Stern-Gerlach Experiment’s Interpretations and Noether’s Theorem

In this paper we suggest that theories treating two interacting objects in a different manner (for instance electromagnetic field of a laser classically, and the interacting atom as a quantum object) should be called “mixed”. Mixed theories are not so rare in Physics. One just should look at the whole area of Atomic, Molecular and Optical Physics in which mixed theories are often used, and, also, theories including quantum object interacting with classical surroundings that are the subject of our present discussion: the field of Quantum decoherence, when applied to resolving the dilemma should classical trajectories be used in explaining the Stern-Gerlach experiment or not. Consequently we are proving one improved corollary to Noether’s theorem, stating that mixed theories are not supporting the law of conservation of angular momentum and spin, as they are not based on the isotropy of space-time.     

Entanglement and it’s Manipulation

In this paper, we substantiate the at very low temperatures entanglement is exhibited manifestly. Also, we show that the phenomena of entanglement can be manipulated with respect to certain parameters in 2D crystals like graphene.

     

Young’s modulus and Poisson’s ratio for seven-constant tetragonal crystals and nano/microtubes

In the paper, the elasticity theory was applied to consider the mechanical properties of rectilinearly anisotropic seven-constant tetragonal crystals and their cylindrically anisotropic nano/microtubes with and with no chiral angle, being the angle between the crystallographic symmetry axis and elongated tube axis. Pt is found that the number of crystals with negative Poisson’s ratio is the least for rectilinear anisotropy and is much larger for curvilinear anisotropy. With a nonzero chiral angle, all nano/microtubes can have negative Poisson’s ratio. The elastic problem on axial tension of cylindrical nano/microtubes is solved for radially inhomogeneous stresses: three normal stresses and one shear stress.     

Mach’s principle and hidden matter

According to the Einstein-Mayer theory of the Riemanniann space-time with Einstein-Cartan teleparallelism, the local Lorentz invariance is broken by the gravitational field defining Machian reference systems. This breaking of symmetry implies the occurrence of “hidden matter” in the Einstein equations of gravity. The hidden matter is described by the non-Lorentz-invariant energy-momentum tensor satisfying the relation . The tensor is formed from the Einstein-Cartan torsion field given by the anholonomy objects, F_Aik=2h_A[i,k], and appears together with Hilbert’s energy-momentum tensor T^* _ik and Poincaré’s pressure λg_ik on the right-hand side of Einstein’s equations so that one has

Bell’s Correlations and Spin Systems

The structure of maximal violators of Bell’s inequalities for Jordan algebras is investigated. It is proved that the spin factor V ₂ is responsible for maximal values of Bell’s correlations in a faithful state. In this situation maximally correlated subsystems must overlap in a nonassociative subalgebra. For operator commuting subalgebras it is shown that maximal violators have the structure of the spin systems and that the global state (faithful on local subalgebras) acts as the trace on local subalgebras.     

Pitowsky’s Kolmogorovian Models and Super-determinism

In an attempt to demonstrate that local hidden variables are mathematically possible, Pitowsky constructed “spin- Open image in new window functions” and later “Kolmogorovian models”, which employs a nonstandard notion of probability. We describe Pitowsky’s analysis and argue (with the benefit of hindsight) that his notion of hidden variables is in fact just super-determinism (and accordingly physically not relevant). Pitowsky’s first construction uses the Continuum Hypothesis. Farah and Magidor took this as an indication that at some stage physics might give arguments for or against adopting specific new axioms of set theory. We would rather argue that it supports the opposing view, i.e., the widespread intuition “if you need a non-measurable function, it is physically irrelevant”.     

Hund’s Rule and Metallic Ferromagnetism

We study tight-binding models of itinerant electrons in two different bands, with effective on-site interactions expressing Coulomb repulsion and Hunds rule. We prove that, for sufficiently large on-site exchange anisotropy, all ground states show metallic ferromagnetism: They exhibit a macroscopic magnetization, a macroscopic fraction of the electrons is spatially delocalized, and there is no energy gap for kinetic excitations.     

Ramanujan’s ‘‘Lost Notebook’’ and the Virasoro Algebra

By using the theory of vertex operator algebras, we gave a new proof of the famous Ramanujans modulus 5 modular equation from his Lost Notebook (p. 139 in [R]). Furthermore, we obtained an infinite list of q-identities for all odd moduli; thus, we generalized the result of Ramanujan.Acknowledgements It was indeed hard to trace all the known proofs of (1.1), (1.2) and (1.3). We apologize if some important references are omitted. We would like to thank Jim Lepowsky for conversations on many related subjects. A few years ago Lepowsky and the author were trying to relate classical Rogers-Ramanujan identities and Zhus work [Z]. We also thank Bruce Berndt for pointing us to [BrO] and Steve Milne for bringing [Mi] to our attention.     

