Paolo Nespoli reads Emily Dickinson

#1695
There is a solitude of space
A solitude of sea
A solitude of death, but these
Society shall be
Compared with that profounder site
That polar privacy
A soul admitted to itself–
Finite Infinity.

Sputnik-2 or: Laika, Our Hero

Laika was a Soviet space dog who became one of the first animals in space, and the first animal to orbit the Earth. Laika, a stray dog from the streets of Moscow, was selected to be the occupant of the Soviet spacecraft Sputnik 2 that was launched into outer space on November 3, 1957.
Little was known about the impact of spaceflight on living creatures at the time of Laika's mission, and the technology to de-orbit had not yet been developed, so Laika's survival was never expected. Some scientists believed humans would be unable to survive the launch or the conditions of outer space, so engineers viewed flights by animals as a necessary precursor to human missions. The experiment aimed to prove that a living passenger could survive being launched into orbit and endure a Micro-g environment, paving the way for human spaceflight and providing scientists with some of the first data on how living organisms react to spaceflight environments.
Laika died within hours from overheating, possibly caused by a failure of the central R-7 sustainer to separate from the payload. The true cause and time of her death were not made public until 2002; instead, it was widely reported that she died when her oxygen ran out on day six or, as the Soviet government initially claimed, she was euthanised prior to oxygen depletion.
On April 11, 2008, Russian officials unveiled a monument to Laika. A small monument in her honour was built near the military research facility in Moscow that prepared Laika's flight to space. It features a dog standing on top of a rocket. She also appears on the Monument to the Conquerors of Space in Moscow.
video via Popular Science

Abstract: The Universe at Lattice-Fields

Guido, G. and Filippelli, G. (2017) The Universe at Lattice-Fields. Journal of High Energy Physics, Gravitation and Cosmology, 3, 828-860. doi:10.4236/jhepgc.2017.34060.
We formulate the idea of a Universe crossing different evolving phases $U_k^*$ where in each phase one can define a basic field at lattice structure $U_k$ increasing in mass (Universe-lattice). The mass creation in $U_k$ has a double consequence for the equivalence "mass-space": Increasing gravity (with varying metric) and increasing space (expansion). We demonstrate that each phase is at variable metric beginning by open metric and to follow a flat metric and after closed. Then we define the lattice-field of intersection between two lattice fields of base into universe and we analyse the universe in the Nucleo-synthesis phase and in the that of recombination. We show that the phase is built on the intersection of the lattices of the proton and electron. We show $U_H$ [the intersection between proton's anch electron's lattices] to be at variable metric (open in the past, flat in the present and closed in the future). Then, we explain some fundamental aspects of this universe $U_H$: Hubble's law by creating the mass-space in it, its age (13.82 million of Years) as time for reaching the flat metric phase and the value of critic density. In last we talk about dark universe lattice, having hadronic nature, and calculating its spatial step and its density in present phase of [the universe].
For some personal problems, I cannot add the LaTeX figures, so I uploaded them on researchgate.

Mathematical joke

A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians to derive humor. The humor may come from a pun, or from a double meaning of a mathematical term, or from a lay person's misunderstanding of a mathematical concept. Mathematician and author John Allen Paulos in his book Mathematics and Humor described several ways that mathematics, generally considered a dry, formal activity, overlaps with humor, a loose, irreverent activity: both are forms of "intellectual play"; both have "logic, pattern, rules, structure"; and both are "economical and explicit".
Some performers combine mathematics and jokes to entertain and/or teach math.
Humor of mathematicians may be classified into the esoteric and exoteric categories. Esoteric jokes rely on the intrinsic knowledge of mathematics and its terminology. Exoteric jokes are intelligible to the outsiders, and most of them compare mathematicians with representatives of other disciplines or with common folk.

Wigner's theorem

The Wigner’s theorem was formulated and demonstrated for the first time by Eugene Paul Wigner on Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektrum(1). It states that for each symmetry transformation in Hilbert’s space there exists a unitary or anti-unitary operator, uniquely determined less than a phase factor.
For symmetry transformation, we intend a space transformation that preserved the characteristics of a given physical system. Asymmetry transformation implies also a change of reference system.
Invariants
Invariants play a key role in physics, being the quantities that, in any reference system, are unchanged. With the advent of quantum physics, their importance increased, particularly in the formulation of a relativistic quantum field theory. One of the most important tools in the study of invariants is the Wigner’s theorem, an instrument of fundamental importance for all the development of quantum theory.
In particular, Wigner was interested in determining the properties of transformations that preserve the transition’s probability between two different quantum states. Given $\phi$ the wave function detected by the first observer, and $\bar {\phi}$ the wave function detected by the second observer, Wigner assumed that the equality \[|\langle \psi | \phi \rangle| = |\langle \bar \psi | \bar \phi \rangle|\] must be valid for all $\psi$ and $\phi$.
In the end, if we exclude time inversions, we find that the operator $\operatorname{O}_{R}$, such that $\bar{\phi} = \operatorname{O} _{R} \phi$, must be unitary and linear, but also anti-unitary and anti-linear. Consequence of this fact is that the two observers’ descriptions are equivalent. So the first observes $\phi$, the second $\bar{\phi}$, while the operator $\operatorname{H}$ for the first will be $\operatorname{O}_R \operatorname{H} \operatorname{O}_R^{-1}$ for the second.

JMP #58, 4: path integrals and friends

The path integral formulation of quantum mechanics replaces the single, classical trajectory of a system with the sum over an infinity of quantum possible trajectories. To compute this sum is used a functional integral. The most famous interpretation is dued by Richard Feynman. In an Euclidean spacetime we speak about Euclidean path integral:
Bernardo, R. C. S., & Esguerra, J. P. H. (2017). Euclidean path integral formalism in deformed space with minimum measurable length. Journal of Mathematical Physics, 58(4), 042103. doi:10.1063/1.4979797
We study time-evolution at the quantum level by developing the Euclidean path-integral approach for the general case where there exists a minimum measurable length. We derive an expression for the momentum-space propagator which turns out to be consistent with recently developed $\beta$-canonical transformation. We also construct the propagator for maximal localization which corresponds to the amplitude that a state which is maximally localized at location $\xi'$ propagates to a state which is maximally localized at location $\xi"$ in a given time. Our expression for the momentum-space propagator and the propagator for maximal localization is valid for any form of time-independent Hamiltonian. The nonrelativistic free particle, particle in a linear potential, and the harmonic oscillator are discussed as examples.
Other papers from JMP #58, 4, follows:

The quantum Zeno paradox

The standard axioms of quantum mechanics imply that in the limit of continuous observation a quantum system cannot evolve.
(Andrew Hodges in Alan Turing: the logical and physical basis of computing - pdf)
Initially known as Turing’s paradox, in honor of the mathematician who formulated it in the 1950s, was subsequently identified as quantum Zeno effect, resulting an advanced version of the famous Zeno’s arrow paradox, whose phylosophical result is the negation of motion. A first formulation and derivation of the effect is found in Does the lifetime of an unstable system depend on the measuring apparatus?(1), while George Sudarshan and Baidyanath Misra were the first to identify it as quantum Zeno paradox. The two theoretical physicists established that an unstable particle will not decay as long as it is kept under continuous observation(2). However they try to save goat and cabbage:
There is a fundamental principle in quantum theory that denies the possibility of continuous observation.(2)
On the other hand, Ghirardi, Omero, Weber and Rimini show that:
if the uncertainty relations are properly taken into account the arguments leading to the paradox are not valid.(3)