An observable on a quantum structure is any σ-homomorphism of quantum structures from the Borel σ-algebra of the real line into the quantum structure which is in our case a monotone σ-complete effect algebra with the Riesz Decomposition Property. We show that every observable is a smearing of a sharp observable which takes values from a Boolean σ-subalgebra of the effect algebra, and we prove that for every element of the effect algebra there corresponds a spectral measure.

Counterpunch, November 23, 2009 In his wild and slanderous "Open Letter to Amnesty International" (signed, fittingly, "Yours, in disgust and despair"),[2] The Guardian - Observer's veteran reporter Ed Vulliamy explains that two "main concerns" motivated him to draft his repudiation of AI's choice of Noam Chomsky to deliver this 2009 Stand Up For Justice lecture: One is that the "pain" individuals such as Chomsky are alleged to cause the "survivors and the bereaved" of the wars in the former Yugoslavia is (...) "immeasurable," and Vulliamy feels some kind of need to help mitigate this pain; the other, apparently, is that the "historical record" as it pertains to these wars is too precious and too fragile to be left in the wrong pair of hands. "For Amnesty International, of all people, to honour this man is to tear up whatever credibility they have estimably and admirably won over the decades, and to reduce all they say hitherto to didactic nonsense," Vulliamy writes. "By inviting Chomsky to give this lecture, Amnesty condemns itself to ridicule at best, hurtful malice at worst -- Amnesty joins the revisionists in spitting on the graves of the dead.". (shrink)

SummaryIn 1968, a prospective study was started in collaboration with the Family Planning Association to try to provide a balanced view of the beneficial and harmful effects of different methods of contraception. This investigation is now in progress at seventeen clinics and over 17,000 women are under observation. At the time of recruitment, all these women were married white British subjects, aged 25–39 years, who voluntarily agreed to participate. Fifty-six per cent were using oral contraceptives, 25% were using a diaphragm (...) and 19% were using an intrauterine device. During follow-up each woman is questioned at return visits to the clinic and a record of pregnancies and their outcome, hospital referrals, changes in contraceptive methods and the results of cervical smears, is accumulated. Women who default are sent a postal questionnaire and, if this is not returned, are telephoned or visited in their homes to collect the necessary information.So far, data obtained during 56,000 woman-years of observation are available for analysis. Follow-up has been maintained with an annual lapse rate of about 0.3%due to withdrawal of co-operation or loss of contact; adherence to the method of contraception in use at recruitment has been reasonably good, and the reporting of pregnancies and hospital admissions appears to have been both reliable and unbiased.The present data include only 24 deaths, so the mortality associated with different contraceptive methods cannot yet be estimated. With regard to morbidity, however, our preliminary results closely resemble those obtained in the prospective study carried out by the Royal College of General Practitioners and in the principal retrospective studies carried out in Britain and the United States. Women who used oral contraceptives at the start of the study experienced adeficiencyof hospital referrals for cancer, benign lesions of the breast, menstrual disorders other than amenorrhoea, duodenal ulcer, and retention cysts of the ovary; they showed anexcessof referrals for cerebrovascular disease, cervical erosion, skin disorders, self-poisoning, migraine, venous thrombosis and embolism, hayfever, gallbladder disease, amenorrhoea, and sterility. Women who used a diaphragm showed adeficiencyof hospital referrals for carcinoma-in-situ and dysplastic lesions of the cervix uteri and accidental injury; and anexcessof referrals for haemorrhoids and cystitis. Women who used an IUD experienced anexcessof hospital referrals for anaemia, varicose veins and salpingitis. About half of these differences were predicted from other studies while some suggestive evidence already existed for a further five. Of the remaining six, some probably reflect the influence of selective factors or chance.Multiple pregnancies, stillbirths, malformations, the sex ratio and birthweight showed no consistent relationship to method of contraception. The outcome of unplanned pregnancies occurring in women using an IUD, however, was remarkably unfavourable both in terms of ectopic gestation and miscarriage.Clear evidence was found of impairment of fertility after discontinuation of oral contraceptives. Whether this is likely to lead to permanent sterility in some women is uncertain.The study has provided data on the efficacy of a wide variety of contraceptive methods. In general the failure rates are in keeping with those obtained in other large-scale studies, save that those for the diaphragm and the sheath are much lower than those usually quoted.The available evidence does not yet allow a final balance to be struck between the benefits and risks associated with the new methods of contraception that have become widely used during the last two decades. It seems clear, however, that there are no material risks associated with the use of the diaphragm apart from the risk of pregnancy and that there may be some unintended benefits. (shrink)

Two different characterizations of POV measures with commutative range are compared using a representation of some stochastic operators by (weak) Markov kernels. A representation by Choquet theorem is obtained as an integral over functions of a sharp observable appearing in one of the characterizations. A Naimark extension is constructed.

