{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:33:01Z","timestamp":1760243581865,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2012,4,2]],"date-time":"2012-04-02T00:00:00Z","timestamp":1333324800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>An experimental test of the \u201cspecial state\u201d theory of quantum measurement is proposed. It should be feasible with present-day laboratory equipment and involves a slightly elaborated Stern\u2013Gerlach setup. The \u201cspecial state\u201d theory is conservative with respect to quantum mechanics, but radical with respect to statistical mechanics, in particular regarding the arrow of time. In this article background material is given on both quantum measurement and statistical mechanics aspects. For example, it is shown that future boundary conditions would not contradict experience, indicating that the fundamental equal-a-priori-probability assumption at the foundations of statistical mechanics is far too strong (since future conditioning reduces the class of allowed states). The test is based on a feature of this theory that was found necessary in order to recover standard (Born) probabilities in quantum measurements. Specifically, certain systems should have \u201cnoise\u201d whose amplitude follows the long-tailed Cauchy distribution. This distribution is marked by the occasional occurrence of extremely large signals as well as a non-self-averaging property. The proposed test is a variant of the Stern\u2013Gerlach experiment in which protocols are devised, some of which will require the presence of this noise, some of which will not. The likely observational schemes would involve the distinction between detection and non-detection of that \u201cnoise\u201d. The signal to be detected (or not) would be either single photons or electric fields (and related excitations) in the neighborhood of the ends of the magnets.<\/jats:p>","DOI":"10.3390\/e14040665","type":"journal-article","created":{"date-parts":[[2012,4,2]],"date-time":"2012-04-02T11:06:22Z","timestamp":1333364782000},"page":"665-686","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Experimental Test of the \u201cSpecial State\u201d Theory of Quantum Measurement"],"prefix":"10.3390","volume":"14","author":[{"given":"Lawrence S.","family":"Schulman","sequence":"first","affiliation":[{"name":"Physics Department, Clarkson University, Potsdam, New York, NY 13699, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,4,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Schulman, L.S. (1997). Times Arrows and Quantum Measurement, Cambridge University Press.","DOI":"10.1017\/CBO9780511622878"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1126\/science.1136303","article-title":"Experimental realization of wheelers delayed-choice gedanken experiment","volume":"315","author":"Jacques","year":"2007","journal-title":"Science"},{"key":"ref_3","unstructured":"di Francia, G.T. (1979). Frontiers of Time, in Problems in the Foundations of Physics, North Holland."},{"key":"ref_4","unstructured":"Rhoads, J.E. (1981). Delayed-Choice Experiments and the Bohr-Einstein Dialog, Amerrican Philosophical Society."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1063\/1.3663722","article-title":"Delayed choice experiments, the arrow of time, and quantum measurement","volume":"1408","author":"Schulman","year":"2011","journal-title":"AIP Conf. Proc."},{"key":"ref_6","unstructured":"The material in [5] was also presented in a lecture at the 20th anniversary celebration of the Center for Theoretical Studies, Prague, Czech Republic, November 2010."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"L293","DOI":"10.1088\/0305-4470\/30\/9\/006","article-title":"Observational line broadening and the duration of a quantum jump","volume":"30","author":"Schulman","year":"1997","journal-title":"J. Phys. A"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1103\/PhysRevA.57.1509","article-title":"Continuous and pulsed observations in the quantum Zeno effect","volume":"57","author":"Schulman","year":"1998","journal-title":"Phys. Rev. A"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Muga, J.G., Mayato, R.S., and Egusquiza, I.L. (2008). Time in Quantum Mechanics, Springer-Verlag. [2nd ed.].","DOI":"10.1007\/978-3-540-73473-4"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1088\/0305-4470\/24\/9\/015","article-title":"Linear decay in multi-level quantum systems","volume":"24","author":"Schulman","year":"1991","journal-title":"J. Phys. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF01015734","article-title":"Consistent histories and the interpretation of quantum mechanics","volume":"36","author":"Griffiths","year":"1984","journal-title":"J. Stat. Phys."},{"key":"ref_12","unstructured":"(1980). A solvable model of particle detection in quantum theory. Acta Fac. Rerum Nat. Univ. Comen. Phys., 20, 65\u201394. I later learned of work of Bona, P."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1209","DOI":"10.1007\/BF01026572","article-title":"Model apparatus for quantum measurements","volume":"58","author":"Gaveau","year":"1990","journal-title":"J. Stat. Phys."