Lorentz-squeezed hadrons and hadronic temperature

American Journal of Physics

1999

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Coupled harmonic oscillators occupy an important place in physics teaching. It is shown that they can be used for illustrating an increase in entropy caused by limitations in measurement. In the system of coupled oscillators, it is possible to make the measurement on one oscillator while averaging over the degrees of freedom of the other oscillator without measuring them. It is shown that such a calculation would yield an increased entropy in the observable oscillator. This example provides a clarification of Feynman's rest of the universe.

Section: Physical Modelsmentioning

confidence: 99%

Illustrative example of Feynman’s rest of the universe

Han¹,

American Journal of Physics

1999

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“…In the meantime, let us study what happens when the matrix G 3 is introduced into the set of matrices given in Eq. (20) and Eq. (21).…”

Section: Non-canonical Transformations In Classical Mechanicsmentioning

confidence: 99%

“…This Wigner function is of the form given in Eq. (32) for the thermal excitation, if we identify the squeeze parameter η as [20] cosh(2η) = 1 tanh(1/2T ) .…”

Section: Canonical Approachmentioning

confidence: 99%

Dirac Matrices and Feynman’s Rest of the Universe

2012

Symmetry

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There are two sets of four-by-four matrices introduced by Dirac. The first set consists of fifteen Majorana matrices derivable from his four γ matrices. These fifteen matrices can also serve as the generators of the group SL(4, r). The second set consists of ten generators of the Sp(4) group which Dirac derived from two coupled harmonic oscillators. It is shown possible to extend the symmetry of Sp(4) to that of SL(4, r) if the area of the phase space of one of the oscillators is allowed to become smaller without a lower limit. While there are no restrictions on the size of phase space in classical mechanics, Feynman's rest of the universe makes this Sp(4)-to-SL(4, r) transition possible. The ten generators are for the world where quantum mechanics is valid. The remaining five generators belong to the rest of the universe. It is noted that the groups SL(4, r) and Sp(4) are locally isomorphic to the Lorentz groups O(3, 3) and O(3, 2) respectively. This allows us to interpret Feynman's rest of the universe in terms of space-time symmetry.

“…The width of the distribution becomes √ cosh η, and becomes wide-spread as the hadronic speed increases. Likewise, the momentum distribution becomes wide-spread [5,29]. This simultaneous increase in the momentum and position distribution widths is called the parton phenomenon in high-energy physics [13,14].…”

Section: Time-separation Variable In Feynman's Rest Of the Universementioning

confidence: 99%

“…Likewise, the momentum distribution becomes wide-spread [5,29]. This simultaneous increase in the momentum and position distribution widths is called the parton phenomenon in high-energy physics [13,14].…”

Section: Time-separation Variable In Feynman's Rest Of the Universementioning

confidence: 99%

Lorentz Harmonics, Squeeze Harmonics and Their Physical Applications

2011

Symmetry

Among the symmetries in physics, the rotation symmetry is most familiar to us. It is known that the spherical harmonics serve useful purposes when the world is rotated. Squeeze transformations are also becoming more prominent in physics, particularly in optical sciences and in high-energy physics. As can be seen from Dirac's light-cone coordinate system, Lorentz boosts are squeeze transformations. Thus the squeeze transformation is one of the fundamental transformations in Einstein's Lorentz-covariant world. It is possible to define a complete set of orthonormal functions defined for one Lorentz frame. It is shown that the same set can be used for other Lorentz frames. Transformation properties are discussed. Physical applications are discussed in both optics and high-energy physics. It is shown that the Lorentz harmonics provide the mathematical basis for squeezed states of light. It is shown also that the same set of harmonics can be used for understanding Lorentz-boosted hadrons in high-energy physics. It is thus possible to transmit physics from one branch of physics to the other branch using the mathematical basis common to them.