In lieu of an abstract, here is a brief excerpt of the content:The Journal of Aesthetic Education 38.1 (2004) 12-22 [Access article in PDF] Art of a Child with Autism:Drawing Systems and Proto Mathematics Julia Kellman Sung, a five year old girl with autism, was enrolled by her mother in the university Saturday art program with the hope that Sung's favorite church school teacher, a graduate student in art education, would be able to tutor her daughter during the weekly classes. (...) Though hesitant because of her inexperience with autistic children and because of Sung's frequently angry tantrums on Sundays and the little girl's inability to speak, the young teacher, nonetheless, agreed to the plan. Her concerns proved unfounded, for Sung was able to work in the midst of the churning mass of noisy pre-K classmates without any signs of the fury that drove her to screaming, biting fits in church school. Additionally, and to everyone's delight, Sung's ability to develop as an image-maker was itself confirmed within the first few weeks of art class, dispelling any remaining doubts of her art aptitude or the value of art classes for the little girl.Additional questions and considerations arose about Sung and her art during the classes. How might one understand Sung's changing imagery? What might such explanations and images suggest about Sung herself and her activities? What might her art indicate about her similarity to other children and their art making? The possible answers to these and related queriespresented themselves during the semester, suggesting new avenues for inquiry surrounding both the wordless little girl and her Saturday morning creations.What follows is the story of Sung and her graphic development as it unfolded during the art class. Further, it is an attempt to uncover what Sung's drawings suggest about methods that are useful in the examination of the art of an autistic child. Documentation was carried out with a 35 mm. camera and color copier throughout the semester. Ethnographic methods including participant observation and interviews were employed to gather contextual data. Alfred Schutz's phenomenological sociology allowed for [End Page 12] consideration of nonverbal and verbal social interactions and behaviors. 1 A search of the literature of early mathematical development and drawing systems provided the underpinnings for early insights and later hypotheses. Here is Sung's story. Sung Sung, thick black hair swung forward to hide her face, lies prone in the middle of the busy classroom oblivious to the surging, chattering children around her, so intent is she on the sketchbook in which she draws. Next to her left elbow teeters a stack of a half dozen boxes of thick craypas from which she snatches colors, never looking at the hue she grabs. Her drawing behavior has a pattern; it looks like this. Shuffle through the identical boxes. Choose a box. Open it. Snatch out a bright waxy craypa. Hold it close to the eyes. Sniff it. Lick it. If the craypa passes muster, scribble with it in rich heavy lines — banana-like arcs, large solid dots the size of cherries, rectangular patches, and a variety of forms that come and go from one drawing to the next, like heat lightening on a summer evening. Her less frequent forms include: an enclosed yellow irregular shape with a dark dot in the middle suggesting a fried egg; a two-sided zig-zag; X forms; and solid and empty trapezoids made sail-like with superimposed crosses serving as mast and boom.Unlike the chosen craypas, however, those that do not pass Sung's inspection suffer a terrible fate; they are broken in two and their pieces tossed without ceremony to opposite sides of the room to be trodden into flat, bright smears by the other children in the class, pathetic traces of Sung's art. The craypas boxes themselves also play a role. For when they are closed they are used as blocks or toys, objects to be neatly stacked and restacked or placed side by side on the floor. When they are open, however, they are mere receptacles, passively holding... (shrink)

