Can the two-time interpretation of quantum mechanics solve the measurement problem?

Over many years, Aharonov and co-authors have proposed a new interpretation of quantum mechanics: the two-time interpretation. This interpretation assigns two wavefunctions to a system, one of which propagates forwards in time and the other backwards. In this paper, I argue that this interpretation does not solve the measurement problem. In addition, I argue that it is neither necessary nor sufficient to attribute causal power to the backwards-evolving wavefunction $〈\Phi |$ and thus its existence should be denied, contra the two-time interpretation. Finally, I follow Vaidman in giving an epistemological reading of $〈\Phi |$.     

Neue Gesichtspunkte zum 5. Buch Euklids

Summary The author's purpose is to read the main work of Euclid with modern eyes and to find out what knowledge a mathematician of today, familiar with the works of V. D. Waerden and Bourbaki, can gain by studying Euclid's theory of magnitudes, and what new insight into Greek mathematics occupation with this subject can provide.The task is to analyse and to axiomatize by modern means (i) in a narrower sense Book V. of the Elements, i.e. the theory of proportion of Eudoxus, (ii) in a wider sense the whole sphere of magnitudes which Euclid applies in his Elements. This procedure furnishes a clear picture of the inherent structure of his work, thereby making visible specific characteristics of Greek mathematics.After a clarification of the preconditions and a short survey of the historical development of the theory of proportions (Part I of this work), an exact analysis of the definitions and propositions of Book V. of the Elements is carried out in Part II. This is done word by word. The author applies his own system of axioms, set up in close accordance with Euclid, which permits one to deduce all definitions and propositions of Euclid's theory of magnitudes (especially those of Books V. and VI.).In this way gaps and tacit assumptions in the work become clearly visible; above all, the logical structure of the system of magnitudes given by Euclid becomes evident: not ratio — like something sui generis — is the governing concept of Book V., but magnitudes and their relation of having a ratio form the base of the theory of proportions. These magnitudes represent a well defined structure, a so-called Eudoxic Semigroup with the numbers as operators; it can easily be imbedded in a general theory of magnitudes equally applicable to geometry and physics.The transition to ratios — a step not executed by Euclid — is examined in Part III; it turns out to be particularly unwieldy. An elegant way opens up by interpreting proportion as a mapping of totally ordered semigroups. When closely examined, this mapping proves to be an isomorphism, thus suggesting the application of the modern theory of homomorphism. This theory permits a treatment of the theory of proportions as developed by Eudoxus and Euclid which is hardly surpassable in brevity and elegance in spite of its close affinity to Euclid. The generalization to a classically founded theory of magnitudes is now self-evident.

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Vorgelegt von J. E. Hofmann     

“The True” in Gottlob Frege's “Über die Grundlagen der Geometrie”

In this essay, I examine the metaphysical and metalogical ramifications of Gottlob Frege's controversy with David Hilbert and Alwin Korselt, over Hilbert's Grundlagen der Geometrie. These ramifications include(1) Korselt's original appeals to general metatheoretic Deutungen (interpretations);(2) Hilbert's puzzling belief that whatever is consistent in some sense exists; and(3) Frege's semantic monist conviction that theoretical sense and reference (mathematical and other) must be eindeutig lösbar (uniquely solvable).My principal conclusions are(4) that Frege's position in (3) represented a pervasively dogmatic presumption that his newly discovered quantification theory must have a propositional metatheory (the True; the False); and(5) that this needless assumption adversely affected not only his polemic against the moderate semantic relativism of Hilbert and Korselt, but also his reception of type-theoretic ideas, and greatly facilitated his vulnerability to the sort of self-referential inconsistency Russell discovered in Grundgesetz V.These conclusions also seem to me to provide a conceptual framework for several of Frege's other arguments and reactions which might seem more particular and disparate. These include(6) his arbitrary restrictions on the range of second-order quantification, which undercut his own tentative attempts to give accounts of independence and semantic consequence;(7) his uncharacteristic hesitation, even dismay, at the prospect that such accounts might eventuate in a genuinely quantificational metamathematics, whose Gegenstände (objects) might themselves be Gedanken (thoughts); and, perhaps most revealingly(8) his otherwise quite enigmatic, quasi-stoic doctrine that genuine formal deduction must be from premises that are true.A deep reluctance to pluralize or iterate the transition from theory to meta-theory would also be consonant, of course, with Frege's vigorous insistence that there can be only one level each of linguistic Begriffe (concepts) and Gegenstände (objects). With hindsight, such an assumption may seem more gratuitous in the philosophy of language (where it contributed, I would argue, to Wittgenstein's famous transition to the mystical in 6.45 and 6.522 of the Tractatus); but its more implausible implications in this wider context seemed to emerge more slowly.In the mathematical test-case discussed here, however, such strains were immediately and painfully apparent; the first models of hyperbolic geometry were described some thirty years before Frege drafted his polemic against Hilbert's pioneering exposition. It is my hope that a careful study of Frege's lines of argument in this relatively straightforward mathematical controversy may suggest other, parallel approaches to the richer and more ambiguous problems of his philosophy of language.Niemand kann zwei Herren dienen. Man kann nicht der Wahrheit dienen und der Unwahrheit. Wenn die euklidische Geometrie wahr ist, so ist die nichteuklidische Geometrie falsch, und wenn die nichteuklidische wahr ist, so ist die euklidische Geometrie falsch.No one can serve two masters. One cannot serve truth and untruth. If Euclidean geometry is true, non-Euclidean geometry is false, and if non-Euclidean [geometry] is true, Euclidean geometry is false. Über Euklidische Geometrie [Frege 1969], p. 183.     

