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THE STATISTICAL NATURE OF QUANTUM MECHANICS

James S. Albertson

The British Journal for the Philosophy of ScienceNov 1, 19621 citation

PROBABILITY IN QUANTUM-MECHANICS ACCORDING TO SCHRODINGER,E.

No author provided

Sep 10, 20260 citations

On the Concept of State in Quantum Mechanics: Another Way to Decoherence?

Luigi E. Picasso

International Journal of Theoretical PhysicsFeb 25, 20231 citation

THE HATSOPOULOS–GYFTOPOULOS RESOLUTION OF THE SCHRÖDINGER–PARK PARADOX ABOUT THE CONCEPT OF "STATE" IN QUANTUM STATISTICAL MECHANICS

Gian Paolo Beretta

A seldom recognized fundamental difficulty undermines the concept of individual "state" in the present formulations of quantum statistical mechanics (and in its quantum information theory interpretation as well). The difficulty is an unavoidable consequence of an almost forgotten corollary proved by Schrödinger in 1936 and perused by Park, Am. J. Phys.36, 211 (1968). To resolve it, we must either reject as unsound the concept of state, or else undertake a serious reformulation of quantum theory and the role of statistics. We restate the difficulty and discuss a possible resolution proposed in 1976 by Hatsopoulos and Gyftopoulos, Found. Phys.6, 15; 127; 439; 561 (1976).A seldom recognized fundamental difficulty undermines the concept of individual "state" in the present formulations of quantum statistical mechanics (and in its quantum information theory interpretation as well). The difficulty is an unavoidable consequence of an almost forgotten corollary proved by Schrödinger in 1936 and perused by Park, Am. J. Phys.36, 211 (1968). To resolve it, we must either reject as unsound the concept of state, or else undertake a serious reformulation of quantum theory and the role of statistics. We restate the difficulty and discuss a possible resolution proposed in 1976 by Hatsopoulos and Gyftopoulos, Found. Phys.6, 15; 127; 439; 561 (1976).

arXiv:quant-ph/0610057Modern Physics Letters ADec 7, 20068 citations

Some comments on the concept of state in quantum mechanics

Wilhelm Ochs

ErkenntnisNov 1, 198124 citations

TOWARDS A MORE FUNDAMENTAL THEORY BEYOND QUANTUM MECHANICS, AVOIDING THE SCHRÖDINGER PARADOX

F. Caravaglios

The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is supposed to exist, nothing can discriminate two apparently identical states even if they give a different result. In this paper we try to put the basis for a more fundamental theory that (approximately) coincides with quantum mechanics when comparing statistics, but it is more fundamental, since it mathematically describes measurement processes giving an explicit time evolution of the wave function during the collapse. The theory is deterministic even if the Heisenberg uncertainty principle is still valid. The theory distinguishes physical states that collapse and physical states that do not collapse. The theory can be made compatible with all experiments done in the past, but new phenomena such as violations of the Born law or the superposition principle could transpire. However, even if we have probably shown that it is possible to build ad hoc a theory that can describe both the wave function collapse and the Schrödinger linear evolution, a simple and unified construction is still missing.The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is supposed to exist, nothing can discriminate two apparently identical states even if they give a different result. In this paper we try to put the basis for a more fundamental theory that (approximately) coincides with quantum mechanics when comparing statistics, but it is more fundamental, since it mathematically describes measurement processes giving an explicit time evolution of the wave function during the collapse. The theory is deterministic even if the Heisenberg uncertainty principle is still valid. The theory distinguishes physical states that collapse and physical states that do not collapse. The theory can be made compatible with all experiments done in the past, but new phenomena such as violations of the Born law or the superposition principle could transpire. However, even if we have probably shown that it is possible to build ad hoc a theory that can describe both the wave function collapse and the Schrödinger linear evolution, a simple and unified construction is still missing.

arXiv:0907.0125International Journal of Modern Physics ADec 20, 20092 citations

THE SCHRÖDINGER-PARK PARADOX ABOUT THE CONCEPT OF “STATE” IN QUANTUM STATISTICAL MECHANICS AND QUANTUM INFORMATION THEORY IS STILL OPEN: ONE MORE REASON TO GO BEYOND?

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THE SCHRÖDINGER-PARK PARADOX ABOUT THE CONCEPT OF “STATE” IN QUANTUM STATISTICAL MECHANICS AND QUANTUM INFORMATION THEORY IS STILL OPEN: ONE MORE REASON TO GO BEYOND?

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