Some difficulties for Clifton,Redhead, and Butterfield's recent proof of nonlocality

Clifton, Redhead, and Butterfield have recently produced a generalization of the new non-locality proof due to Greenberger, Horne, and Zeilinger. Their proof is intended to have certain advantages over the standard Belltype arguments. One of these is that, although the proof allows for causally relevant apparatus hidden variables, it avoids the need for making certain standard locality assumptions about those parameters. On closer inspection, the part of the proof which supposedly removes the need for such assumptions is shown to rest on a fallacy. This renders the proof invalid. Two other, related difficulties are explored along the way.1. CRB actually provide two nonlocality proofs, but our concern here is with the first.2. Cf. p.173 for a precise formulation of these. (Any references in these footnotes are to [1].) Note that, due to the way CRB define the µ's, these conditions are not entirely independent.3. Cf. p.174. Note that CRB claim to derive the independence of outcomes from apparatus existents via our other assumptions without imposing any other conditions on their distributions, citing Lemma 2, which we shall object to in Sec. 4 below. This should be given a careful reading; Lemma 2 only purports to derive the statistical independence of outcomes fromlocal (i.e., nearby) apparatus hidden variables. The independence of outcomes fromdistant apparatus hidden variables is assumed, rather, in OL.4. Here, and in many places, I shall rely on [1] for the details.5. CRB have endorsed this definition of M (personal correspondence).6. More precisely, those values of do so for at least one possible quadruple of apparatus existents, and measurement results; and foruncountably many setting quadruples in (p.167).7. Given CRB's way of defining the µ's so as to include the information found in the 's, the terms in OF and most of those in OL would actually be ill-defined in most cases (for each ) inany theory. This is simply because the measuring devices cannot be set to measure in two different directions at once. However, it should be possible to remedy that situation by simply redefining µ so that it includes only information about the state of the apparatus not covered by .8. CRB endorse the first of these two suggestions (personal correspondence).9. I have omitted the arguments fromA,B,C andD. Wherever they appear without arguments they will implicitly have the three with which they were first introduced. Note that M⁺ should ideally be indexed by and , as there is no reason to think that all the same members of M will makeABCD = +1 for different values of and .10. Cf. note 6 above.11. Note that in light of this objection to their proof, we can see that CRB also fail to establish the link they claim exists between TF, strict correlations, and the condition they call TF.TF is the four-particle analogue of the conjunction of Shimony's outcome independence and his parameter independence (p.162). They rest their claim about the link on Lemma 2 (pp.162 and 165).     

Stochastic Komatu–Loewner evolutions and BMD domain constant

For Komatu–Loewner equation on a standard slit domain, we randomize the Jordan arc in a manner similar to that of Schramm (2000) to find the SDEs satisfied by the induced motion $\xi \left(t\right)$ on $?\mathbb{H}$ and the slit motion $\mathbf{s}\left(t\right)$. The diffusion coefficient $\alpha$ and drift coefficient $b$ of such SDEs are homogeneous functions.Next with solutions of such SDEs, we study the corresponding stochastic Komatu–Loewner evolution, denoted as ${\mathrm{SKLE}}_{\alpha ,b}$. We introduce a function $b_{\mathrm{BMD}}$ measuring the discrepancy of a standard slit domain from $\mathbb{H}$ relative to BMD. We show that ${\mathrm{SKLE}}_{\sqrt{6},?b_{\mathrm{BMD}}}$ enjoys a locality property.     

Objectivity in Perspective: Relationism in the Interpretation of Quantum Mechanics

Pekka Lahti is a prominent exponent of the renaissance of foundational studies in quantum mechanics that has taken place during the last few decades. Among other things, he and coworkers have drawn renewed attention to, and have analyzed with fresh mathematical rigor, the threat of inconsistency at the basis of quantum theory: ordinary measurement interactions, described within the mathematical formalism by Schrödinger-type equations of motion, seem to be unable to lead to the occurrence of definite measurement outcomes, whereas the same formalism is interpreted in terms of probabilities of precisely such definite outcomes. Of course, it is essential here to be explicit about how definite measurement results (or definite properties in general) should be represented in the formalism. To this end Lahti et al. have introduced their objectification requirement that says that a system can be taken to possess a definite property if it is certain (in the sense of probability 1) that this property will be found upon measurement. As they have gone on to demonstrate, this requirement entails that in general definite outcomes cannot arise in unitary measuring processes.In this paper we investigate whether it is possible to escape from this deadlock. As we shall argue, there is a way out in which the objectification requirement is fully maintained. The key idea is to adapt the notion of objectivity itself, by introducing relational or perspectival properties. It seems that such a “relational perspective” offers prospects of overcoming some of the long-standing problems in the interpretation of quantum mechanics.     

