a second-order Zeeman shift of the clock transition frequency
https://arxiv.org/ftp/arxiv/papers/1612/1612.07469.pdf
to excite the corresponding two-photon transitions. To produce a large
detuning from the excited state F’=2, the input laser was red
shifted to 200 MHz by a double-pass optical path using an
acoustic optical modulator (AO
all possible electric-dipole
transitions with ∆m=0, ±1, ±2 will occur
https://apps.dtic.mil/sti/pdfs/ADA385576.pdf
Basil J. Hiley - Wigner Institute lecture on noncommutativity
A single particle has TWO positions in configuration space...
In the imaginary part of the complex number there is the Osmotic Momentum - "in other words the particle is embedded in some kind of quantum fluid"
This is what people of the Wigner function do.
https://bingweb.binghamton.edu/~suzuki/QM_Graduate/Wigner_representation.pdf
Wigner distribution function in the phase space is a special representation of the density matrix. It provides a third, alternative, formulation of quantum mechanics, independent of the conventional Hilbert space or path integral formulations.
https://nanohub.org/resources/21741/download/Wigner-Formalism-Sellier-L1.pdf
The Moyal Algebra shows you that when you do this transform from the x to the p you're actually hologramming the whole space. So every point in X space is hologrammed a little bit to over point in P space and vice versa. It's got NOTHING to do with the uncertainty principle! We just interpret as the uncertainty principle. It's actually changing the whole structure that underlies quantum mechanics. What this means is that Quantum processes are NOT going on in space and time. It's going on in a hidden way...some hidden variables, in the sense of the old fashion hidden variables: We've got an implicate order which is described by the noncommutative functions, but we can only project out explicit manifolds and we can't project them out all together. ...So we can not stand outside of physics and like God say, "That is what is going on." We're actually involved in the order and we see these...shadow manifolds...(a Polish mathematician called them shadow manifolds). The classical world emerges when you find commutativity and the two pictures come out the same. The classical world emerges from the quantum world and not the other way around. One of the big problems is that people try to start with the classical world and put in quantum mechanics.
Basil J. Hiley
these localized frequency events are not pure tones but packets of close frequencieshttps://www.di.ens.fr/~mallat/College/Chap4-Time-Frequency.pdf
https://dsp.stackexchange.com/questions/42867/uncertainty-principle-duration-bandwidth-principle
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