On some definition of physical state

Michel Paty

Despite its power as the conceptual basis for a huge range of physical phenomena in atomic and subatomic physics, quantum mechanics still suffers from a lack of clarity regarding the physical meaning of its fundamental theoretical concepts, such as those of quantum state and of quantum theoretical quantities or variables , dealt with by the known mathematical-theoretical rules. These concepts have generally been considered as not giving a direct description of physical systems, for they do not correspond to what is usually understood by `physical states' or `physical properties', notably characterized by definite numerical values such as those obtained from measurement. The situation has been tentatively expressed in terms of various `interpretations', conceived not only with regard to the physical meanings of mathematical quantities, but also in connection with philosophical statements about `physical reality'. The question of whether or not quantum theoretical quantities describe definite physical systems existing in nature has therefore generally been considered as beyond the possibilities of physics, because of the definitions that are commonly taken for `physical state' and `physical quantity'. We sketch the main ideas on this problem and propose a possible way out of the puzzle, in terms of an extension of the meaning given to the concepts of the physical state and physical quantity of a system, which would allow one, without any theoretical change in quantum mechanics, to speak consistently of real quantum systems as having definite physical properties .

David Hodgson

In classical physics, the ‘state’ of a particle, at any particular time, is taken to involve a definite position in space and a definite motion; and the state of a system of particles is taken to involve a definite position in space and a definite motion for each of the particles. The situation in relation to quantum mechanics is completely different. As in classical physics, calculations can be made concerning the position and motion of a particle. However, this representation is not by means of symbols for scalar or vector quantities: it is by a more complex mathematical object. This quantum state does not indicate or represent position or motion in any direct way: what it does in substance is to enable calculation of the probability of the particle in question being found to have a position or momentum if an appropriate measurement is made.

Roger G. Newton

James G. Gilson

Fan Xie

This paper aims to clarify the true physical relation of photon pairs and to falsify the "entanglement collapse" hypothesis that standard quantum mechanics imposes upon them. Bell experiments violating Bell's inequality only rule out "local independent hidden variables," and are not a sufficient condition for proving "superposition plus wave-function collapse." The physical definition of entanglement in standard quantum mechanics is: subsystems are strongly correlated, the system is inseparable, and the individual subsystem has no definite independent physical state; its mathematical expressions are the non-factorizability of pure-state wave functions and the non-convex-combination of mixed-state density matrices. The physical definition and mathematical expressions are fully aligned: the individual subsystem cannot be written as a separate expression and has no definite independent physical state. Operationally, it is also absolutely impossible to realize an individual measurement of the subsystem. However, in Bell experiments, photon pairs are separately and individually measured on spatially separated detectors, which directly falsifies the premise that "the photon pair is in an entangled state." Stripping away mysticism, the true relation of two photons is a linear equation with two unknowns (independent particles under an initial-state constraint); the three-photon logic (a linear equation with three unknowns) proves that after measuring one photon, the other two still have not collapsed into definite values and must still be measured individually to obtain their states—"wave-function collapse into a definite value" is purely fictitious in algebraic logic.