From Koopman-von Neumann Theory to Quantum Theory

Koopman and von Neumann (KvN) extended the Liouville equation by introducing a phase space function $S^{(K)}(q,p,t)$ whose physical meaning is unknown. We show that a different $S(q,p,t)$, with well-defined physical meaning, may be introduced without destroying the attractive "quantum-like" mathematical features of the KvN theory. This new $S(q,p,t)$ is the classical action expressed in phase space coordinates. It defines a mapping between observables and operators which preserves the Lie bracket structure. The new evolution equation reduces to Schr\"odinger's equation if functions on phase space are reduced to functions on configuration space. This new kind of "quantization" does not only establish a correspondence between observables and operators, but provides in addition a derivation of quantum operators and evolution equations from corresponding classical entities. It is performed by replacing $\frac{\partial}{\partial p}$ by $0$ and $p$ by $\frac{\hbar}{\imath} \frac{\partial}{\partial q}$, thus providing an explanation for the common quantization rules.Comment: 7 pages, no figures, Quantum Stud.: Math. Found., 5(2), 219-22

Is the individuality interpretation of quantum theory wrong ?

We analyze the question whether or not quantum theory should be used to describe single particles. Our final result is that a rational basis for such an 'individuality interpretation' does not exist. A critical examination of three principles, supporting the individuality interpretation, leads to the result that no one of these principles seems to be realized in nature. The well-known controversy characterized by the names of Einstein (EPR), Bohr and Bell is analyzed. EPR proved 'predictive incompleteness' of quantum theory, which implies that no individuality interpretation exists. Contrary to the common opinion, Bell's proof of 'metaphysical completeness' does not invalidate EPR's proof because two crucially different meanings of 'completeness' are involved. The failure to distinguish between these two meanings is closely related to a fundamentally deterministic world view, which dominated the thinking of the 19th century and determines our thinking even today.Comment: 11 pages, no figure

Taboo, the Game: Patent Office Edition—The New Preissuance Submissions Under the America Invents Act

Thorough patent examination ensures that issued patents confer constitutionally granted incentives to innovate but do not create inappropriately broad monopolies. Examiners at the United States Patent and Trademark Office are alone tasked with striking this proper balance, in part by searching the universe of existing published knowledge to determine the originality of the applied-for invention. In 2011, Congress enacted the Leahy-Smith America Invents Act, which included a provision allowing the public to present examiners with relevant publications that the examiners’ own searches might not otherwise uncover. However, this “preissuance submissions” provision and its related administrative rule are tempered by 35 U.S.C. § 122(c) (2006), which prohibits any third-party, pre-grant “protest or other form of [preissuance] opposition” to an application. Thus, although a party may describe to an examiner how its submission is relevant to an application, that party is prohibited from arguing how the submission renders that application unpatentable. This Note argues that Congress should amend § 122(c) to permit preissuance third-party argumentation for two reasons. First, the current scheme arguably violates that law already. Second, a rule allowing submitter argumentation would better incentivize participation by competitive parties who fear that examiners might not recognize their submitted publications\u27 full invalidating potential

Regularization Methods for Nuclear Lattice Effective Field Theory

We investigate Nuclear Lattice Effective Field Theory for the two-body system for several lattice spacings at lowest order in the pionless as well as in the pionful theory. We discuss issues of regularizations and predictions for the effective range expansion. In the pionless case, a simple Gaussian smearing allows to demonstrate lattice spacing independence over a wide range of lattice spacings. We show that regularization methods known from the continuum formulation are necessary as well as feasible for the pionful approach.Comment: 7 pp, 2 figs, to appear in Physics Letters

Die Demethylierung von Dimethylselenid ist eine adaptive Antwort des Archaeons Methanococcus voltae

