A critical analysis of N. Bohr's reply to the EPR argument

N. Bohr's counter-argument to EPR assumes that the complementarity principle imposes a limitation on the types of predictions permissible in quantum theory, similar to the limitation imposed on the types of measurements by the Heisenberg uncertainty relation. Since this assumption has no quantum-theoretical justification, the EPR argument cannot be refuted on the basis of the complementarity principle.     

Weyl’s Gauge Argument

The standard $\mathbb{U}(1)$ “gauge principle” or “gauge argument” produces an exact potential A=dλ and a vanishing field F=d ² λ=0. Weyl (in Z. Phys. 56:330–352, 1929; Rice Inst. Pam. 16:280–295, 1929) has his own gauge argument, which is sketchy, archaic and hard to follow; but at least it produces an inexact potential A and a nonvanishing field F=dA≠0. I attempt a reconstruction.     

The maximization of Tsallis entropy with complete deformed functions and the problem of constraints

By only requiring the q deformed logarithms (q exponentials) to possess arguments chosen from the entire set of positive real numbers (all real numbers), we show that the q-logarithm (q exponential) can be written in such a way that its argument varies between 0 and 1 (among negative real numbers) for 1?q<2, while the interval 0<q?1 corresponds to any real argument greater than 1 (positive real numbers). These two distinct intervals of the nonextensivity index q, also the expressions of the deformed functions associated with them, are related to one another through the relation (2−q), which is so far used to obtain the ordinary stationary distributions from the corresponding escort distributions, and vice versa in an almost ad hoc manner. This shows that the escort distributions are only a means of extending the interval of validity of the deformed functions to the one of ordinary, undeformed ones. Moreover, we show that, since the Tsallis entropy is written in terms of the q-logarithm and its argument, being the inverse of microstate probabilities, takes values equal to or greater than 1, the resulting stationary solution is uniquely described by the one obtained from the ordinary constraint. Finally, we observe that even the escort stationary distributions can be obtained through the use of the ordinary averaging procedure if the argument of the q-exponential lies in (−∞,0]. However, this case corresponds to, although related, a different entropy expression than the Tsallis entropy.     

On principle of inertia in closed universe

If our universe is asymptotic to a de Sitter space, it should be closed with curvature in O(Λ)$O(\Lambda )$ in view of dS special relativity. Conversely, its evolution can fix on Beltrami systems of inertia in the ds-space without Einstein's ‘argument in a circle’. Gravity should be local ds-invariant based on localization of the principle of inertia.     

Distinguishing Initial State-Vectors from Each Other in Histories Formulations and the PBR Argument

Following the argument of Pusey et al. (in Nature Phys. 8:476, 2012), new interest has been raised on whether one can interpret state-vectors (pure states) in a statistical way (ψ-epistemic theories), or if each one of them corresponds to a different ontological entity. Each interpretation of quantum theory assumes different ontology and one could ask if the PBR argument carries over. Here we examine this question for histories formulations in general with particular attention to the co-event formulation. State-vectors appear as the initial state that enters into the quantum measure. While the PBR argument goes through up to a point, the failure to meet some of the assumptions they made does not allow one to reach their conclusion. However, the author believes that the “statistical interpretation” is still impossible for co-events even if this is not proven by the PBR argument.     

Semiconductor intersubband laser/detector performance optimization using a simulated annealing algorithm

A numerical method for global optimization of semiconductor intersubband laser/detector performance parameters is presented. The single-band effective-mass Schroedinger equation is solved by employing the argument principle method (APM) to extract both the bound (B) and quasibound (QB) eigen-energies of the quantum heterostructure. APM is combined with a simulated annealing (SA) algorithm to determine a set of device design parameters such as potential barrier height V_i, layer thickness d_i, applied biasV_Bias , for which the intersubband device performance is within a predetermined convergence criterion. The method presented incorporates the energy-dependent effective mass of electrons in nonparabolic conduction bands. The performance of the method is evaluated for the design of an asymmetric Fabry–Perot electron-wave interference filter (laser structure) and a dual-band quantum well infrared photodetector (QWIP). Results with and without nonparabolic effects are presented. In addition, results from the present method are compared to results obtained via the optimization technique based on super-symmetric quantum mechanics (SUSYQM) for the case of an optically-pumped quantum cascade (QC) laser. The present method is shown to improve the device performance beyond that obtained via SUSYQM optimization. Further, the present model can handle many optimization parameters and can incorporate fabrication constraints to achieve physically realizable devices.     

Mirror Symmetry and Other Miracles in Superstring Theory

The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam’s ‘no miracles argument’ that, I argue, many string theorists in fact espouse in some form or other. String theory has generated many surprising, useful, and well-confirmed mathematical ‘predictions’—here I focus on mirror symmetry and the mirror theorem. These predictions were made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for the framework that generated them. I shall attempt to defend this argument, but there are nonetheless some serious objections to be faced. These objections can only be evaded at a considerably high (philosophical) price.     

