Classical Mechanics (Vol. I and Vol. II)

Desloge, Edward A.; Rand, Richard H.

doi:10.1115/1.3167080

Cited by 17 publications

(28 citation statements)

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“…The velocity difference depends on energy slightly, by splitting the events into two groups with energies above or below 20 Gev, the velocity difference is given by δc ν = (2.74 ± 0.74 ± 0.30) × 10 −5 For E = 42.9GeV (20) δc ν = (2.16 ± 0.76 ± 0.36) × 10 −5 For E = 13.9GeV (21) The OPERA experiment is consistent with earlier experiments, as summarized in Table 1 [23], [25].…”

Section: Neutrinos Velocity From Ds-srmentioning

confidence: 99%

Superluminal Neutrinos From Special Relativity With De Sitter Spacetime Symmetry

et al. 2012

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We explore the recent OPERA experiment of superluminal neutrinos in the framework of Special Relativity with de Sitter space-time symmetry (dS-SR). According to Einstein a photon is treated as a massless particle in the framework of Special Relativity. In Special Relativity (SR) we have the universal parameter c, the photon velocity c photon and the phase velocity of a light wave in vacuum c wave = λν. Due to the null experiments of Michelson-Morley we have c = c wave . The parameter c photon is determined by the Noether charges corresponding to the space-time symmetries of SR. In Einstein's Special Relativity (E-SR) we have c = c photon . In dS-SR, i.e. the Special Relativity with SO(4, 1) de Sitter space-time symmetry, we have c photon > c. In this paper, the OPERA datum are examined in the framework of dS-SR. We show that OPREA anomaly is in agreement with the prediction of dS-SR with R ≃ 1.95×10 12 l.y. Based on the p-E relation of dS-SR, we also prove that the Cohen and Glashow's argument of possible superluminal neutrino's Cherenkov-like radiation is forbidden. We conclude that OPERA and ICARUS results are consistent and they are explained in the dS-SR framework.

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Section: Neutrinos Velocity From Ds-srmentioning

confidence: 99%

Superluminal Neutrinos From Special Relativity With De Sitter Spacetime Symmetry

et al. 2012

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“…The equations of motion which can be obtained from Euler-Lagrange equations or Hamilton equations with (15)(16), besides the equations y i =ẋ i , arė…”

Section: First Order Lagrangian Hamiltonian Formalism and The Exmentioning

confidence: 99%

“…We can also get the Noether charges by the Noether theorem [15] corresponding to the Lagrangian (14). When the time t is fixed, the NH transformations become…”

Section: First Order Lagrangian Hamiltonian Formalism and The Exmentioning

confidence: 99%

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Acceleration-extended Newton–Hooke symmetry and its dynamical realization

Liu

Tian

2008

Physics Letters A

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Newton-Hooke group is the nonrelativistic limit of de Sitter (anti-de Sitter) group, which can be enlarged with transformations that describe constant acceleration. We consider a higher order Lagrangian that is quasi-invariant under the acceleration-extended Newton-Hooke symmetry, and obtain the Schrödinger equation quantizing the Hamiltonian corresponding to its first order form.We show that the Schrödinger equation is invariant under the acceleration-extended Newton-Hooke transformations. We also discuss briefly the exotic conformal Newton-Hooke symmetry in 2 + 1 dimension.

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“…Physical laws may be expressed by variational principle not only by differential formulas, in fact, differential formulas can be derived from variational principle [1], and there are the variational principles of differential and integral styles [2,3]. Hilbert outlined 23 major mathematical problems to be studied in the coming century, variational problem is one of the problems.…”

Section: Introductionmentioning

confidence: 99%

Unified Expressions of All Integral Variational Principles

2006

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In terms of the quantitative causal principle, this paper obtains a general variational principle, gives unified expressions of the general, Hamilton, Voss, Hölder, Maupertuis-Lagrange variational principles of integral style, the invariant quantities of the general, Voss, Hölder, Maupertuis-Lagrange variational principles are given, finally the Noether conservation charges of the general, Voss, Hölder, Maupertuis-Lagrange variational principles are deduced, and the intrinsic relations among the invariant quantities and the Noether conservation charges of the all integral variational principles are achieved.

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Classical Mechanics (Vol. I and Vol. II)

Cited by 17 publications

References 0 publications

Superluminal Neutrinos From Special Relativity With De Sitter Spacetime Symmetry

Superluminal Neutrinos From Special Relativity With De Sitter Spacetime Symmetry

Acceleration-extended Newton–Hooke symmetry and its dynamical realization

Unified Expressions of All Integral Variational Principles

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