The simplest derivation of the Lorentz transformation

Starting from the well-known light-clock thought experiment to derive time dilation and length contraction, it is shown that finding the Lorentz Transformation requires nothing more than the most trivial vector addition formula. The form which is obtaine for the L.T. allows an easy derivation of the velocity and acceleration transformations which are also given.Comment: Latex, 4 pages, 1 figure. Two first paragraphs rewritten. Error in formula corrected. Various typo corrected. Example added (Should really be V3. But V3 identical to V2 for some reason

Power Laws are Logarithmic Boltzmann Laws

Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative dynamics might be the natural origin for the emergence of criticality and scale hierarchies without fine-tuning.Comment: latex, 9 pages with 3 figure

Spontaneous Scaling Emergence in Generic Stochastic Systems

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction. The systems present power laws with exponents which in a wide range ($\alpha < -2.$) are universally determined by the ratio between the minimal and the average values of the degrees of freedom. The time fluctuations are governed by Levy distributions of corresponding power. For exponents $\alpha > -2$ there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos and bursts/intermitency.Comment: latex, 11 page

A consistent interpretation of the Karmen anomaly

The Karmen anomaly can be interpreted as being due to a heavy neutrino of mass around 137 MeV produced in $\pi_{e 2}$ decays. This interpretation is consistent with the present limits on the couplings of such an object.Comment: 11pages, 4figures, Te

Different steady states for spin currents in noncollinear multilayers

We find there are at least two different steady states for transport across noncollinear magnetic multilayers. In the conventional one there is a discontinuity in the spin current across the interfaces which has been identified as the source of current induced magnetic reversal; in the one advocated herein the spin torque arises from the spin accumulation transverse to the magnetization of a magnetic layer. These two states have quite different attributes which should be discerned by current experiments.Comment: 8 pages, no figure. Accepted for publication in Journal of Physics: Condensed Matte

Towards a European Union Child Basic Income? Within and between country effects

ABSTRACT: This paper explores the within and between country distributional implications of an illustrative Child Basic Income (CBI) operated at EU level. Using EUROMOD, we establish that a universal payment of €50 per month per child aged under 6 could take 800,000 children in this age group out of poverty. It could be financed by an EU flat tax of 0.2% on all household income, assuming that it would also be taxed nationally as income. Most member states and virtually all families with children aged under 6 would be net gainers. We simulate two versions of EU CBI, with the benefit rate of €50 per month adjusted or not for differences in purchasing power between member states. In general, fiscal flows between member states, and also poverty reduction, would be smaller under the adjusted version. The political feasibility of such a scheme might be questioned, especially within the net contributor countries. Nevertheless, for those seeking ways to strengthen solidarity across national boundaries, a scheme supporting the incomes of families with young children, wherever in the EU they might reside &quot;could be a demonstration of the EU&apos;s commitment to children, to the future&quot; (EC 2012a: 62)

Context unification is in PSPACE

Contexts are terms with one `hole', i.e. a place in which we can substitute an argument. In context unification we are given an equation over terms with variables representing contexts and ask about the satisfiability of this equation. Context unification is a natural subvariant of second-order unification, which is undecidable, and a generalization of word equations, which are decidable, at the same time. It is the unique problem between those two whose decidability is uncertain (for already almost two decades). In this paper we show that the context unification is in PSPACE. The result holds under a (usual) assumption that the first-order signature is finite. This result is obtained by an extension of the recompression technique, recently developed by the author and used in particular to obtain a new PSPACE algorithm for satisfiability of word equations, to context unification. The recompression is based on performing simple compression rules (replacing pairs of neighbouring function symbols), which are (conceptually) applied on the solution of the context equation and modifying the equation in a way so that such compression steps can be in fact performed directly on the equation, without the knowledge of the actual solution.Comment: 27 pages, submitted, small notation changes and small improvements over the previous tex

The steady state in noncollinear magnetic multilayers

There are at least two different putative steady state solutions for current across noncollinear magnetic multilayers; one has a discontinuity in the spin current at the interface the other is continuous. We compare the resistance of the two and find the solution with the continuous spin currents is lower. By using the entropic principle we can state that this solution is a better estimate of the resistance for a noncollinear magneticComment: 14 pages, 4 figures,Submitted to Physical Review