Im natürlichen Lebensraum von Methanococcus voltae kommt Selen in unterschiedlichen Verbindungen und Konzentration vor. So variiert der Selengehalt im Mündungswasser verschiedener Flüsse zwischen 0,1 und 63 nM. Aufgrund der guten Löslichkeit sind die Oxianionen des Selens biologisch am interessantesten. Sie sind daher aber auch in hohen Konzentrationen toxisch. Selen in geringen Mengen ist dagegen essentiell, da es als Selenomethionin oder -cystein in Proteinen vorkommen kann. Eine häufig anzutreffende organische Selenverbindungen ist das Dimethylselenid (DMSe). Diese flüchtige Substanz wird von einer Vielzahl Organismen zur Detoxifizierung gebildet. Aus M. voltae sind insgesamt 4 Hydrogenasen bekannt, wovon zwei ein Selenocystein aufweisen und konstitutiv exprimiert werden. Die Induktion der Transkription der selenfreien Isoenzyme erfolgt dagegen bei Selenmangel. In Expressionsanalysen zeigte sich, dass 5 weitere Proteine ebenfalls nur unter Selenlimitierung synthetisiert werden. Von zweien wurde jeweils die N-terminale Peptidsequenz und von einem zusätzlich interne Peptidsequenzen bestimmt. In der vorliegenden Arbeit wurde zunächst das Gen eines dieser Proteine identifiziert. In einer Datenbanksuche stellte sich dann heraus, dass es Sequenzidentitäten mit Corrinoid-Proteinen aus Methanosarcina aufwies. Es wurde als SdmA bezeichnet (für Dimethylselenid Demethylierung). Das Gen sdmA liegt zusammen mit sdmB und sdmC auf einem gemeinsamen polycistronischen Messenger, der nur bei Selenmangel nachweisbar war. SdmB und SdmC haben gemeinsame Sequenzmotive mit Methyltransferasen, die in einigen Methanoarchaeen an der methylotrophen Methanogenese beteiligt sind. Dabei übertragen diese die Methylgruppe von Corrinoid-Proteinen auf den Akzeptor Coenzym M. Die Methylgruppe stammt dabei beispielsweise aus methylierten Aminen bzw. Thiolen oder aus Methanol. Normalerweise werden von M. voltae für die Methanogenese nur Formiat oder H2/CO2 erschlossen, so bestätigte sich die Vermutung nicht, dass bei Selenmangel SdmA, SdmB und SdmC die Erschließung der oben genannten methylierten Substrate erlauben könnten. Versetzt man das Selenmangelmedium jedoch mit DMSe, dann führt dies zur Repression des Promotors der Gene einer selenfreien Hydrogenase, der normalerweise nur unter Selenlimitierung aktiv wäre. Eine Deletion von sdmA oder sdmC führte zur Aktivität des Promotors trotz der Anwesenheit von DMSe. Der Austausch von sdmB hatte dagegen keinen Effekt. Zudem waren die Wachstumsraten der Mutanten delta sdmA und delta sdmB im Vergleich zum Wildtyp trotz DMSe-Zugabe reduziert. In M. voltae scheint es daher zwei verschiedene Anpassungsmechanismen an Selenmangel zu geben. Zum einen werden unter Selenlimitierung die selenfreien Isoenzyme der selenhaltigen Hydrogenasen exprimiert und zum anderen lässt sich unter diesen Bedingungen ein alternatives Selensubstrat, wie das DMSe, von M. voltae zur Biosynthese der Selenoproteine erschließen. Daran ist vermutlich das Corrinoid-Proteine SdmA und die Methyltransferase SdmC beteiligt

From probabilistic mechanics to quantum theory

We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation for a probability density. We extend this theory in two respects: (1) The same structure is defined for arbitrary observables. Thus we have all of the above entities generated not only by Hamilton's function but by every observable. (2) We introduce for each observable a phase space function representing the classical action. This is a redundant quantity in a classical context but indispensable for the transition to QT. The basic equations of the resulting theory take a ``quantum-like'' form, which allows for a simple derivation of QT by means of a projection to configuration space reported previously [Quantum Stud.:Math. Found.(2018) 5:219-227]. We obtain the most important relations of QT, namely the form of operators, Schr\"odinger's equation, eigenvalue equations, commutation relations, expectation values, and Born's rule. Implications for the interpretation of QT are discussed, as well as an alternative projection method allowing for a derivation of spin

Lattice Improvement in Lattice Effective Field Theory

Lattice calculations using the framework of effective field theory have been applied to a wide range few-body and many-body systems. One of the challenges of these calculations is to remove systematic errors arising from the nonzero lattice spacing. Fortunately, the lattice improvement program pioneered by Symanzik provides a formalism for doing this. While lattice improvement has already been utilized in lattice effective field theory calculations, the effectiveness of the improvement program has not been systematically benchmarked. In this work we use lattice improvement to remove lattice errors for a one-dimensional system of bosons with zero-range interactions. We construct the improved lattice action up to next-to-next-to-leading order and verify that the remaining errors scale as the fourth power of the lattice spacing for observables involving as many as five particles. Our results provide a guide for increasing the accuracy of future calculations in lattice effective field theory with improved lattice actions.Comment: 10 pages, 8 figure