},{"key":"ref_14","unstructured":"We also use probability when\u2014even if the initial point is known\u2014it is impractical to calculate the later phase space point, for example for chaotic dynamics. Taking this into account would lead to a slight restatement of the assertions in the text, but the quantum issues, which are the point of the discussion, are the same."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1086\/288666","article-title":"Model of implication in statistical mechanics","volume":"42","author":"Schulman","year":"1975","journal-title":"Philos. Sci."},{"key":"ref_16","unstructured":"Something rare can still be abundant. Here is an example that will make this utterance sound less mystical. Consider the melting ice story from the arrow of time discussion. The 2 p.m. ice-plus-cold-water into which the 1 p.m. ice cube has melted has far more microstates than just those coming from an ice cube of one particular size. Therefore, as discussed, when thinking of the 2 p.m. state as the image of an earlier state there is an order 1 in \n\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t              10\n\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t                10\n\t\t\t\t\t\t\t                24\n\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t         restriction on its microstates. However, there are many possible forms the 1 p.m. piece of ice could take\u2014a small and a large cube, a cube and 12 chips, an ice sculpture of a polar bear, of a tulip, etc., etc. So final state microstates are relatively rare, but still have \n\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t              10\n\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t                10\n\t\t\t\t\t\t\t                24\n\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t        \u2019s in their abundances. Well, maybe it\u2019s only \n\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t              10\n\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t                10\n\t\t\t\t\t\t\t                23.99\n\t\t\t\t\t\t\t              \n\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t        ."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Adler, R.J., Feldman, R.E., and Taqqu, M.S. (1998). A Practical Guide to Heavy Tails: Statistical Techniques and Applications, Birkh\u00e4user.","DOI":"10.21236\/ADA336956"},{"key":"ref_18","unstructured":"Samorodnitsky, G., and Taqqu, M.S. (1994). Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance, Chapman and Hall."},{"key":"ref_19","unstructured":"Arnold, V.I., and Avez, A. (1968). Ergodic Problems of Classical Mechanics, Benjamin."},{"key":"ref_20","unstructured":"Boltzmann, L. (1995). Lectures on Gas Theory, Dover Publications. Section 90."},{"key":"ref_21","unstructured":"L. Landau is said to have characterized cosmologists as, \u201cOften in error; never in doubt\u201d."},{"key":"ref_22","unstructured":"\u03d5 in this section corresponds to the 2\u03c8 of Equation (7). The definition of a also changes by a factor 2."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0003-4916(91)90119-S","article-title":"Definite quantum measurements","volume":"212","author":"Schulman","year":"1991","journal-title":"Ann. Phys."},{"key":"ref_24","unstructured":"Hille, E. (1959). Analytic Function Theory, Volume I, Ginn and Company. Section 9.3, Equation 9.3.14."},{"key":"ref_25","unstructured":"MIT Dept. Physics, Junior lab. The Stern-Gerlach experiment: Quantization of angular momentum. Available online: web.mit.edu\/8.13\/JLExperiments\/JLExp_18_rev1.pdf."},{"key":"ref_26","unstructured":"They could as well tilt along the x-axis, although details of our calculation would be slightly different. Note too, that for, say 50\u2218, one would select from the output of the first SG setup. However, for the 0\u2218 experiment this is not necessary, since there would still be an absence of \u201cnoise\u201d even if both orientations are incoherently recombined and sent through the second SG setup."},{"key":"ref_27","unstructured":"See the following link for what may be the source of this expression. Available online: http:\/\/en.wikiquote.org\/wiki\/Niels_Bohr."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"041307:1","DOI":"10.1103\/PhysRevB.67.041307","article-title":"Mesoscopic Stern-Gerlach device to polarize spin currents","volume":"67","author":"Ionicioiu","year":"2003","journal-title":"Phys. Rev. B"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/4\/665\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:49:39Z","timestamp":1760219379000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/14\/4\/665"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,4,2]]},"references-count":28,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,4]]}},"alternative-id":["e14040665"],"URL":"https:\/\/doi.org\/10.3390\/e14040665","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2012,4,2]]}}}