In Dirac-Bergmann constrained dynamics, a first-class constraint typically does not _alone_ generate a gauge transformation. By direct calculation it is found that each first-class constraint in Maxwell's theory generates a change in the electric field E by an arbitrary gradient, spoiling Gauss's law. The secondary first-class constraint p^i,_i=0 still holds, but being a function of derivatives of momenta, it is not directly about E. Only a special combination of the two first-class constraints, the Anderson-Bergmann -Castellani gauge generator G, leaves E (...) unchanged. This problem is avoided if one uses a first-class constraint as the generator of a _canonical transformation_; but that partly strips the canonical coordinates of physical meaning as electromagnetic potentials and makes the electric field depend on the smearing function, bad behavior illustrating the wisdom of the Anderson-Bergmann Lagrangian orientation of interesting canonical transformations. The need to keep gauge-invariant the relation dot{q}- dH/dp= -E_i -p^i=0 supports using the primary Hamiltonian rather than the extended Hamiltonian. The results extend the Lagrangian-oriented reforms of Castellani, Sugano, Pons, Salisbury, Shepley, _etc._ by showing the inequivalence of the extended Hamiltonian to the primary Hamiltonian even for _observables_, properly construed in the sense implying empirical equivalence. Dirac and others have noticed the arbitrary velocities multiplying the primary constraints outside the canonical Hamiltonian while apparently overlooking the corresponding arbitrary coordinates multiplying the secondary constraints _inside_ the canonical Hamiltonian, and so wrongly ascribed the gauge quality to the primaries alone, not the primary-secondary team G. Hence the Dirac conjecture about secondary first-class constraints rests upon a false presupposition. The usual concept of Dirac observables should also be modified to employ the gauge generator G, not the first-class constraints separately, so that the Hamiltonian observables become equivalent to the Lagrangian ones such as the electromagnetic field F. (shrink)

Several arguments are considered which purport to demonstrate the impossibility of theory-neutral observation. The most important of these infers the continuity of observation with theory from the presumed continuity of perception with cognition, a doctrine widely espoused in recent cognitive psychology. An alternative psychological account of the relation between cognition and perception is proposed and its epistemological consequences for the observation/theory distinction are then explored.

In this paper, a novel approach for word extraction and character segmentation from the handwritten Bangla document images is reported. At first, a modified Run Length Smoothing Algorithm, called Spiral Run Length Smearing Algorithm, is applied for the extraction of words from the text lines of unconstrained handwritten Bangla document images. This technique has helped to overcome some of the drawbacks of standard horizontal and vertical RLSA techniques. SRLSA technique has been applied on the Bangla handwritten document image database (...) CMATERdb1.1.1 and the success rate of the word extraction is found to be 86.01%. In the second part of the work, we have presented a useful solution to the problem on how best word images of handwritten Bangla script can be segmented into constituent characters. Moreover, the technique can segment the words having discontinuity in Matra, a prominent feature of Bangla script. It also optimizes the trade-off between under/over segmentation as Matra region and segmentation points are estimated more precisely. As a result, better word segmentation accuracy is achieved with minimal data loss. Here, a success rate of 92.48% is observed on a dataset of 750 handwritten Bangla words which is 3.35% higher than that of our earlier techniques. (shrink)

The program of a physical concept of information is outlined in the framework of quantum theory. A proposal is made for how to avoid the intuitive introduction of observables. The conventional and the Everett interpretations in principle may lead to different dynamical consequences. An ensemble description occurs without the introduction of an abstract concept of information.

The concept of observability of entities in physical science is typically analysed in terms of the nature and significance of a dichotomy between observables and unobservables. In the present work, however, this categorization is resisted and observability is analysed in a descriptive way in terms of the information which one can receive through interaction with objects in the world. The account of interaction and the transfer of information is done using applicable scientific theories. In this way, the question of (...) observability of scientific entities is put to science itself. The result is a demonstration that observability has many dimensions, some more epistemically significant than others. (shrink)

In this chapter I consider what recent work on background independent physics can do for structuralism, and what structuralism can do for background independent physics. I focus on the problems of time and observables in gravitational physics. The ‘frozen’ character of the observables of general relativity is usually considered to constitute a serious problem for the theory. I argue that by invoking correlations between physical quantities we can provide a natural explanation of the appear- ance of time and (...) change in timeless structures. I argue that this response can resolve a problem with Max Tegmark’s ‘extreme structuralist’ position. I then consider what bearing the mathematical representation used has on the debate over the nature of structure in discussions of structural realism. I argue that it has both the resources to ground the notion of structure in physics and to answer the ‘no relations without relata’ objection. (shrink)

Bohmian mechanics is arguably the most naively obvious embedding imaginable of Schr¨ odinger’s equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at first appear to have little to do with the spectrum of predictions of quantum mechanics. It turns out, however, that as a consequence of the defining dynamical equations of Bohmian mechanics, when a system has wave function ψ its configuration is typically (...) random, with probability density ρ given by |ψ|2, the quantum equilibrium distribution. It also turns out that the entire quantum formalism, operators as observables and all the rest, naturally emerges in Bohmian mechanics from the analysis of “measurements.” This analysis reveals the status of operators as observables in the description of quantum phenomena, and facilitates a clear view of the range of applicability of the usual quantum mechanical formulas. (shrink)