The information paradox: Conflicts and resolutions

Many relativists have been long convinced that black hole evaporation leads to information loss or remnants. String theorists have however not been too worried about the issue, largely due to a belief that the Hawking argument for information loss is flawed in its details. A recently derived inequality shows that the Hawking argument for black holes with horizon can in fact be made rigorous. What happens instead is that in string theory, black hole microstates have no horizons. Thus the evolution of radiation quanta with E??kT is modified by order unity at the horizon, and we resolve the information paradox.     

The thermodynamic limit for long-range random systems

Long-range spin systems with random interactions are considered. A simple argument is presented showing that the thermodynamic limit of the free energy exists and depends neither on the specific random configuration nor on the sample shape, provided there is no external field. The argument is valid for both classical and quantum spin systems, and can be applied to (a) spins randomly distributed on a lattice and interacting via dipolar interactions; and (b) spin systems with potentials of the formJ(x ₁,x ₂)/|x ₁ -x ₂| ^αd , where theJ(x ₁,x ₂) are independent random variables with mean zero,d is the dimension, and α > 1/2. The key to the proof is a (multidimensional) subadditive ergodic theorem. As a corollary we show that, for random ferromagnets, the correlation length is a nonrandom quantity.     

Temperature Fluctuations for a System in Contact with a Heat Bath

The problem of how to define and compute temperature fluctuations for a small system in contact with a heat bath is an old one and originates from Einstein’s theory of Brownian motion. Only for a small enough system does their relative size allow a straightforward experimental verification. Here we focus on a mesoscopic system in contact with a heat bath at temperature T _° and provide a self-consistent argument showing as to why, and in what sense, the observable standard deviation of temperature from T _° equals $\sqrt{k_{\rm B}/C}T_{\circ}$ where C is the mesoscopic system’s heat capacity. Our argument is based on ergodic decomposition, a simple fact that holds for a system in thermodynamic equilibrium and away from phase-transition points. In this way we close a line of argument opened by de Haas-Lorentz a century ago.     

Connecting the Dots: Mott for Emulsions,Collapse Models,Colored Noise,Frame Dependence of Measurements,Evasion of the “Free Will Theorem”

We review the argument that latent image formation is a measurement in which the state vector collapses, requiring an enhanced noise parameter in objective reduction models. Tentative observation of a residual noise at this level, plus several experimental bounds, imply that the noise must be colored (i.e., non-white), and hence frame dependent and non-relativistic. Thus a relativistic objective reduction model, even if achievable in principle, would be incompatible with experiment; the best one can do is the non-relativistic CSL model. This negative conclusion has a positive aspect, in that the non-relativistic CSL reduction model evades the argument leading to the Conway–Kochen “Free Will Theorem”.     

How particular is the physics of the free energy principle?

The free energy principle (FEP) states that any dynamical system can be interpreted as performing Bayesian inference upon its surrounding environment. Although, in theory, the FEP applies to a wide variety of systems, there has been almost no direct exploration or demonstration of the principle in concrete systems. In this work, we examine in depth the assumptions required to derive the FEP in the simplest possible set of systems – weakly-coupled non-equilibrium linear stochastic systems. Specifically, we explore (i) how general the requirements imposed on the statistical structure of a system are and (ii) how informative the FEP is about the behaviour of such systems. We discover that two requirements of the FEP – the Markov blanket condition (i.e. a statistical boundary precluding direct coupling between internal and external states) and stringent restrictions on its solenoidal flows (i.e. tendencies driving a system out of equilibrium) – are only valid for a very narrow space of parameters. Suitable systems require an absence of perception-action asymmetries that is highly unusual for living systems interacting with an environment. More importantly, we observe that a mathematically central step in the argument, connecting the behaviour of a system to variational inference, relies on an implicit equivalence between the dynamics of the average states of a system with the average of the dynamics of those states. This equivalence does not hold in general even for linear stochastic systems, since it requires an effective decoupling from the system's history of interactions. These observations are critical for evaluating the generality and applicability of the FEP and indicate the existence of significant problems of the theory in its current form. These issues make the FEP, as it stands, not straightforwardly applicable to the simple linear systems studied here and suggest that more development is needed before the theory could be applied to the kind of complex systems that describe living and cognitive processes.     

A modified Eguchi-Kawai model

A modified version of the Eguchi-Kawai model is proposed. We show that this modified model is equivalent to U(N) gauge theory in the infinite volume when N → ∞. The argument is based on investigations both in the continuum and on a lattice. We show that our modified model does not suffer from the notorious spontaneous symmetry breaking.     

Laguerre-Gaussian beams with complex and real arguments in a uniaxial crystal

A solution to the paraxial wave equation for Laguerre-Gaussian beams with complex and real arguments in a uniaxial crystal is found and analyzed. It is shown that the beams with a complex argument form a complete group of the solution, while the beams with a real argument satisfy the equation only for an arbitrary radial index, with the azimuthal index being fixed and equal to l = 1. The evolution of phase singularities is considered by the example of transformation of the structure of topological multipoles and generation of optical vortices.     

