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 $〈\Phi |$.     

Linear structures,causal sets and topology

Causal set theory and the theory of linear structures (which has recently been developed by Tim Maudlin as an alternative to standard topology) share some of their main motivations. In view of that, I raise and answer the question how these two theories are related to each other and to standard topology. I show that causal set theory can be embedded into Maudlin׳s more general framework and I characterise what Maudlin׳s topological concepts boil down to when applied to discrete linear structures that correspond to causal sets. Moreover, I show that all topological aspects of causal sets that can be described in Maudlin׳s theory can also be described in the framework of standard topology. Finally, I discuss why these results are relevant for evaluating Maudlin׳s theory. The value of this theory depends crucially on whether it is true that (a) its conceptual framework is as expressive as that of standard topology when it comes to describing well-known continuous as well as discrete models of spacetime and (b) it is even more expressive or fruitful when it comes to analysing topological aspects of discrete structures that are intended as models of spacetime. On one hand, my theorems support (a). The theory is rich enough to incorporate causal set theory and its definitions of topological notions yield a plausible outcome in the case of causal sets. On the other hand, the results undermine (b). Standard topology, too, has the conceptual resources to capture those topological aspects of causal sets that are analysable within Maudlin׳s framework. This fact poses a challenge for the proponents of Maudlin׳s theory to prove it fruitful.     

Space–time philosophy reconstructed via massive Nordström scalar gravities? Laws vs. geometry,conventionality, and underdetermination

What if gravity satisfied the Klein–Gordon equation? Both particle physics from the 1920–30s and the 1890s Neumann–Seeliger modification of Newtonian gravity with exponential decay suggest considering a “graviton mass term” for gravity, which is algebraic in the potential. Unlike Nordström׳s “massless” theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman–Cunningham conformal group. It therefore exhibits the whole of Minkowski space–time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein׳s principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the ‘true’ geometry, one might wonder, in line with Poincaré׳s modal conventionality argument? Infinitely many theories exhibit this bimetric ‘geometry,’ all with the total stress–energy׳s trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers–Pirani–Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities—indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein׳s equations along the lines of Einstein׳s newly re-appreciated “physical strategy” and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz found in 1939). The Putnam–Grünbaum debate on conventionality is revisited with an emphasis on the broad modal scope of conventionalist views. Massive scalar gravity thus contributes to a historically plausible rational reconstruction of much of 20th–21st century space–time philosophy in the light of particle physics. An appendix reconsiders the Malament–Weatherall–Manchak conformal restriction of conventionality and constructs the ‘universal force’ influencing the causal structure.Subsequent works will discuss how massive gravity could have provided a template for a more Kant-friendly space–time theory that would have blocked Moritz Schlick׳s supposed refutation of synthetic a priori knowledge, and how Einstein׳s false analogy between the Neumann–Seeliger–Einstein modification of Newtonian gravity and the cosmological constant Λ generated lasting confusion that obscured massive gravity as a conceptual possibility.     

“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.     

Kinetic studies on soluble and membrane-bound dopamineβ-hydroxylase isolated from storage vesicles of heart and adrenal medulla of different species

Summary IdenticalK _m-values for soluble and membrane-bound dopamine -hydroxylase isolated from adrenal medullary vesicles of different species were obtained; the same holds true for both forms of the enzyme of heart vesicles.The excellent technical assistance of MissSabine Klemt is gratefully acknowledged.     

Misspecified prediction for time series

Let {X_t} be a stationary process with spectral density g(λ).It is often that the true structure g(λ) is not completely specified. This paper discusses the problem of misspecified prediction when a conjectured spectral density f_θ(λ), θ∈Θ, is fitted to g(λ). Then, constructing the best linear predictor based on f_θ(λ), we can evaluate the prediction error M(θ). Since θ is unknown we estimate it by a quasi‐MLE . The second‐order asymptotic approximation of is given. This result is extended to the case when X_t contains some trend, i.e. a time series regression model. These results are very general. Furthermore we evaluate the second‐order asymptotic approximation of for a time series regression model having a long‐memory residual process with the true spectral density g(λ). Since the general formulae of the approximated prediction error are complicated, we provide some numerical examples. Then we illuminate unexpected effects from the misspecification of spectra. Copyright © 2001 John Wiley & Sons, Ltd.     