Chordal Komatu–Loewner equation for a family of continuously growing hulls

In this paper, we discuss the chordal Komatu–Loewner equation on standard slit domains in a manner applicable not just to a simple curve but also a family of continuously growing hulls. Especially a conformally invariant characterization of the Komatu–Loewner evolution is obtained. As an application, we prove a sort of conformal invariance, or locality, of the stochastic Komatu–Loewner evolution ${\mathrm{SKLE}}_{\sqrt{6},?b_{\mathrm{BMD}}}$ in a fully general setting, which solves an open problem posed by Chen et al. (2017).     

Extensions and traces of functions of bounded variation on metric spaces

In the setting of a metric space equipped with a doubling measure and supporting a Poincaré inequality, and based on results by Björn and Shanmugalingam (2007) [7], we show that functions of bounded variation can be extended from any bounded uniform domain to the whole space. Closely related to extensions is the concept of boundary traces, which have previously been studied by Hakkarainen et al. (2014) [17]. On spaces that satisfy a suitable locality condition for sets of finite perimeter, we establish some basic results for the traces of functions of bounded variation. Our analysis of traces also produces novel pointwise results on the behavior of functions of bounded variation in their jump sets.     

Differential structure associated to axiomatic Sobolev spaces

The aim of this note is to explain in which sense an axiomatic Sobolev space over a general metric measure space (à la Gol’dshtein–Troyanov) induces – under suitable locality assumptions – a first-order differential structure.     

Einstein—Podolsky—Rosen experiments: The structure of the probability space. II

In part I, we have described the Einstein-Podolsky-Rosen experiments in the framework of an axiomatic probability theory. In part II, we present the proofs of the results stated in part I.     

Speed of particles and a relativity of locality in κ-Minkowski quantum spacetime

The last decade of research on κ-Minkowski noncommutative spacetime has been strongly characterized by a controversy concerning the speed of propagation of massless particles. Most arguments suggested that this speed should depend on the momentum of the particle strongly enough to be of interest for some ongoing experimental studies. But the only explicit derivations of worldlines in κ-Minkowski predicted no momentum dependence for the speed of massless particles. We return to this controversy equipped with the recent understanding that in some quantum spacetimes coincidences of events assessed by an observer who is distant from the events can be artifactual. We therefore set up our investigation in such a way that we never rely on the assessment of coincidences of events by distant observers. This allows us to verify explicitly that in κ-Minkowski simultaneously-emitted massless particles of different momentum are detected at different times, and establish a linear dependence of the detection times on momentum.     

二里头遗址绿松石的红外光谱产地识别

湖北十堰是世界著名优质绿松石产地,所产松石颜色鲜艳、质地细腻。距十堰绿松石矿区直线距离300 km的河南偃师二里头遗址于2002年以来出土了大量绿松石器。有学者推测二者存在供与用玉的关系,即存在古老的“绿松石之路”。然而,为了考证该推测,并试图给出二里头松石的矿源地,本次研究以十堰地区三个矿区(秦古、文峰和云盖寺)的三组样品、及一组二里头出土样品为研究对象,通过对获得的红外光谱特征进行比对与分析。谱学特征显示, 秦古、文峰和云盖寺样品红外光谱于1 200～950和700～400 cm-1峰位存在细微的,但可以识别的差异。在1 174 cm-1处,文峰样品中出现吸收峰,而秦古和云盖寺样品均没有出现。在700～400 cm-1范围内,文峰样品出现5个吸收峰,而秦古和云盖寺样品出现7个相似的吸收峰。二里头样品的红外光谱特征在以上峰位上与文峰绿松石差异较大,而与秦古、云盖寺松石的谱学特征相似。在1 159 cm-1附近,其吸收峰特征与云盖寺样品更加吻合。利用公式A=lg(1/T),将透射光谱值转换为吸光度光谱值,计算出二峰值相对吸收强度比值(R=A_{783 cm-1}/A_{837 cm-1})。文峰、秦古、云盖寺及二里头绿松石的比值范围依次为0.819～0.920,0.870～1.010,0.806～0.860和0.827～0.878。显然,二里头与云盖寺样品重合率最高。综上,我们认为所测二里头绿松石来自于云盖寺的可能性最大,并认为用红外光谱示踪出土文物来源有一定的参考或诊断意义。     

Locality of reference and the use of sojourn time variance for measuring queue unfairness

Sojourn time variance is widely used as an indication of queue unfairness. We demonstrate that this quantity has a disadvantage, since it is not local to the busy period in which it is measured. We show that RAQFM, a recently proposed queue fairness metric, does possess such a locality property.