On longitudinal acoustic propagation in convergent and divergent nozzle flows

The longitudinal propagation of sound in quasi-one-dimensional low Mach number nozzle flow is considered in section 1. The solution in the ray approximation (section 2.1) is used to transform the wave equation into a Schrödinger form, which is studied for the family of power-law ducts, including, as a particular case, the conical nozzle. It is shown that the coincidence of flow sources/sinks with sound sources can lead to appearance of essential singularities (section 2.2), which can be removed by using a Riccati transformation (section 2.4). The exact solutions of the acoustic equations for the parabolic (Figure 1) and hyperbolic (Figure 2) nozzles are obtained in terms of Bessel functions (section 2.3), respectively of complex order and argument. The general formulas, together with limiting forms in the compactness, ray and asymptotic approximations (section 3.1), are used to establish properties of the acoustic velocity and pressure (section 3.2), kinetic and compression energies, and energy flux and wave action (section 3.3); for example, it is shown that the equipartition of energies for moderate variations in cross-section, gives way (Table 2) to a predominance of kinetic/compression energies respectively near blockages/openings. The effects of non-uniform mean flow (Table 1) are discussed by comparing horns with nozzles (section 3.4): e.g., it is shown that the duality principle, in three alternative forms, does not extend from horn to nozzles, and the acoustic equations have no elementary solutions for the latter, in contrast with the former.     

Chiral hyperbags

We construct and studySU (3) chiral bags (called chiral hyperbags) in the scheme of collective-coordinate quantization with chiral symmetry breaking treated as perturbation. We show how the Wess-Zumino constraint arises from the quark-bag sector, complementing the soliton sector, in a manner analogous to what happens in (1+1) dimensional chiral bags. Due to the Wess-Zumino term, all the quantum numbers — baryon charge, isopin, angular momentum, hypercharge etc. are fractionized in a prescribed manner. One notable aspect of the fractionization is that for all ranges of bag radius, there is alwaysmore angular momentum lodged in the soliton sector than in the quark sector. It is shown thatwithin the scheme we have adopted, the symmetry breaking termobstructs the Cheshire Cat principle and that consequently when strange quarks are present, the baryons (i.e. hyperons) favor a bigger bag (say R ? 1 fm) than non-strange baryons; this confirms a phenomenological argument put forward some time ago by Brown, Klimpt, Rho and Weise (at least in the collective-coordinate scheme). Our approach allows us to calculate the strangeness content of the proton — a highly topical issue — and we find that while a perturbative treatment of the symmetry breaking term can be made to work (for a big bag) for hyperon spectroscopy, the strangeness content of the proton is insensitive to the bag radius; for relevant ranges of bag radius, the ¯ss admixture stays significant, say, ?19%. This result is in stark contrast to the Callan-Klebanov Skyrmion — a remarkably successful model for hyperons — which predicts only about 3%. A subtle role of the Wess-Zumino term is suggested.     

Breakup of Universality in the Generalized Spinodal Nucleation Theory

The problem of nucleation near spinodal is revisited. It is shown that the standard scaling argument due to Unger and Klein [Phys. Rev. B 29:2698–2708 (1984)] based on neglecting all but the first two terms of the Taylor expansion of the potential in the free energy functional is only valid below critical dimension. At critical dimension, the nucleating droplet has a bigger amplitude and a smaller spatial extent than predicted by the standard scaling argument. In this case the structure of the droplet is determined in a nontrivial fashion by the next order term in the expansion of the potential. Above critical dimension, the amplitude of the nucleating droplet turns out to be too big to justify expanding the potential in Taylor series, and no universality is to be expected in the shape and size of the droplet. Both at and above critical dimension, however, the free energy barrier remains finite, which indicates that the nucleation rate does not vanish at spinodal as predicted by the standard scaling argument.     

Reply to “Comment on ‘Contextuality within quantum mechanics manifested in subensemble mean values’ [Phys. Lett. A 373 (2009) 3430]” [Phys. Lett. A 374 (2010) 1397]

In this reply, we point out that the claim by De Zela (2010) [2] is unjustified because the setup he discusses is not equivalent to the setup analysed in our paper (Pan and Home (2009) [1]). Hence his subsequent argument claiming the reproducibility of our demonstrated quantum effect of path-spin contextuality by the Kochen-Specker realist model is not relevant.     

Fractional charge and automatic U(1) symmetry without domain walls

All fermion representations compatible with fractional charge in asymptotically free SU(N) gauge theories are constructed. With a survival hypothesis argument it is shown that none of them have three light ordinary fermion families. Automatic U(1) symmetry is constructed for each case, but all of them are plagued with domain-wall problems, unresolvable by the Lazarides and Shafi method.     

The necessity of quantizing the gravitational field

The assumption that a classical gravitational field interacts with a quantum system is shown to lead to violations of either momentum conservation or the uncertainty principle, or to result in transmission of signals faster thanc. A similar argument holds for the electromagnetic field.Work supported in part by NSF Grant GP30799X.