1,312 research outputs found
Essay Review of: Maximilian Schlosshauer, Decoherence and the Quantum-To-Classical Transition (Springer, Berlin, 2007)
No full textBook revie
[Review of] Gail H. Landsman, Sovereignty and Symbol: Indian-White Conflict at Ganienkeh
No full textAnthropologist Landsman has written a fascinating study about the events surrounding the seizure of a 612-acre abandoned girls\u27 camp in upstate New York in May 1974 by a group of Mohawks who named their settlement Ganienkeh. The ensuing Indian-white land dispute eventually culminated in the relocation of the Indians to parkland near the Canadian border in 1978 as a result of a unique arrangement, the Turtle Island Trust Agreement, which for charitable, religious and educational purposes under New York State law established a permanent, non-reservation settlement of Indians claiming sovereign status
Macroscopic observables and the Born rule. I. Long run frequencies
No full textWe clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a noncommutative C*-algebra of observables is empirically accessible only through associated commutative C*-algebras. The Born probabilities emerge as the relative frequencies of outcomes in long runs of measurements on a quantum system; it is not necessary to adopt the frequency interpretation of single-case probabilities (which will be the subject of a sequel paper). Our derivation of the Born rule uses ideas from a program begun by Finkelstein (1965) and Hartle (1968), intending to remove the Born rule as a separate postulate of quantum mechanics. Mathematically speaking, our approach refines previous elaborations of this program - notably the one due to Farhi, Goldstone, and Gutmann (1989) as completed by Van Wesep (2006) - in replacing infinite tensor products of Hilbert spaces by continuous fields of C*-algebras. In combination with our interpretational context, this technical improvement circumvents valid criticisms that earlier derivations of the Born rule have provoked, especially to the effect that such derivations were mathematically flawed as well as circular. Furthermore, instead of relying on the controversial eigenvector-eigenvalue link in quantum theory, our derivation just assumes that pure states in classical physics have the usual interpretation as truthmakers that assign sharp values to observables
Reliability and Relevance of Fair Values: Private Equity Investments and Investee Fundamentals
No full textWe directly test the reliability and relevance of fair values reported by listed private equity firms (LPEs), where the unit of account for fair value measurement attribute (FVM) is an investment stake in an individual investee company. FVMs are observable for multiple investment stakes, fair values are economically important, and granular data on investee economic fundamentals that should underpin fair values are available in public disclosures. We find that LPE fund managers determine valuations based on accounting-based fundamentals—equity book value and net income—that are in line with those investors derive for listed companies. Additionally, our findings suggest that LPE fund managers apply a lower valuation weight to investee net income if direct market inputs are unobservable during investment value estimation. We interpret these findings as evidence that LPE fund managers do not appear mechanically to apply market valuation weights for publicly traded investees when determining valuations of non-listed. We also document that the judgments that LPE fund managers apply when determining investee valuations appear to be perceived as reliable by their investors
A Flea on Schroedinger's Cat
No full textWe propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr's views. Unlike the usual formulation (in which the post-measurement state is a a unit vector in Hilbert space, such as a wave-function), our version actually admits a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this theory, or introduce unusual and controversial interpretative rules and/or ontologies).
To that effect, we recall a remarkable phenomenon in the theory of Schroedinger operators (discovered in 1981 by Jona-Lasinio, Martinelli, and Scoppola), according to which the ground state of a symmetric double-well Hamiltonian (which is paradigmatically of Schroedinger's Cat type) becomes exponentially sensitive to tiny perturbations of the potential as h -> 0. We show that this instability emerges also from the textbook WKB approximation, extend it to time-dependent perturbations, and study the dynamical transition from the ground state of the double well to the perturbed ground state (in which the cat is typically either dead or alive, depending on the details of the perturbation).
Numerical simulations show that, in an individual experiment, certain (especially adiabatically rising) perturbations may (quite literally) cause the collapse of the wavefunction in the classical limit. Thus we combine the technical and conceptual virtues of dynamical collapse models a la GRW (which do solve the measurement problem) with those of decoherence (in that our perturbations come from the environment) without sharing their drawbacks: although single measurement outcomes are obtained (instead of merely diagonal reduced density matrices), no modification of quantum mechanics is needed
Some results on Denault's capital allocation rule.
No full textDenault (2001) introduces a capital allocation principle where the capital allocated to any risk unit is expressed in terms of the contribution of that risk to the aggregate conditional tail expectation. Panjer (2002) derives a closed-form expression for this allocation rule in the multivariate normal case. Landsman & Valdez (2003) generalize Panjer's result to the class of multivariate elliptical distributions. In this paper we provide an alternative and much simpler proof for the allocation formula in the elliptical case. Further, we show how to derive accurate closed-form approximations for Denault's allocation formula in case of lognormal risks.Capital allocation;
Calculation of Bayes Premium for Conditional Elliptical Risks
No full textIn this paper we discuss the calculation of the Bayes premium for conditionally elliptical multivariate risks. In our framework the prior distribution is allowed to be very general requiring only that its probability density function satisfies some smoothness conditions. Based on previous results of Landsman and Nešlehová (2008) and Hamada and Valdez (2008) we show in this paper that for conditionally multivariate elliptical risks the calculation of the Bayes premium is closely related to Brown identity and the celebrated Stein’s Lemma. ⺠We extend the Bayes premium calculation to general multivariate elliptical risks. ⺠The paper discusses the connection of Stein’s Lemma and Brown identity. ⺠Interesting aspects of multivariate Gaussian model are revealed for special choice of covariance matrix
When champions meet: Rethinking the Bohr--Einstein debate
No full textEinstein's philosophy of physics (as clarified by Fine, Howard, and Held) was predicated on his Trennungsprinzip, a combination of separability and locality, without which he believed objectification, and thereby "physical thought" and "physical laws", to be impossible. Bohr's philosophy (as elucidated by Hooker, Scheibe, Folse, Howard, Held, and others), on the other hand, was grounded in a seemingly different doctrine about the possibility of objective knowledge, namely the necessity of classical concepts. In fact, it follows from Raggio's Theorem in algebraic quantum theory that - within an appropriate class of physical theories - suitable mathematical translations of the doctrines of Bohr and Einstein are equivalent. Thus - upon our specific formalization - quantum mechanics accommodates Einstein's Trennungsprinzip if and only if it is interpreted a la Bohr through classical physics. Unfortunately, the protagonists themselves failed to discuss their differences in this constructive way, since their debate was dominated by Einstein's ingenious but ultimately flawed attempts to establish the "incompleteness" of quantum mechanics. This aspect of their debate may still be understood and appreciated, however, as reflecting a much deeper and insurmountable disagreement between Bohr and Einstein about the knowability of Nature. Using the theological controversy on the knowability of God as a analogy, we can say that Einstein was a Spinozist, whereas Bohr could be said to be on the side of Maimonides. Thus Einstein's off-the-cuff characterization of Bohr as a 'Talmudic philosopher' was spot-on
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