Observables on hypergraphs are described by event-valued measures. We first distinguish between finitely additive observables and countably additive ones. We then study the spectrum, compatibility, and functions of observables. Next a relationship between observables and certain functionals on the set of measures M(H) of a hypergraph H is established. We characterize hypergraphs for which every linear functional on M(H) is determined by an observable. We define the concept of an “effect” and show that observables are (...) related to effect-valued measures. Finally, we define “operational” transformations from M(H) to itself and show that they can be described as a certain combination of effects. (shrink)

This paper is devoted to clarification of the notion of entanglement through decoupling it from the tensor product structure and treating as a constraint posed by probabilistic dependence of quantum observable _A_ and _B_. In our framework, it is meaningless to speak about entanglement without pointing to the fixed observables _A_ and _B_, so this is _AB_-entanglement. Dependence of quantum observables is formalized as non-coincidence of conditional probabilities. Starting with this probabilistic definition, we achieve the Hilbert space characterization (...) of the _AB_-entangled states as amplitude non-factorisable states. In the tensor product case, _AB_-entanglement implies standard entanglement, but not vise verse. _AB_-entanglement for dichotomous observables is equivalent to their correlation, i.e., \(\langle AB\rangle _{\psi} \not = \langle A\rangle _{\psi} \langle B\rangle _{\psi}.\) We describe the class of quantum states that are \(A_{u} B_{u}\) -entangled for a family of unitary operators (_u_). Finally, observables entanglement is compared with dependence of random variables in classical probability theory. (shrink)

We address the problem of observables in generally invariant spacetime theories such as Einstein’s general relativity. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we propose a generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, that is naturally identified with the physical spacetime.

How should we characterise the observable aspects of quantum theory? This paper argues that philosophers and physicists should jettison a standard dogma: that observables must be represented by self-adjoint or Hermitian operators. Four classes of non-standard observables are identified: normal operators, symmetric operators, real-spectrum operators, and none of these. The philosophical and physical implications of each are explored.

This article begins with a review of the framework of fuzzy probability theory. The basic structure is given by the σ-effect algebra of effects (fuzzy events) $\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ and the set of probability measures $M_1^ + {\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ on a measurable space $\left( {\Omega ,\mathcal{A}} \right)$ . An observable $X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right)$ is defined, where $\begin{gathered} X:\mathcal{B} \to {\text{ }}\mathcal{E}{\text{ }}\left( {\Omega ,\mathcal{A}} \right) \\ \left( {\Lambda ,{\text{ }}\mathcal{B}} \right) (...) \\ \end{gathered} $ is the value space of X. It is noted that there exists a one-to-one correspondence between states on $\mathcal{E} \left( {\Omega ,\mathcal{A} } \right)$ and elements of $M_1^ + {\text{ }}\left( {\Omega ,\mathcal{A} } \right)$ and between observables $X:\mathcal{B} \to \mathcal{E} \left( {\Omega ,\mathcal{A} } \right)$ and σ-morphisms from $\mathcal{E} \left( {\Lambda , \mathcal{B}} \right)$ to $\mathcal{E} \left( {\Omega , \mathcal{A}} \right)$ . Various combinations of observables are discussed. These include compositions, products, direct products, and mixtures. Fuzzy stochastic processes are introduced and an application to quantum dynamics is considered. Quantum effects are characterized from among a more general class of effects. An alternative definition of a statistical map $M_1^ + {\text{ }}\left( {\Lambda ,\mathcal{B} } \right)$ is given and it is shown that any statistical map has a unique extension to a statistical operator. Finally, various combinations of statistical maps are discussed and their relationships to the corresponding combinations of observables are derived. (shrink)

Is change missing in Hamiltonian Einstein–Maxwell theory? Given the most common definition of observables, observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive electromagnetism with gauge freedom are inequivalent to those of massive electromagnetism without gauge freedom. The alternative Pons–Salisbury–Sundermeyer definition of observables, aiming for Hamiltonian–Lagrangian equivalence, uses the gauge generator G, a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent (...) class='Hi'>observables for equivalent massive electromagnetisms. For General Relativity, G generates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time versus 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that G must generate the 4-dimensional Lie derivative for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein–Maxwell theory? Pons, Salisbury and Shepley have studied G for Einstein–Yang–Mills. For Einstein–Maxwell, both \ and \ are invariant under electromagnetic gauge transformations and covariant under 4-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds. (shrink)

