude of the homogeneous gravitational field, and this fact constitutes the formulation of Einstein's principle of equivalence, which is valid both in quantum mechanics and KvN mechanics.
KW - SCHRODINGER-EQUATION
KW - QUANTUM-MECHANICS
KW - PARTICLE
KW - SYSTEMS
KW - GALILEO
KW - MOTION
KW - INTERFERENCE
KW - GEOMETRY
KW - GRAVITY
KW - TIME
UR - http://www.scopus.com/inward/record.url?scp=85090561428&partnerID=8YFLogxK
U2 - 10.1016/j.aop.2020.168302
DO - 10.1016/j.aop.2020.168302
M3 - Article
AN - SCOPUS:85090561428
VL - 422
JO - Annals of Physics
JF - Annals of Physics
SN - 0003-4916
M1 - 168302
ER -
ID: 25301440