Peres experiment using photons: No test for hypercomplex (quaternionic) quantum theories

被引:6
作者
Adler, Stephen L. [1 ]
机构
[1] Inst Adv Study, Einstein Dr, Princeton, NJ 08540 USA
关键词
MECHANICS; COMPLEX;
D O I
10.1103/PhysRevA.95.060101
中图分类号
O43 [光学];
学科分类号
070207 ; 0803 ;
摘要
Assuming the standard axioms for quaternionic quantum theory and a spatially localized scattering interaction, the S matrix in quaternionic quantum theory is complex valued, not quaternionic. Using the standard connections between the S matrix, the forward scattering amplitude for electromagnetic wave scattering, and the index of refraction, we show that the index of refraction is necessarily complex, not quaternionic. This implies that the recent optical experiment of Procopio et al. [Nat. Commun. 8, 15044 (2017)] based on the Peres proposal does not test for hypercomplex or quaternionic quantum effects arising within the standard Hilbert space framework. Such a test requires looking at near zone fields, not radiation zone fields.
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页数:3
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共 13 条
[1]  
Adler SL., 1995, Quaternionic quantum mechanics and quantum fields
[2]  
Akhiezer A. I., 1965, QUANTUM ELECTRODYNAM, P39
[3]   SELF-CONSISTENT FIELD APPROACH TO THE MANY-ELECTRON PROBLEM [J].
EHRENREICH, H ;
COHEN, MH .
PHYSICAL REVIEW, 1959, 115 (04) :786-790
[4]  
Fermi E., 1950, NUCL PHYS, P201
[5]  
KAISER H, 1984, PHYS REV A, V29, P2276, DOI 10.1103/PhysRevA.29.2276
[6]   SCHRODINGER INVIOLATE - NEUTRON OPTICAL SEARCHES FOR VIOLATIONS OF QUANTUM-MECHANICS [J].
KLEIN, AG .
PHYSICA B & C, 1988, 151 (1-2) :44-49
[7]  
LINDHARD J, 1954, MAT FYS MEDD DAN VID, V28, P1
[8]   OPTICAL THEOREM AND BEYOND [J].
NEWTON, RG .
AMERICAN JOURNAL OF PHYSICS, 1976, 44 (07) :639-642
[9]   PROPOSED TEST FOR COMPLEX VERSUS QUATERNION QUANTUM-THEORY [J].
PERES, A .
PHYSICAL REVIEW LETTERS, 1979, 42 (11) :683-686
[10]   Single-photon test of hyper-complex quantum theories using a metamaterial [J].
Procopio, Lorenzo M. ;
Rozema, Lee A. ;
Wong, Zi Jing ;
Hamel, Deny R. ;
O'Brien, Kevin ;
Zhang, Xiang ;
Dakic, Borivoje ;
Walther, Philip .
NATURE COMMUNICATIONS, 2017, 8