33 research outputs found
Jacobi equations and particle accelerator beam dynamics
A geometric formulation of the linear beam dynamics in accelerator physics is
presented. In particular, it is proved that the linear transverse and
longitudinal dynamics can be interpret geometrically as an approximation to the
Jacobi equation of an affine averaged Lorentz connection. We introduce a
specific notion reference trajectory as integral curves of the main velocity
vector field. A perturbation caused by the statistical nature of the bunch of
particles is considered.Comment: 16 page
Quantum Systems as results of Geometric Evolutions
In the framework of deterministic finslerian models, a mechanism producing
dissipative dynamics at the Planck scale is introduced. It is based on a
geometric evolution from Finsler to Riemann structures defined in .
Quantum states are generated and interpreted as equivalence classes, composed
by the configurations that evolve through an internal dynamics, to the same
final state. The existence of an hermitian scalar product in an associated
linear space is discussed and related with the quantum pre-Hilbert space. This
hermitian product emerges from geometric and statistical considerations. Our
scheme recovers the main ingredients of the usual Quantum Mechanics. Several
testable consequences of our scheme are discussed and compared with usual
Quantum Mechanics. A tentative solution of the cosmological constant problem is
proposed, as well as a mechanism for the absence of quantum interferences at
classical scales.Comment: paper withdraw
A Finslerian version of 't Hooft Deterministic Quantum Models
Using the Finsler structure living in the phase space associated to the
tangent bundle of the configuration manifold, deterministic models at the
Planck scale are obtained. The Hamiltonian function are constructed directly
from the geometric data and some assumptions concerning time inversion
symmetry. The existence of a maximal acceleration and speed is proved for
Finslerian deterministic models. We investigate the spontaneous symmetry
breaking of the orthogonal symmetry SO(6N) of the Hamiltonian of a
deterministic system. This symmetry break implies the non-validity of the
argument used to obtain Bell's inequalities for spin states. It is introduced
and motivated in the context of Randers spaces an example of simple 't Hooft
model with interactions.Comment: 25 pages; no figures. String discussion deleted. Some minor change
The maximal acceleration, Extended Relativistic Dynamics and Doppler type shift for an accelerated source
Based on the generalized principle of relativity and the ensuing symmetry, we
have shown that there are only two possible types of transformations between
uniformly accelerated systems. The first allowable type of transformation holds
if and only if the Clock Hypothesis is true. If the Clock Hypothesis is not
true, the transformation is of Lorentz-type and implies the existence of a
universal maximal acceleration .
We present an extension of relativistic dynamics for which all admissible
solutions will have have a speed bounded by the speed of light and the
acceleration bounded by . An additional Doppler type shift for an
accelerated source is predicted. The formulas for such shift are the same as
for the usual Doppler shift with replaced by .
The W. K\"{u}ndig experiment of measurement of the transverse Doppler shift
in an accelerated system was also exposed to a longtitudal shift due to the
acceleration. This experiment, as reanalyzed by Kholmetskii et al, shows that
the Clock Hypothesis is not valid. Based on the results of this experiment, we
predict that the value of the maximal acceleration is of the order
. Moreover, our analysis provides a way to measure experimentally
the maximal acceleration with existing technology.Comment: 10 pages, 1 figur
Lower Neutrino Mass Bound from SN1987A Data and Quantum Geometry
A lower bound on the light neutrino mass is derived in the framework
of a geometrical interpretation of quantum mechanics. Using this model and the
time of flight delay data for neutrinos coming from SN1987A, we find that the
neutrino masses are bounded from below by eV, in
agreement with the upper bound
eV currently available. When the model is applied to photons with effective
mass, we obtain a lower limit on the electron density in intergalactic space
that is compatible with recent baryon density measurements.Comment: 22 pages, 3 figure