Abstract
Inspired by recently published researches, we present two protocols for setting an upper limit to the claimed variation of hbar upon the position. The protocols, both within today state of art, involve the use of two delayed laser pulses driving an atom. The distinct positions of the laboratory, due to the Earth motion, affects hbar and hence the atomic dynamics. The first protocol measures the difference in population of the atomic ground state while the second one the red-shift of the harmonics emitted by the atom in the two moments of the experiment. The protocols improve the reported upper limit of varDelta hbar /hbar . The theory shows that hbar (varvec{r}) induces a chaotic evolution to the atom. This form of Chaos is generated by a variation of a physical parameter and is one example of Parametric Chaos.
Highlights
At the very base of any physical theory phenomenological numerical parameters are found; generally assumed space-time independent, they are the fundamental constants
Inspired by recently published researches, we present two protocols for setting an upper limit to the claimed variation of hupon the position
The observations are inhomogeneous and need to be attentively calibrated; new experiments must be designed with the alone aim of observing a variation of hor of setting an upper limit to Δh /h
Summary
At the very base of any physical theory phenomenological numerical parameters are found; generally assumed space-time independent, they are the fundamental constants. The constants c, hand e represent limiting quantities: they are the natural units for velocity, angular momentum and electric charge Their value depends on the units and on their operational definition. The dual role of the potential energy U (r) is note worth: it acts as the potential energy inside H0, and as a time dependent perturbation in the full Hamiltonian In this way without interaction the form of the plane wave is not affected by the change of h. With R and ωE = 2π/86400 sec−1 the laboratory distance from the polar axis and Earth angular velocity around it This is the simplest way to describe a dipolar spatial dependence of hwith respect to some fixed direction and has been suggested in [6] to model a potential spatial dependence of α.
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