Results on the observational indistinguishability of spacetimes demonstrate the impossibility of determining by deductive inference which is our spacetime, no matter how extensive a portion of the spacetime is observed. These results do not illustrate an underdetermination of theory by evidence, since they make no decision between competing theories and they make little contact with the inductive considerations that must ground such a decision. Rather, these results express a variety of indeterminism in which a specification of the observable past always (...) fails to fix the remainder of a spacetime. This form of indeterminism is more troubling than the familiar indeterminism of quantum theory. The inductive inferences that can discriminate among the different spacetime extensions of the observed past are here called “opaque,” which means that we cannot readily see the warrant that lies behind them. (shrink)

We define two types of convergence for observables on a quantum logic which we call M-weak and uniform M-weak convergence. These convergence modes correspond to weak convergence of probability measures. They are motivated by the idea that two (in general unbounded) observables are “close” if bounded functions of them are “close.” We show that M-weak and uniform M-weak convergence generalize strong resolvent and norm resolvent convergence for self-adjoint operators on a Hilbert space. Also, these types of convergence strengthen (...) the weak operator convergence and operator norm convergence of bounded self-adjoint operators on a Hilbert space. Finally, we consider spectral perturbation by showing that the spectra of approximating observables approach the spectrum of the limit in a certain sense. (shrink)

The extended semantic realism (ESR) model proposes a new theoretical perspective which embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) into a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide in this review an overall view on the present status of our research on this topic. We attain in a new, shortened way a mathematical representation of the generalized observables introduced by the ESR model and a generalization of the projection postulate of (...) elementary QM. Basing on these results we prove that the Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, a modified BCHSH inequality and quantum predictions hold together in the ESR model because they refer to different parts of the picture of the physical world supplied by the model. Then we show that a new mathematical representation of mixtures must be introduced in the ESR model which does not coincide with the standard representation in QM and avoids some deep problems that arise from the representation of mixtures provided by QM. Finally we get a nontrivial generalization of the Lüders postulate, which is justified in a special case by introducing a reasonable physical assumption on the evolution of the compound system made up of the measured system and the measuring apparatus. (shrink)

Science is at a cross-roads. For several decades, the Standard Model of particle physics has managed to fit vast amounts of particle scattering data remarkably well, but many questions remain. During those decades, some sophisticated theoretical hypotheses such as string theory, quantum gravity, and quantum cosmology have been proposed and studied intensively, in an effort to break the log-jam of the Standard Model. None of those hypotheses have succeeded to date. Of greater concern is the increasing tendency by some practitioners (...) in those fields to downplay the empirical principles of science. In response, this book is a restatement of those principles, covering numerous aspects of observation. A particular focus is on contextuality versus realism, the two fundamentally contrasting ideologies that underpin modern physics. (shrink)

In climate science, observational gridded climate datasets that are based on in situ measurements serve as evidence for scientific claims and they are used to both calibrate and evaluate models. However, datasets only represent selected aspects of the real world, so when they are used for a specific purpose they can be a source of uncertainty. Here, we present a framework for understanding this uncertainty of observational datasets which distinguishes three general sources of uncertainty: (1) uncertainty that arises during the (...) generation of the dataset; (2) uncertainty due to biased samples; and (3) uncertainty that arises due to the choice of abstract properties, such as resolution and metric. Based on this framework, we identify four different types of dataset ensembles — parametric, structural, resampling, and property ensembles—as tools to understand and assess uncertainties arising from the use of datasets for a specific purpose. We advocate for a more systematic generation of dataset ensembles by using these sorts of tools. Finally, we discuss the use of dataset ensembles in climate model evaluation. We argue that a more systematic understanding and assessment of dataset uncertainty is needed to allow for a more reliable uncertainty assessment in the context of model evaluation. The more systematic use of such a framework would be beneficial for both scientific reasoning and scientific policy advice based on climate datasets. (shrink)

Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, an aspect of the problem of time. Definitions can be tested using equivalent formulations of a theory, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, thus constraining definitions. For massive photons, the (...) de Broglie-Proca non-gauge formulation observable A_{\mu} is equivalent to the Stueckelberg-Utiyama gauge formulation quantity A_{\mu} + \partial_{\mu} \phi, which must therefore be an observable. To achieve that result, observables must have 0 Poisson bracket not with each first-class constraint, but with the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints, in accord with the Pons-Salisbury-Sundermeyer definition of observables. The definition for external gauge symmetries can be tested using massive gravity, where one can install gauge freedom by parametrization with clock fields X^A. The non-gauge observable g^{\mu\nu} has the gauge equivalent X^A,_{\mu} g^{\mu\nu} X^B,_{\nu}. The Poisson bracket of X^A,_{\mu} g^{\mu\nu} X^B,_{\nu} with G turns out to be not 0 but a Lie derivative. This non-zero Poisson bracket refines and systematizes Kuchař's proposal to relax the 0 Poisson bracket condition with the Hamiltonian constraint. Thus observables need covariance, not invariance, in relation to external gauge symmetries. The Lagrangian and Hamiltonian for massive gravity are those of General Relativity + \Lambda + 4 scalars, so the same definition of observables applies to General Relativity. Local fields such as g_{\mu\nu} are observables. Thus observables change. Requiring equivalent observables for equivalent theories also recovers Hamiltonian-Lagrangian equivalence. (shrink)

Recently there have emerged an assortment of theorems relating to the ‘absoluteness of emerged events,’ and these results have sometimes been used to argue that quantum mechanics may involve some kind of metaphysically radical non-absoluteness, such as relationalism or perspectivalism. However, in our view a close examination of these theorems fails to convincingly support such possibilities. In this paper we argue that the Wigner’s friend paradox, the theorem of Bong et al and the theorem of Lawrence et al are all (...) best understood as demonstrating that if quantum mechanics is universal, and if certain auxiliary assumptions hold, then the world inevitably includes various forms of ‘disaccord,’ but this need not be interpreted in a metaphysically radical way; meanwhile, the theorem of Ormrod and Barrett is best understood either as an argument for an interpretation allowing multiple outcomes per observer, such as the Everett approach, or as a proof that quantum mechanics cannot be universal in the sense relevant for this theorem. We also argue that these theorems taken together suggest interesting possibilities for a different kind of relational approach in which _interaction_ states are relativized whilst observed events are absolute, and we show that although something like ‘retrocausality’ might be needed to make such an approach work, this would be a very special kind of retrocausality which would evade a number of common objections against retrocausality. We conclude that the non-absoluteness theorems may have a significant role to play in helping converge towards an acceptable solution to the measurement problem. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Five Poems AMIT MAJMUDAR Observing Orpheus I hear the meaning turn back in his throat like Eurydice on the way up from the darkness. Music’s meaning is its making. As for me, I am one more animal in his entourage, learning a new thirst, finding a new south. None of us knew we had this instinct in us. If deserts hide wildflowers until first rain, bright ears are blossoming (...) out of our skulls. He doesn’t have much longer. I know this myth. A God douses the fire with a beehive. The Maenads smear their faces with a warpaint made of stoneground fireflies and pine sap. Hands—hands like his, that drew music through lyre strings into our forest like pieces of bread through a prison fence— are reaching for his body now, his lyre. Their weapons are hands, nothing but hands. They are infinite. They are enough. arion 27.1 spring/summer 2019 Her Metamorphoses First a beetle, body armor forged of chitin, exoskeleton he’ll never bruise, Undiscovered, unapologetically hermetic on her own Galapagos. Next a fruit bat, echolocating tangerines like a blind woman singing up at stars. Then a patio lizard, sunning herself for as long as she needs, A better place for keeping warm than bed with him. Next a sleek water moccasin, quick to make out another woman’s heat signature on his neck, Even quicker to strike. A caterpillar to poke holes in his lying roses And from that destruction to fashion two beautiful wings for herself. A buzzard, to clean up the roadside pile he left of her. A woman in full with no more soft blind pupa stages of her life cycle left, No more forms to force herself to fit for the sake of his pleasure, No more shapeshifts, no more slimming stripes, no more abdominal crunches: Just this body, just this last name, just this apartment, just this bowl of midnight cereal. Just her. 106 five poems Sisyphus Shove hard, shove, shove hard, eyes bloodshot, knees bent Till your boulder goes weightless and races ahead in descent. Force its dark door open inch by grim inch, Shove hard, shove, shove hard, eyes bloodshot, knees bent, Heels dug deep in hell’s steep hillside, teeth clenched. What gravity strips from you, gravity grants you again. Shove hard, shove, shove hard, eyes bloodshot, knees bent Till your body goes weightless and races ahead in ascent. Amit Majmudar 107 A Trinket for Persephone A deathwatch beetle burrows in the pale hall of your marrow, your underground, your tube of bone on which you’re riding home alone. This blackwinged locket with your soul emerges rattling from a hole, a rattle in your emptied throat, the diva’s final, graceless notes, a clicking echoed in the rafters, this bugbear insect coming after to scuttle across the marshy chest, sinkhole navel, and pubic nest out to the yard, below the porch untrackable by any torch until this bug with you inside has burrowed to the other side. It drops into the underworld, as if from some cocoon unfurled, to scale a queenly wrist and rest your brooch of black upon her breast. 108 five poems Four Ways of Looking at Argus 1. His Vigil These hundred eyes, these hundred balloons Tied to the boy-small wrist of my mind Are down to ninety-nine. I lost one to a bee sting late last June— I never thought of them as fragile Until that pinprick broke my vigil. I’m slowing down. I didn’t blink in time. I have no inkling why I keep This vigil—surely not to watch, Panoptic from this mountaintop, A heifer drifting off to sleep? I’m here, I must be here, to see A signal fire from the east That warns of Olympus under siege And Ares gory from a rout, Athena’s owl’s eyes gouged out, The naiads naked in a pen, The whole world given up to men. The Gods will need a monster then. 2. After Martial Hermes was in a fix: He needed lullabies To shutter Argus’s one hundred eyes And get the tethered heifer—coal-eyed Io—free Of Hera’s... (shrink)

