Quantum Gravity 397.2: Turkey Discovers Generalization/Extension of QM That Raises Questions
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From: OsherD on 27 May 2010 00:15 From Osher Doctorow The curious things that are happening with modified/generalized GR or even alternative theories of Gravity and with Rigged and Nested Hilbert Spaces, are now happening with "Pseudo-Hermitian" representations of QM that appear to generalize/extend QM and reveal some new physical applications that could not be obtained from standard QM, as shown by Ali Mostafazadeh of Kac University Istanbul Turkey. Before I go on, skeptics might be interested in what happens in Linguistics of all places when "slight modifications" are noticed by researchers in languages, dialects, etc. It turns out quite often that "slight modifications" indicate enormous changes over centuries or even millenia in languages and whole language families. The paper of Mostafazadeh is: 1) "Pseudo-Hermitian representation of quantum mechanics," arXiv: 0810.5643 [quant-ph] 25 May 2010, 76 pages. Roughly speaking, the idea is that there's a certain freedom in choosing the inner product for Hilbert Spaces because it isn't "independently measured" from anything. This may seem on the surface like a triviality, but it leads to new applications in nuclear physics, condensed matter physics, quantum chaos, biophysics, magnetohydrodynamics, electromagnetic wave propagation, open quantum systems, quantum cosmology, relativistic quantum mechanics and quantum field theory, etc. It turns out that a "metric operator" plays a central role in this, and that inner products that make 2 complex vector spaces into 2 separable Hilbert Spaces are in a 1-1 correspondence with metric operators acting in ONE of these Hilbert spaces. I will try to continue this later. Lately, financial difficulties (especially ones that hurt Seniors) are requiring me to divide my typing time on the internet in unusual ways (usually much less typing time than before). Osher Doctorow
From: OsherD on 27 May 2010 01:19
From Osher Doctorow Indefinite-Metric Quantum theories are examples of such generalizations and extensions. ArXiv has 8 papers and 30 papers respectively on: 1) "Indefinite-Metric quantum" 8 papers. 2) "Indefinite Metric" 30 papers. Note that a given quantum system admits an infinity of unitary- equivalent representations in terms of Hilbert Space - Hermitian operator pairs, which gives considerable freedom in choice of representations somewhat analogous to Gauge Symmetries in elementary particle physics. By the way, in reference to an earlier post, Jan Lukaciewicz of Poland lived from 1878 to 1956. Osher Doctorow |