Über die Speicherung von Lipiden durch Knallgasbakterien

Summary The ability to accumulate lipids was investigated in two strains of hydrogen oxidizing bacteria (Hydrogenomonas H 16 and strain 11/x). Along with the deposition of poly--hydroxybutyrate the amount of other lipids is shown to increase 1.8 times in strain H 16. It is suggested that the increase of the latter lipids is due to the formation of membrane lipids that are needed for the formation of membranes around the intracellular globules of poly--hydroxybutyrate. In strain 11/x the amount of lipids increases 7 times along with the storage of carbohydrates. In this case, the majority of lipids consists of triglycerides. It is suggested that there is a true storage of neutral fat in strain 11/x.     

Der Eigenartige Einfluß Witelos auf die Entwicklung der Dioptrik

Summary Witelo's Perspectiva, which was printed three times in the sixteenth century, profoundly influenced the science of dioptrics until the Age of Newton. Above all, the optical authors were interested in the so-called Vitellian tables, which Witelo must have copied from the nearly forgotten optical Sermones of Claudius Ptolemy. Research work was often based on these tables. Thus Kepler relied on the Vitellian tables when he invented his law of refraction. Several later authors adopted Kepler's law, not always because they believed it to be true, but because they did not know of any better law. Also Harriot used the Vitellian tables until his own experiments convinced him that Witelo's angles were grossly inaccurate. Unfortunately Harriot kept his results and his sine law for himself and for a few friends. The sine law was not published until 1637, by Descartes, who gave an indirect proof of it. Although this proof consisted in the first correct calculation of both rainbows, accomplished by means of the sine law, the Jesuits Kircher (Ars Magna, 1646) and Schott (Magia Optica, 1656) did not mention the sine law. Marci (Thaumantias, 1648) did not know of it, and Fabri (Synopsis Opticæ, 1667) rejected it. It is true that the sine law was accepted by authors like Maignan (Perspectiva Horaria, 1648) and Grimaldi (Physico-Mathesis, 1665), but since they used the erroneous Vitellian angles for computing the refractive index, they discredited the sine law by inaccurate and even ludicrous results.That even experimental determinations might be unduly biased by the Vitellian angles is evident from the author's graphs of seventeenth century refractive angles. These graphs also show how difficult it was to measure such angles accurately, and how the Jesuit authors of the 1640's adapted their experimental angles to the traditional Vitellian ones. Witelo's famous angles, instead of furthering the progress of dioptrics, delayed it. Their disastrous influence may be traced for nearly thirty years after Descartes had published the correct law of refraction.

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Vorgelegt von C. Truesdell     

Proposition II (Book I) of Newton’s <Emphasis Type="Italic">Principia</Emphasis>

After preparing the way with comments on evanescent quantities and then Newton’s interpretation of his second law, this study of Proposition II (Book I)— Proposition II Every body that moves in some curved line described in a plane and, by a radius drawn to a point, either unmoving or moving uniformly forward with a rectilinear motion, describes areas around that point proportional to the times, is urged by a centripetal force tending toward that same point. —asks and answers the following questions: When does a version of Proposition II first appear in Newton’s work? What revisions bring that initial version to the final form in the 1726 Principia? What, exactly, does this proposition assert? In particular, what does Newton mean by the motion of a body “urged by a centripetal force”? Does it assert a true mathematical claim? If not, what revision makes it true? Does the demonstration of Proposition II persuade? Is it as convincing, for example, as the most convincing arguments of the Principia? If not, what revisions would make the demonstration more persuasive? What is the importance of Proposition II, to the physics of Book III and the mathematics of Book I?