We argue that in contrast to the classical physics, measurements in quantum mechanics should provide simultaneous information about all relevant relative amplitudes (pure states and the transitions between them) and a...We argue that in contrast to the classical physics, measurements in quantum mechanics should provide simultaneous information about all relevant relative amplitudes (pure states and the transitions between them) and all relevant relative phases. Simultaneity is needed since measurement changes the state of the system (in both quantum and in classical physics). We call that measurement procedure holographic detection. Mathematically, it is described by a set of mutually commuting selfadjoint operators that are similar and closely related to projections. We present explicit examples and discuss general features of the corresponding experimental setup which we identify as the quantum reference frame.展开更多
We present here a realization of Hurwitz algebra in terms of 2 × 2 vector matrices which maintain the correspondence between the geometry of vector spaces that is used in the classical physics and the algebraic f...We present here a realization of Hurwitz algebra in terms of 2 × 2 vector matrices which maintain the correspondence between the geometry of vector spaces that is used in the classical physics and the algebraic foundation underlying quantum theory. The multiplication rule we use is a modification of the one originally introduced by M. Zorn. We demonstrate that our multiplication is not intrinsically non-associative;the realization of the real and complex numbers is commutative and associative, the real quaternions maintain associativity and the real octonion matrices form an alternative algebra. Extension to the calculus of the matrices (with Hurwitz algebra valued matrix elements) of the arbitrary dimensions is straightforward. We briefly discuss applications of the obtained results to extensions of standard Hilbert space formulation in quantum physics and to alternative wave mechanical formulation of the classical field theory.展开更多
文摘We argue that in contrast to the classical physics, measurements in quantum mechanics should provide simultaneous information about all relevant relative amplitudes (pure states and the transitions between them) and all relevant relative phases. Simultaneity is needed since measurement changes the state of the system (in both quantum and in classical physics). We call that measurement procedure holographic detection. Mathematically, it is described by a set of mutually commuting selfadjoint operators that are similar and closely related to projections. We present explicit examples and discuss general features of the corresponding experimental setup which we identify as the quantum reference frame.
文摘We present here a realization of Hurwitz algebra in terms of 2 × 2 vector matrices which maintain the correspondence between the geometry of vector spaces that is used in the classical physics and the algebraic foundation underlying quantum theory. The multiplication rule we use is a modification of the one originally introduced by M. Zorn. We demonstrate that our multiplication is not intrinsically non-associative;the realization of the real and complex numbers is commutative and associative, the real quaternions maintain associativity and the real octonion matrices form an alternative algebra. Extension to the calculus of the matrices (with Hurwitz algebra valued matrix elements) of the arbitrary dimensions is straightforward. We briefly discuss applications of the obtained results to extensions of standard Hilbert space formulation in quantum physics and to alternative wave mechanical formulation of the classical field theory.