Consciousness and the Wigner’s Friend Problem

It is generally agreed that decoherence theory is, if not a complete answer, at least a great step forward towards a solution of the quantum measurement problem. It is shown here however that in the cases in which a sentient being is explicitly assumed to take cognizance of the outcome the reasons we have for judging this way are not totally consistent, so that the question has to be considered anew. It is pointed out that the way the Broglie–Bohm model solves the riddle suggests a possible clue, consisting in assuming that even very simple systems may have some sort of a proto-consciousness, but that their “internal states of consciousness” are not predictive. It is, next, easily shown that if we imagine the systems get larger, in virtue of decoherence their internal states of consciousness progressively gain in predictive value. So that, for macro-systems, they may be identified (in practice) with the predictive states of consciousness on which we ground our observational predictions. The possibilities of carrying over this idea to standard quantum mechanics are then investigated. Conditions of conceptual consistency are considered and found rather strict, and, finally, two solutions emerge, differing conceptually very much from one another but in both of which the, possibly non-predictive, generalized internal states of consciousness play a crucial role.     

Elastic Properties of Graphene-Like Compounds: the Keating’s and Harisson’s Models

Physics of the Solid State - The third-order elastic constants, the pressure dependences of the second-order elastic constants, the Kleinman and Grüneisen parameters, and the thermal expansion...     

Nature’s optics and our understanding of light

Optical phenomena visible to everyone have been central to the development of, and abundantly illustrate, important concepts in science and mathematics. The phenomena considered from this viewpoint are rainbows, sparkling reflections on water, mirages, green flashes, earthlight on the moon, glories, daylight, crystals and the squint moon. And the concepts involved include refraction, caustics (focal singularities of ray optics), wave interference, numerical experiments, mathematical asymptotics, dispersion, complex angular momentum (Regge poles), polarisation singularities, Hamilton’s conical intersections of eigenvalues (‘Dirac points’), geometric phases and visual illusions.     

Quantum Perfect Correlations and Hardy’s Nonlocality Theorem

In this paper the failure of Hardy's nonlocality proof for the class of maximally entangled states is considered. A detailed analysis shows that the incompatibility of the Hardy equations for this class of states physically originates from the fact that the existence of quantum perfect correlations for the three pairs of two-valued observables (D ₁₁, D ₂₁), (D ₁₁, D ₂₂), and (D ₁₂, D ₂₁) [in the sense of having with certainty equal (different) readings for a joint measurement of any one of the pairs (D ₁₁, D ₂₁), (D ₁₁, D ₂₂), and (D ₁₂, D ₂₁)], necessarily entails perfect correlation for the pair of observables (D ₁₂, D ₂₂) [in the sense of having with certainty equal (different) readings for a joint measurement of the pair (D ₁₂, D ₂₂)]. Indeed, the set of these four perfect correlations is found to satisfy the CHSH inequality, and then no violations of local realism will arise for the maximally entangled state as far as the four observables D _ij, i,j = 1 or 2, are concerned. The connection between this fact and the impossibility for the quantum mechanical predictions to give the maximum possible theoretical violation of the CHSH inequality is pointed out. Moreover, it is generally proved that the fulfillment of all the Hardy nonlocality conditions necessarily entails a violation of the resulting CHSH inequality. The largest violation of this latter inequality is determined.     

Landauer’s limit and the physicality of information

Landauer’s lower bound on the dissipative cost of information erasure is revisited within a new physical conception of information. The notion of strong physical information is introduced, and the new conception of physical information – observer-local referential (OLR) information – is defined, shown to be strongly physical, and related to other measures that arise in physical information contexts. A generalization of Landauer’s limit is then obtained for OLR information from quantum dynamics and entropic inequalities alone. Specializations of this bound are compared and contrasted to similar bounds under conditions for which they coincide, and important distinctions between seemingly identical bounds expressed in terms of various information measures are discussed. The controversial distinction between Landauer erasure of known and unknown data – and the alleged difference between their respective erasure costs – is then explored via OLR information. This physically grounds and clarifies distinctions between known and unknown data and between unconditional and conditional erasure operations, enables a straightforward physical accounting of associated lower bounds on erasure costs, and illustrates the advantages of OLR information for resolution of controversies related to the dissipative cost of information erasure. Applications of OLR information to determination of irreversibility induced dissipation bounds in more complex computing scenarios are briefly discussed.     

Benford’s law and half-lives of unstable nuclei

We find that the experimental data of the -decay half-lives for 627 nuclei are in good agreement with Benford’s law, which states that the frequency of the appearance of each figure, 1-9, as the first significant digit, follows a logarithmic distribution favoring the smallest value. In order to generalize the applicability of Benford’s law, we systematically investigate the data of the total half-lives for 3177 nuclides in their ground and isomeric states, where the half-lives of many nuclei are determined by -decay and spontaneous fission. We find that they are also in excellent agreement with Benford’s law, although they are determined by different interactions such as strong, weak and electromagnetic interactions. The possible physics behind them is discussed. Moreover, Benford’s law can be used to test theoretical models or methods.     

On Shor’s Channel Extension and Constrained Channels

Several equivalent formulations of the additivity conjecture for constrained channels, which formally is substantially stronger than the unconstrained additivity, are given. To this end a characteristic property of the optimal ensemble for such a channel is derived, generalizing the maximal distance property. It is shown that the additivity conjecture for constrained channels holds true for certain nontrivial classes of channels. After giving an algebraic formulation for Shors channel extension, its main asymptotic property is proved. It is then used to show that additivity for two constrained channels can be reduced to the same problem for unconstrained channels, and hence, global additivity for channels with arbitrary constraints is equivalent to additivity without constraints.     

Hyperkähler Implosion and Nahm’s Equations

We use Nahm data to describe candidates for the universal hyperkähler implosion with respect to a compact Lie group.