The noncommutative values of quantum observables |
| |
| Institution: | 1. Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt;2. Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762–4900, USA;3. Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia;4. Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Shosse, Moscow 115409, Russian Federation;5. School of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg, Wits-2050, South Africa;6. Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia;7. Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, Yozgat 66100, Turkey;8. Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar;1. Department of Physics, The University of Azad Jammu and Kashmir, Muzaffarabad 13100, Azad Kashmir, Pakistan;2. National Center for Physics at QAU Campus, Shahdra Valley Road, Islamabad 44000, Pakistan;1. Nuclear Technology Research Centre, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), 43600 Bangi, Selangor, Malaysia;2. Department of Applied Physics, Faculty of Science and Technology, Universiti Kebangsaan Malaysia (UKM), 43600 Bangi, Selangor, Malaysia;3. Department of Physics, Mawlana Bhashani Science and Technology University, Santosh, Tangail-1902, Bangladesh |
| |
| Abstract: | We discuss the notion of representing the values of physical quantities by the real numbers, and its limits to describe the nature to be understood in the relation to our appreciation that the quantum theory is a better theory of natural phenomena than its classical analog. Getting from the algebra of physical observables to their values for a fixed state is, at least for classical physics, really a homomorphic map from the algebra into the real number algebra. The limitation of the latter to represent the values of quantum observables with noncommutative algebraic relation is obvious. We introduce and discuss the idea of the noncommutative values of quantum observables and its feasibility, arguing that at least in terms of the representation of such a value as an infinite set of complex numbers, the idea makes reasonable sense theoretically as well as practically. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
