Interferometers and decoherence matrices

Han, D.; Kim, Y. S.; Noz, Marilyn E.

doi:10.1103/physreve.61.5907

Cited by 36 publications

(63 citation statements)

References 20 publications

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“…We thus conclude that it is hidden in Feynman's rest of the universe [6,7], which is well defined in terms of the twomode squeezed state. Since this variable is hidden, it causes an increase in entropy and uncertainty.…”

Section: Proton and Electronmentioning

confidence: 88%

“…Finally, in Sec. 5, we illustrate Feynman's rest of universe using the coupled harmonic oscillators and two-mode squeezed states [6,7]. We then show that the time-separation variable can be interpreted as one of the oscillator variables not observed.…”

Section: Proton and Electronmentioning

confidence: 99%

“…On the other hand, the present form of quantum mechanics does not include this time-separation variable. The best way we can do at the present time is to treat this time-separation as a variable in Feynman's rest of the universe [7]. In his book on statistical mechanics [6]…”

Section: Hidden In Feynman's Rest Of the Universementioning

confidence: 99%

“…To motivate the use of density matrices, let us see what happens when we include the part of the universe outside the system. This abstract statement can be studied in terms of two coupled oscillators [7], and also in terms of two-mode squeezed states [5]. The failure to include what happens outside the system results in an increase of entropy.…”

Section: Feynman Statesmentioning

confidence: 99%

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Time separation as a hidden variable to the Copenhagen school of quantum mechanics

Kim¹,

Noz²,

Khrenniko³

et al. 2011

AIP Conference Proceedings

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The Bohr radius is a space-like separation between the proton and electron in the hydrogen atom. According to the Copenhagen school of quantum mechanics, the proton is sitting in the absolute Lorentz frame. If this hydrogen atom is observed from a different Lorentz frame, there is a time-like separation linearly mixed with the Bohr radius. Indeed, the time-separation is one of the essential variables in high-energy hadronic physics where the hadron is a bound state of the quarks, while thoroughly hidden in the present form of quantum mechanics. It will be concluded that this variable is hidden in Feynman's rest of the universe. It is noted first that Feynman's Lorentz-invariant differential equation for the bound-state quarks has a set of solutions which describe all essential features of hadronic physics. These solutions explicitly depend on the time separation between the quarks. This set also forms the mathematical basis for two-mode squeezed states in quantum optics, where both photons are observable, but one of them can be treated a variable hidden in the rest of the universe. The physics of this two-mode state can then be translated into the time-separation variable in the quark model. As in the case of the un-observed photon, the hidden time-separation variable manifests itself as an increase in entropy and uncertainty.

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Section: Proton and Electronmentioning

confidence: 88%

Section: Proton and Electronmentioning

confidence: 99%

Section: Hidden In Feynman's Rest Of the Universementioning

confidence: 99%

Section: Feynman Statesmentioning

confidence: 99%

See 2 more Smart Citations

Time separation as a hidden variable to the Copenhagen school of quantum mechanics

Kim¹,

Noz²,

Khrenniko³

et al. 2011

AIP Conference Proceedings

Self Cite

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show abstract

“…Well known, especially in the past decade, the group theory of SL͑2,c͒ and of some of its subgroups was extensively applied in various fields of classical and quantum optics, e.g., ray optics, 40 beam propagation through firstorder systems, 41 analysis of the states of light with orbital angular momentum, 42 polarization optics, 43 multilayer optics, 44,45 interferometry, 46 and coherent and squeezed states of light. 47 Bearing in mind that SL͑2,c͒ is locally isomorphic to the six-parameter Lorentz group SO͑3,1͒, a physical system that can be analyzed in terms of SL͑2,c͒ language can be equally explained in the language of the Lorentz group.…”

Section: Discussionmentioning

confidence: 99%

Pauli algebraic forms of normal and nonnormal operators

Tudor

Gheondea

2007

J. Opt. Soc. Am. A

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A unified treatment of the Pauli algebraic forms of the linear operators defined on a unitary linear space of two dimensions over the field of complex numbers C 1 is given. The Pauli expansions of the normal and nonnormal operators, unitary and Hermitian operators, orthogonal projectors, and symmetries are deduced in this frame. A geometrical interpretation of these Pauli algebraical results is given. With each operator, one can associate a generally complex vector, its Pauli axis. This is a natural generalization of the well-known Poincaré axis of some normal operators. A geometric criterion of distinction between the normal and nonnormal operators by means of this vector is established. The results are exemplified by the Pauli representations of the normal and nonnormal operators corresponding to some widespread composite polarization devices.

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Wigner's spins, Feynman's partons, and their common ground

Kim

2002

Czech J Phys

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The connection between spin and symmetry was established by Wigner in his 1939 paper on the Poincaré group. For a massive particle at rest, the little group is O(3) from which the concept of spin emerges. The little group for a massless particle is isomorphic to the two-dimensional Euclidean group with one rotational and two translational degrees of freedom. The rotational degree corresponds to the helicity, and the translational degrees to the gauge degree of freedom. The question then is whether these two different symmetries can be united. Another hard-pressing problem is Feynman's parton picture which is valid only for hadrons moving with speed close to that of light. While the hadron at rest is believed to be a bound state of quarks, the question arises whether the parton picture is a Lorentz-boosted bound state of quarks. We study these problems within Einstein's framework in which the energy-momentum relations for slow particles and fast particles are two different manifestations one covariant entity.This note is based on the lectures delivered at the Advanced Study Institute on Symmetries and Spin (Praha, Czech Republic, July 2001).

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Interferometers and decoherence matrices

Cited by 36 publications

References 20 publications

Time separation as a hidden variable to the Copenhagen school of quantum mechanics

Time separation as a hidden variable to the Copenhagen school of quantum mechanics

Pauli algebraic forms of normal and nonnormal operators

Wigner's spins, Feynman's partons, and their common ground

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