Posts Tagged ‘quantum mechanics’

The connection between quantum mechanics and logic

December 4, 2008

Scott at Shtetl-Optimized is forced to write a post (which, I think is a good thing; otherwise, how else are we to get such nice posts?):

… I see colleagues who I respect and admire enormously—in this case, several who have done pioneering experiments that tested quantum mechanics in whole new regimes—making statements that can be so easily misinterpreted by a public and a science press hungry to misinterpret, that I find my fingers rushing to type even as my brain struggles in vain to stop them.

Now, to the more interesting parts of the post — about quantum logic:

So is there a connection between quantum mechanics and logic?  There is—and it was worked out by Birkhoff and von Neumann in 1936.  Recall that Paterek et al. identify propositions with projective measurements, and axioms with states.  But in logic, an axiom is just any proposition you assume; otherwise it has the same form as any other proposition.  So it seems to me that we ought to identify both propositions and axioms with projective measurements.  States that are eigenstates of all the axioms would then correspond to models of those axioms.  (Interestingly, the notion of a model never appears in the Paterek et al. paper.)  Also, logical inferences would derive some propositions from other propositions, like so: “any state that is an eigenstate of both X and Y is also an eigenstate of Z.”  As it turns out, this is precisely the approach Birkhoff and von Neumann took.  The field they started is called “quantum logic.”

A nice post!

Nanotechnology for medicine, geometric and atomic world view, objective measure for citations and research style!

November 12, 2008

Here are a few technical and academic links — three from PNAS and one from Arunn’s Unruled Notebook:

Nanotechnology for medicine: R H Austin and S-f Lim in PNAS:

The Sackler Colloquium entitled “Nanomaterials in Biology and Medicine: Promises and Perils” was held on April 10–11, 2007. We have been able to assemble a representative sampling of 17 of the invited talks ranging over the topics presented. Any new technology carries with it both a promise of transforming the way we do things and the possibility that there are unforeseen consequences. The papers collected here represent a cross-section of these issues. As an example, we present our own work on nano-upconversion phosphors as an example of this new class of nanomaterials with potential use in medicine and biology.

Geometric and atomic world views: A Bohr, B R Mottelson and O Ulfbeck:

The atomic world view is based on the notion that matter is built of elementary constituents called atoms, and quantum mechanics was created in the pursuit of this view with probabilistic events caused by atomic particles. This conception involves unresolved ambiguities linked to the notion of an elementary quantum of action. The resolution of these problems in quantum mechanics requires a new, geometric, world view, which recognizes the occurrence of events, clicks in counters, coming without a cause, referred to as fortuitous. The possibility of a rational theory of probabilities for such events is based on the assignment to the individual click of a proper value of an element of (flat) space–time symmetry. Thereby, the distributions of uncaused clicks can be endowed with a geometric content in terms of the irreducible representations of space–time symmetry. Through fortuity, space–time invariance itself thus acquires a hitherto unrecognized role. Departing from the norms of physical theory, the uncaused click is not a measurement of something, and the reality mirrored in the distributions is the geometry of space time itself, and not a property of an imagined object. The geometric world view involves only the dimensions of space and time, and the absence of an irreducible dimension of mass is seen as the result of the discovery of new physical phenomena. Accordingly Planck’s constant has no place in fundamental theory and is seen as a relic of dimensions that have become superfluous.

Objective measure of scientific impact: F Radicchi, S Fortunato, and C Castellano:

We study the distributions of citations received by a single publication within several disciplines, spanning broad areas of science. We show that the probability that an article is cited c times has large variations between different disciplines, but all distributions are rescaled on a universal curve when the relative indicator cf = c/c0 is considered, where c0 is the average number of citations per article for the discipline. In addition we show that the same universal behavior occurs when citation distributions of articles published in the same field, but in different years, are compared. These findings provide a strong validation of cf as an unbiased indicator for citation performance across disciplines and years. Based on this indicator, we introduce a generalization of the h index suitable for comparing scientists working in different fields.

Science: as individual pursuit and Empire building activity — Arunn in Unruled Notebook:

Individual or Empire? Should we remain individual scientists or should I forge or join a research group for pursuing research. This is not an age old question, if we reckon the time span of human thought and scientific inquiry.

Science, until recently, has been an individual pursuit. There are reasons in our history and her-story on how it became a group pursuit. Industrial revolution, academic institutions, World Wars, funding based research, scientists (and Science) migration, state-run funding agencies, peer review, Ph. D. degree, academic business models, tenure track, publish or perish, research grants, proposal based funding, funding based Science, post docs, research sans teaching professors, research empires, professors as research managers, quantity as quality, scientists as entrepreneurs, students as workers, the sequence is telling.

But Individuals remain. Why?

Revenge of the heirs of Bohr

October 15, 2007

Against those of Einstein, and the revenge of the heirs of Einstein against those of Bohr:

Theoretical physicists are now divided into two main factions. Those who look forward to another revolution mostly believe that it will grow out of a grand mathematical scheme known as string theory. Those who are content with the outcome of the old revolution are mostly studying more mundane subjects such as high-temperature superconductors and quantum computers. String theory may be considered to be the counterattack of those who lost the debate over complementarity in physics in Copenhagen in 1932. It is the revenge of the heirs of Einstein against the heirs of Bohr. The new discipline of systems biology, describing living creatures as emergent dynamic organizations rather than as collections of molecules, is the counterattack of those who lost the debate over complementarity in biology in 1953. It is the revenge of the heirs of Bohr against the heirs of Einstein.

Mundane subjects such as high-temperature superconductors and quantum computersMundane, did he say? Ouch! That hurts!

The New York Review of Books piece of Freeman Dyson from which Jenny Davidson quotes is, alas, not available online to non-subscribers, I was given to understand — though, I could get it on my computer. So, dear readers, keep you fingers crossed and click! If the Lord of Open Access is in a benevolent mood, you might get to read it.