We describe a particular class of pairs of quantum observables which are extremal in the convex set of all pairs of compatible quantum observables. The pairs in this class are constructed as uniformly noisy versions of two mutually unbiased bases with possibly different noise intensities affecting each basis. We show that not all pairs of MUB can be used in this construction, and we provide a criterion for determining those MUB that actually do yield extremal compatible observables. (...) We apply our criterion to all pairs of Fourier conjugate MUB, and we prove that in this case extremality is achieved if and only if the quantum system Hilbert space is odd-dimensional. Remarkably, this fact is no longer true for general non-Fourier conjugate MUB, as we show in an example. Therefore, the presence or the absence of extremality is a concrete geometric manifestation of MUB inequivalence, that already materializes by comparing sets of no more than two bases at a time. (shrink)

The paper explores how, in economics and biology, theoretical models are used as explanatory devices. It focuses on a modelling strategy by which, instead of starting with an unexplained regularity in the world, the modeller begins by creating a credible model world. The model world exhibits a regularity, induced by a mechanism in that world. The modeller concludes that there may be a part of the real world in which a similar regularity occurs and that, were that the case, the (...) model would offer an explanation. Little concrete guidance is given about where such a regularity might be found. Three modelling exercises in evolutionary game theory—one from economics and two from biology—are used as case studies. Two of these (one from each discipline) exemplify ‘explanation in search of observation’. The third goes a step further, analysing a regularity in a model world and treating it as informative about the real world, but without saying anything about real phenomena. The paper argues that if the relation between the model and real worlds is understood in terms of similarity, and if modelling is understood as an ongoing discovery process rather than as the demonstration of empirical truths, there can be value in creating explanations before finding the regularities that are to be explained. (shrink)

Every linear perspective image has a center of the perspective construction. Only when observed from that location does a 2D image provide the same stimulus as the original 3D scene. Geometric analyses indicate that observing the image from other vantage points should affect the perceived spatial structure of the scene conveyed by the image, involving transformations such as shear, compression, and dilation. Based on previous research, this paper presents a detailed account of these transformations. The analyses are presented in a (...) uniform manner, illustrated with special 3D diagrams, and embedded in a wider framework of related perspective paradigms. Such analyses provide the potential theoretical basis for empirical work on the effects of changes of observer vantage points on the perception of spatial structure in perspective images. (shrink)

Two postulates concerning observables on a quantum logic are formulated. By Postulate 1 compatibility of observables is defined by the strong topology on the set of observables. Postulate 2 requires that the range of the sum of observables ought to be contained in the smallestC-closed sublogic generated by their ranges. It is shown that the Hilbert space logicL(H) satisfies the two postulates. A theorem on the connection between joint distributions of types 1 and 2 on the (...) logic satisfying Postulate 2 is proved. (shrink)

The notion of fuzzy event is introduced in the theory of measurement in quantum mechanics by indicating in which sense measurements can be considered to yield fuzzy sets. The concept of probability measure on fuzzy events is defined, and its general properties are deduced from the operational meaning assigned to it. It is pointed out that such probabilities can be derived from the formalism of quantum mechanics. Any such probability on a given fuzzy set is related to the frequency of (...) occurrence within that set of points in a random sample, where the sample points are themselves fuzzy sets obtained as outcomes of measurements of, in general, incompatible observables on replicas of the system in the same prepared state. (shrink)

