Why space could be quantised on a different scale to matter

The scale of quantum mechanical effects in matter is set by Planck’s constant, \hbarℏ. This represents the quantisation scale for material objects. In this article, we present a simple argument why the quantisation scale for space, and hence for gravity, may not be equal to \hbarℏ. Indeed, assuming a single quantisation scale for both matter and geometry leads to the `worst prediction in physics’, namely, the huge difference between the observed and predicted vacuum energies. Conversely, assuming a different quantum of action for geometry, \beta \ll \hbarβ≪ℏ, allows us to recover the observed density of the Universe. Thus, by measuring its present-day expansion, we may in principle determine, empirically, the scale at which the geometric degrees of freedom should be quantised.

Strong anomaly and phases of chiral gauge theories

We present a simple argument which seems to favor, when applied to a large class of strongly-coupled chiral gauge theories, a dynamical-Higgs-phase scenario, characterized by certain bifermion condensates. Flavor symmetric confining vacua described in the infrared by a set of baryonlike massless composite fermions saturating the conventional ’t Hooft anomaly matching equations, appear instead disfavored. Our basic criterion is that it should be possible to write a strong-anomaly effective action, analogous to the one used in QCD to describe the solution of the U(1)A problem in the low-energy effective action, by using the low-energy degrees of freedom in the hypothesized infrared theory. We also comment on some well-known ideas such as the complementarity and the large N planar dominance in the context of these chiral gauge theories. Some striking analogies and contrasts between the massless QCD and chiral gauge theories seem to emerge from this discussion.

Ion and electron energization by Alfvén waves in magnetic shears

<p>In order to efficiently convert AW energy into particle energy, the original fluctuation must decay from the initial macroscopic (fluid) scales to smaller (kinetic) scales. This decay can be promoted by the interaction of counter-propagating AWs or by the interaction between AWs and an inhomogeneous background. It has been shown that AWs interacting with an inhomogeneous background can cascade to smaller scales via the phase-mixing process [1]. When the cascade reaches scales comparable with the ion Larmor radius, AWs can efficiently be converted into ”kinetic” Alfvén  waves (KAWs), which represent the natural extension of AWs in the kinetic branch of the wave dispersion relation for wavevectors nearly perpendicular to the background magnetic field [2]. In this work we present the results of a numerical experiment in which the decay of AWs into KAWs is studied self-consistently in a range that goes from fluid to kinetic electron scales. We show how the AW-to-KAW transition, promoted by an inhomogeneous background, leads to the heating of both ions and electrons via two different physical mechanisms. Both mechanisms are illustrated via a simple argument on how the two species can access the kinetic and magnetic energy carried by AWs. Our findings are supported by in-situ observations of KAWs in the Earth’s magnetosphere [3].</p><p>[1]  J. Heyvaerts  and  E.  Priest,  Coronal  heating  by  phase-mixed shear Alfv ́en waves, Astronomy and Astrophysics117, 220 (1983).<br>[2]  J. Hollweg, Kinetic Alfv ́en wave revisited, Journal of Geo-physical Research:  Space Physics104, 14811 (1999)<br>[3] D. Gershman, F. Adolfo, J. Dorelli, S. Boardsen, L. Avanov, P. Bellan, S. Schwartz, B. Lavraud, V. Cof-fey, M. Chandler,et  al., Wave-particle energy exchangedirectly observed in a kinetic Alfv ́en-branch wave, Naturecommunications8, 1 (2017).</p>

Uniformly Embedding Topological Manifolds into $L^{2}$ Spaces

With a simple argument, we show as a main note that every locally compact second-countableHausdorff space is topologically embeddable into some $L^{2}$ space with respect to some finite nonzero Borel measure, where the embedding may be chosen so that it is uniform and its range is included in some open proper subset of the $L^{2}$ space.

A simple note on the Yoneda (co)algebra of a monomial algebra

UDC 512.7 If is a monomial -algebra, it is well-known that is isomorphic to the space of (Anick) -chains for . The goal of this short note is to show that the next result follows directly from well-established theorems on -algebras, without computations: there is an -coalgebra model on satisfying that, for and , is a linear combination of , where , and . The proof follows essentially from noticing that the Merkulov procedure is compatible with an extra grading over a suitable category. By a simple argument based on a result by Keller we immediately deduce that some of these coefficients are .

Arithmetic proof of the multiplicity-weighted Euler characteristic for symmetrically arranged space-filling polyhedra

The puzzling observation that the famous Euler's formula for three-dimensional polyhedra V − E + F = 2 or Euler characteristic χ = V − E + F − I = 1 (where V, E, F are the numbers of the bounding vertices, edges and faces, respectively, and I = 1 counts the single solid itself) when applied to space-filling solids, such as crystallographic asymmetric units or Dirichlet domains, are modified in such a way that they sum up to a value one unit smaller (i.e. to 1 or 0, respectively) is herewith given general validity. The proof provided in this paper for the modified Euler characteristic, χm = V m − E m + F m − I m = 0, is divided into two parts. First, it is demonstrated for translational lattices by using a simple argument based on parity groups of integer-indexed elements of the lattice. Next, Whitehead's theorem, about the invariance of the Euler characteristic, is used to extend the argument from the unit cell to its asymmetric unit components.

Demise of Unruh radiation

Unruh radiation has attracted much interest, particularly because of its relationship to Hawking radiation. But its existence has been challenged by a variety of authors, including ourselves [Phys. Lett. A 158, 31 (1991)]. The absence of a consensus may be traced to the complex challenge of dealing with the infinite number of particles of the associated heat bath. Here, we show how this problem may be obviated by using the quantum Langevin equation [Ford et al., Phys. Rev. A 37, 4419 (1988); J. Math. Phys. 6, 504 (1965)], which enables us to present a simple argument to show that, despite the existence of an Unruh temperature, there is no Unruh radiation. A key point is that the Unruh system is an equilibrium system, in contrast to the Hawking system which is a non-equilibrium system.

Word-to-text integration in English as a second language reading comprehension

We assessed the relationship between word-to-text-integration (WTI) and reading comprehension in 7th grade students (n = 441) learning English as a second language (L2). The students performed a self-paced WTI reading task in Fall (T1) and Spring (T2), consisting of three text manipulation types (anaphora resolution, argument overlap, anomaly detection), divided in simple and complex passages. The passages contained proximate versus distant anaphora, explicit repetitions versus implicit inferences, and no anomalies versus anomalies. We first examined how WTI complexity was related to reading times on target, target plus one, and target plus two, controlling for word frequency, decoding fluency, gender, and age. Mixed-effects models showed shorter reading times on T2 than on T1 and for simple compared to complex passages, indicating improvement of L2 reading speed. Complexity affected WTI for our L2 learners, as was reflected by longer reading times on complex compared to simple argument overlap and anomaly detection passages. We then assessed whether reading comprehension could be predicted by WTI. Longer reading times on complex compared to simple argument overlap and anomaly detection passages predicted offline reading comprehension. These WTI-measures of complexity are thus indicators of WTI proficiency for novice L2 learners.