Alkaloide ausVinca minor L. Vincadin,Minovin und Vincorin

Summary The isolation and characterisation of three new alkaloids fromVinca minor L. is described: Vincadine C₂₁H₂₈N₂O₂, Minovine C₂₂H₂₈N₂O₂, and Vincorine C₂₂H₂₈N₂O₃ belonging to the indol- and dihydroindol alkaloids.

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VII. Mitteilung, VI. Mitt.: sieheJ. Mokrý I. Kompi, P. efovi, und. Bauer, Coll. Czech. Chem. Comm., im Druck.     

Defensive steroids from a carrion beetle (Silpha americana)

Summary The defensive anal effluent discharged bySilpha americana in response to disturbance contains a mixture of steroids stemming from a glandular annex of the rectum. The compounds have been characterized as 15-hydroxyprogesterone (1, principal component), 5-pregnan-15-ol-3, 20-dione (2), 5-pregnan-3, 15-diol-20-one (3), 5-pregnan-7, 15-diol-3,20-dione (4), 5-pregnan-3, 7, 15-triol-20-one (5), 5-pregnan-16-ol-3,20-dione (6), and 5-pregnan-3, 16-diol-20-one (7), none previously found in insects. Bioassays with jumping spiders showed compounds1 and6 to be feeding deterrents at the 1 g level.Paper No. 78 of the series: Defense Mechanisms of Arthropods. Study supported by NIH (Grants AI-02908, AI-12020). We thank Maura Malarcher and Maria Eisner for excellent technical help, and the Squibb Institute of Medical Research for samples of authentic reference compounds.     

The effects of some tetracycline derivates on Ehrlich ascites carcinoma and HeLa cells in vitro

Zusammenfassung In-vitro-Nachweis der Hemmung der Proteo- und Nukleosynthese in den EAC-Zellen, sowie des Wachstums der HeLa-Zellen mit folgenden Derivaten des Tetrazyklins: Anhydrotetrazyklin, 4, 12-Anhydrodedimethylaminotetrazyklin und 12-Deoxydedimethylaminotetrazyklin.     

The “day of Brahman” in the work of Āryabhata

Summary In the astronomical treatise ryabhatya of ryabhata several verses are interpolated, namely all those verses in which either Brahman was mentioned or extremely large periods were introduced. The interpolator was known to AlBrn as ryabhata of Kusumapura, who belongs to the school of the elder ryabhata. The aim of the interpolator was to bring the teaching of the elder ryabhata into accordance with the revelation of Svayambh. Svayambh is another name for Brahm.     

The use mitochondrial mutants of yeast in the screening for new antimetabolites

Candida utilis Torulopsis globosa, , . T. globosa II-, 5% , .     

A history of the axiomatic formulation of probability from Borel to Kolmogorov: Part I

This paper, the first of two, traces the origins of the modern axiomatic formulation of Probability Theory, which was first given in definitive form by Kolmogorov in 1933. Even before that time, however, a sequence of developments, initiated by a landmark paper of E. Borel, were giving rise to problems, theorems, and reformulations that increasingly related probability to measure theory and, in particular, clarified the key role of countable additivity in Probability Theory.This paper describes the developments from Borel's work through F. Hausdorff's. The major accomplishments of the period were Borel's Zero-One Law (also known as the Borel-Cantelli Lemmas), his Strong Law of Large Numbers, and his Continued Fraction Theorem. What is new is a detailed analysis of Borel's original proofs, from which we try to account for the roots (psychological as well as mathematical) of the many flaws and inadequacies in Borel's reasoning. We also document the increasing realization of the link between the theories of measure and of probability in the period from G. Faber to F. Hausdorff. We indicate the misleading emphasis given to independence as a basic concept by Borel and his equally unfortunate association of a Heine-Borel lemma with countable additivity. Also original is the (possible) genesis we propose for each of the two examples chosen by Borel to exhibit his new theory; in each case we cite a now neglected precursor of Borel, one of them surely known to Borel, the other, probably so. The brief sketch of instances of the Cantelli lemma before Cantelli's publication is also original.We describe the interesting polemic between F. Bernstein and Borel concerning the Continued Fraction Theorem, which serves as a rare instance of a contemporary criticism of Borel's reasoning. We also discuss Hausdorff's proof of Borel's Strong Law (which seems to be the first valid proof of the theorem along the lines sketched by Borel).In retrospect, one may ask why problems of geometric (or continuous) probability did not give rise to the (Kolmogorov) view of probability as a form of measure, rather than the study of repeated independent trials, which was Borel's approach. This paper shows that questions of geometric probability were always the essential guide to the early development of the theory, despite the contrary viewpoint exhibited by Borel's preferred interpretation of his own results.