On the limits of quantum theory: Contextuality and the quantum–classical cut

This paper is based on four assumptions: 1. Physical reality is made of linearly behaving components combined in non-linear ways. 2. Higher level behaviour emerges from this lower level structure. 3. The way the lower level elements behaves depends on the context in which they are embedded. 4. Quantum theory applies to the lower level entities. An implication is that higher level effective laws, based on the outcomes of non-linear combinations of lower level linear interactions, will generically not be unitary; hence the applicability of quantum theory at higher levels is strictly limited. This leads to the view that both state vector preparation and the quantum measurement process are crucially based on top-down causal effects, and helps provide criteria for the Heisenberg cut that challenge some views on Schrödinger’s cat.     

Direct gauging of the Poincaré group V. Group scaling,classical gauge theory,and gravitational corrections

Homogeneous scaling of the group space of the Poincaré group,P ₁₀, is shown to induce scalings of all geometric quantities associated with the local action ofP ₁₀. The field equations for both the translation and the Lorentz rotation compensating fields reduce toO(1) equations if the scaling parameter is set equal to the general relativistic gravitational coupling constant 8Gc ^–4. Standard expansions of all field variables in power series in the scaling parameter give the following results. The zeroth-order field equations are exactly the classical field equations for matter fields on Minkowski space subject to local action of an internal symmetry group (classical gauge theory). The expansion process is shown to breakP ₁₀-gauge covariance of the theory, and hence solving the zeroth-order field equations imposes an implicit system ofP ₁₀-gauge conditions. Explicit systems of field equations are obtained for the first- and higher-order approximations. The first-order translation field equations are driven by the momentum-energy tensor of the matter and internal compensating fields in the zeroth order (classical gauge theory), while the first-order Lorentz rotation field equations are driven by the spin currents of the same classical gauge theory. Field equations for the first-order gravitational corrections to the matter fields and the gauge fields for the internal symmetry group are obtained. Direct Poincaré gauge theory is thus shown to satisfy the first two of the three-part acid test of any unified field theory. Satisfaction of the third part of the test, at least for finite neighborhoods, seems probable.     

The theory of interaction between wave and basic flow

This paper investigates the interaction between transient wave and non-stationary and non-conservative basic flow. An interaction equation is derived from the zonally symmetric and non-hydrostatic primitive equations in Cartesian coordinates by using the Momentum-Casimir method. In the derivation, it is assumed that the transient disturbances satisfy the linear perturbation equations and the basic states are non-conservative and slowly vary in time and space. The diabatic heating composed of basic-state heating and perturbation heating is also introduced. Since the theory of wave-flow interaction is constructed in non-hydrostatic and ageostrophic dynamical framework, it is applicable to diagnosing the interaction between the meso-scale convective system in front and the background flow.
It follows from the local interaction equation that the local tendency of pseudomomentum wave-activity density depends on the combination of the perturbation flux divergence second-order in disturbance amplitude, the local change of basic-state pseudomomentum density, the basic-state flux divergence and the forcing effect of diabatic heating. Furthermore, the tendency of pseudomomentum wave-activity density is opposite to that of basic-state pseudomomentum density. The globally integrated basic-state pseudomomentum equation and wave-activity equation reveal that the global development of basic-state pseudomomentum is only dominated by the basic-state diabatic heating while it is the forcing effect of total diabatic heating from which the global evolution of pseudomomentum wave activity results. Therefore, the interaction between the transient wave and the non-stationary and non-conservative basic flow is realized in virtue of the basic-state diabatic heating.     

Luis Santaló and classical field theory

Considered one of the founding fathers of integral geometry, Luis Santaló has contributed to various areas of mathematics. His work has applications in number theory, in the theory of differential equations, in stochastic geometry, in functional analysis, and also in theoretical physics. Between the 1950’s and the 1970’s, he wrote a series of papers on general relativity and on the attempts at generalizing Einstein’s theory to formulate a unified field theory. His main contribution in this subject was to provide a classification theorem for the plethora of tensors that were populating Einstein’s generalized theory. This paper revisits his work on theoretical physics.

     

Application of extended Hückel theory to the geometry of molecules: propylene,methylallene and methylketene

The extended Hückel method has been applied to the calculation of the geometry of propylene, methylallene and methylketene. A good result is obtained for the CCC angle in these compounds as compared with the experimental data. The choice of the value for the H(1s) orbital exponent and the constant in the expression for the non-diagonal elements H_ij is discussed.     

Quantum theory of single events: Localized De Broglie wavelets,Schrödinger waves,and classical trajectories

For an arbitrary potential V with classical trajectoriesx=g(t), we construct localized oscillating three-dimensional wave lumps (x, t,g) representing a single quantum particle. The crest of the envelope of the ripple follows the classical orbitg(t), slightly modified due to the potential V, and (x, t,g) satisfies the Schrödinger equation. The field energy, momentum, and angular momentum calculated as integrals over all space are equal to the particle energy, momentum, and angular momentum. The relation to coherent states and to Schrödinger waves is also discussed.     

Application of the “electronic bridge” theory to some highly converted nuclear transitions

The influence of the atomic electron cloud on the gamma decay constantλ _γ was evaluated in third-order approximation according to the theory of Krutov for some highly converted nuclear transitions (resonance case only). The results areλ _γ ⁽³⁾ =1.5×10⁵ λ _γ ⁽³⁾ for the 73 eV transition of U-235m andλ _γ ⁽³⁾ =1.01λ _γ ⁽¹⁾ for the 2.17 keV transition of Tc-99m. Values calculated forZ=80,E _γ =2 keV are in good agreement with those of Krutov. Experimental evidence of the calculated effects does not seem to be obtainable at present because of the extremely low gamma intensity of the transitions in question.     

Equivalence principle,the general theory of relativity,ang “black holes”

The equivalence principle is necessary for the validity of Newtonian mechanics, since only in this case can one consider an isolated system, neglecting the attraction of distant bodies. The possibility of verifying the equivalence principle by observations of the structure of galaxies and the large-scale structure of the universe is discussed. It is pointed out that the existence of horizons with valve properties -a one-way exchange of information—contradicts the equivalence principle.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 11–15, January, 1984.     

The meaning of time in the theory of relativity and “Einstein's later view of the Twin Paradox”

The purpose of the present paper is to reply to a misleading paper by M. Sachs entitled Einstein's later view of the Twin Paradox (TP) (Found. Phys. 15, 977 (1985)). There, by selecting some passages from Einstein's papers, he tried to convince the reader that Einstein changed his mind regarding the asymmetric aging of the twins on different motions. Also Sachs insinuates that he presented several years ago convincing mathematical arguments proving that the theory of relativity does not predict asymmetrical aging in the TP. Here we give a definitive treatment to the clocks problem showing that Sachs' convincing mathematical arguments are non sequitur. Also, by properly quoting Einstein, we show that his later view of the TP coincides with the one derived from the rigorous theory of time developed in this paper.     

Quantum uncertainty and a counterexample of nonlocal classical “realism”

We analyze the scheme of an experiment in which, by examining suppression effects of the cross correlation of photons in a beamsplitter and by preparing squeezed states, it is proven that the phase difference of photons in Fock states cannot acquire a certain value, since, otherwise, the simultaneous existence of these two effects would be impossible. We show that this reveals an intrinsic inconsistency of the nonlocal classical interpretation of quantum mechanics on the basis of nonlocal classical “realism.”     

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.