Observables have a dual nature in both classical and quantum kinematics: they are at the same time quantities, allowing to separate states by means of their numerical values, and generators of transformations, establishing relations between different states. In this work, we show how this twofold role of observables constitutes a key feature in the conceptual analysis of classical and quantum kinematics, shedding a new light on the distinguishing feature of the quantum at the kinematical level. We first take (...) a look at the algebraic description of both classical and quantum observables in terms of Jordan–Lie algebras and show how the two algebraic structures are the precise mathematical manifestation of the twofold role of observables. Then, we turn to the geometric reformulation of quantum kinematics in terms of Kähler manifolds. A key achievement of this reformulation is to show that the twofold role of observables is the constitutive ingredient defining what an observable is. Moreover, it points to the fact that, from the restricted point of view of the transformational role of observables, classical and quantum kinematics behave in exactly the same way. Finally, we present Landsman’s general framework of Poisson spaces with transition probability, which highlights with unmatched clarity that the crucial difference between the two kinematics lies in the way the two roles of observables are related to each other. (shrink)

We show how effect algebras arise in physics and how they can be used to tie together the observables, states and symmetries employed in the study of physical systems. We introduce and study the unifying notion of an effect-observable-state-symmetry-system (EOSS-system) and give both classical and quantum-mechanical examples of EOSS-systems.

The structure of covariant observables—normalized positive operator measures (POMs)—is studied in the case of a type I symmetry group. Such measures are completely determined by kernels which are measurable fields of positive semidefinite sesquilinear forms. We produce the minimal Kolmogorov decompositions for the kernels and determine those which correspond to the extreme covariant observables. Illustrative examples of the extremals in the case of the Abelian symmetry group are given.

In this article I reply to Fleming׳s response to my ‘Time and quantum theory: a history and a prospectus.’ I take issue with two of his claims: (i) that quantum theory concerns the (potential) properties of eternally persisting objects; (ii) that there is an underdetermination problem for Positive Operator Valued Measures (POVMs). I advocate an event-first view which regards the probabilities supplied by quantum theory as probabilities for the occurrence of physical events rather than the possession of properties by persisting (...) objects. (shrink)

A reproducibility principle is formulated and adopted as the guiding criterion for the acceptance of an experimental procedure as a simultaneous measurement of several observables. It is pointed out that this criterion can be applied to classical as well as quantum physics, and that it incorporates compatible as well as incompatible observables. The concept of fuzzy probability measure is presented as a possible mathematical tool for the description of statistical processes involving measurements of incompatible observables.

This paper challenges a central tenet of constructive empiricism, namely that empirical adequacy has a privileged epistemic status. I argue that perceptions of observables are theory-wrought, and theory-wrought in the same ways as the observation sentences we use to describe those perceptions, van Fraassen can draw no privileged or fundamental distinction between what we observe and interpreting those observations through theory. Since empirical adequacy depends upon accurately describing what we observe, and we have no theory-independent reason to believe that (...) what we ‘observe’ is a reflection of what is true, then empirical adequacy can inherit no special connection to what is real via what we observe. The epistemological significance of empirical adequacy is thereby reduced. (shrink)

Change and local spatial variation are missing in Hamiltonian general relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian–Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson–Bergmann–Castellani gauge generator G, a tuned sum of first-class constraints. Kuchař waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two (...) reforms might use the gauge generator but permit non-zero Lie derivative Poisson brackets for the external gauge symmetry of General Relativity. Fortunately one can test definitions of observables by calculation using two formulations of a theory, one without gauge freedom and one with gauge freedom. The formulations, being empirically equivalent, must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg–Utiyama electromagnetism, one finds that the usual definition fails while the Pons–Salisbury–Sundermeyer definition with G succeeds. This definition does not readily yield change in GR, however. Should GR’s external gauge freedom of general relativity share with internal gauge symmetries the 0 Poisson bracket, or is covariance sufficient? A graviton mass breaks the gauge symmetry, but it can be restored by parametrization with clock fields. By requiring equivalent observables, one can test whether observables should have 0 or the Lie derivative as the Poisson bracket with the gauge generator G. The latter definition is vindicated by calculation. While this conclusion has been reported previously, here the calculation is given in some detail. (shrink)

Existing "no hidden variable proofs" for quantum mechanics deal exclusively with observables with discrete spectra. This note shows that similar results hold for observables with continuous spectra.