Il Nuovo Cimento B

Popper's experiment and the centre-of-mass wave function

F. Miglietta

Published Apr 1, 2005• 0 citations

Abstract

Popper's ideal experiment, concerning a pair of momentum-entangled particles, is analysed from the point of view of standard quantum mechanics, taking into account the centre-of-mass wave function.

DOI: 10.1393/ncb/i2005-10038-y

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Il Nuovo Cimento B

Popper's experiment and the centre-of-mass wave function

F. Miglietta

Published Apr 1, 2005• 0 citations

Publisher

Abstract

Popper's ideal experiment, concerning a pair of momentum-entangled particles, is analysed from the point of view of standard quantum mechanics, taking into account the centre-of-mass wave function.

DOI: 10.1393/ncb/i2005-10038-y

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What happens to the entropy increase principle as the Universe evolve to form the big-crunch singularity? What happens to the uncertainity relations along the process of gravitational collapses? What is the quantum mechanical description of a Radon atom in a rigid box when the distance of consecutive nodes and antinodes of $ψ$ is equal to or less than the diameter of the atom? What is the position-space wave function of two finite volume massive bosons if we take contact interaction into account? How a photon produce electron-positron pair with finite volume concentrate rest masses? What are the charges of the electron-positron pairs forming loops in the vacuum? How two particles with three-momentums $k_1, k_2$ $(k_1 \neq k_2)$ produced to form a loop at a space-time point always arrive at another spacial point simultaneously? What is the microscopic explanation in terms of particle exchanges of the force in the Casimir effect? What is the mechanism of the collapse of the momentum-space wave function of a particle knocking out an elctron from an atom? What is meant by $|Ψ> = {c_1 (t)}|Ψ_{U^{238}}> + {c_2 (t)}|Ψ_{Th^{234}}> ~?$ Quantum mechanically the region between the rigid walls (which is equiprobable in classical mechanics) is non-homogeneous for a particle in a rigid box. A photon can not reproduce Maxwell's equations apart from moving with velocity $c$ . How can a process involving only a few photons be described starting from the Maxwell's equations? The large scale structure of the Universe is homogeneous. What is the screen in our brains to view objects, as they are, of sizes larger than our brains?What happens to the entropy increase principle as the Universe evolve to form the big-crunch singularity? What happens to the uncertainity relations along the process of gravitational collapses? What is the quantum mechanical description of a Radon atom in a rigid box when the distance of consecutive nodes and antinodes of $ψ$ is equal to or less than the diameter of the atom? What is the position-space wave function of two finite volume massive bosons if we take contact interaction into account? How a photon produce electron-positron pair with finite volume concentrate rest masses? What are the charges of the electron-positron pairs forming loops in the vacuum? How two particles with three-momentums $k_1, k_2$ $(k_1 \neq k_2)$ produced to form a loop at a space-time point always arrive at another spacial point simultaneously? What is the microscopic explanation in terms of particle exchanges of the force in the Casimir effect? What is the mechanism of the collapse of the momentum-space wave function of a particle knocking out an elctron from an atom? What is meant by $|Ψ> = {c_1 (t)}|Ψ_{U^{238}}> + {c_2 (t)}|Ψ_{Th^{234}}> ~?$ Quantum mechanically the region between the rigid walls (which is equiprobable in classical mechanics) is non-homogeneous for a particle in a rigid box. A photon can not reproduce Maxwell's equations apart from moving with velocity $c$. How can a process involving only a few photons be described starting from the Maxwell's equations? The large scale structure of the Universe is homogeneous. What is the screen in our brains to view objects, as they are, of sizes larger than our brains?

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INTRODUCTION In his essay ‘Quantum Mechanics Without “the Observer”’ (in [20], 7–44), Popper criticizes the Copenhagen Interpretation and suggests construing the quantum theory as a ‘generalization of classical statistical mechanics’ ([20], 16). The uncertainty relations, he says, set ‘limits to the statistical dispersion … of the results of sequences of experiments’ ([20], 20) and not to what can be said about individual systems. Some strange features of orthodox microphysics are due either to a misinterpretation of probability, involving some ‘very simple mistakes’ ([20], 42); or else they are a straightforward consequence of the fact that the quantum theory is a statistical theory. For example, ‘the reduction of the wave packet … has nothing to do with quantum theory: it is a trivial feature of probability theory’ ([20], 37). The idea of probability that is presupposed in all these arguments, however, is Popper's propensity interpretation. Adopting this interpretation suffices for making clear what the quantum theory really is: a ‘generalization of classical statistical mechanics’ ([20], 16). This is Popper's position as I understand it. This position, it seems to me, is attractive enough as long as one does not carry the analysis too far. But it breaks down when confronted with all the facts which Bohr wanted to take into account. Altogether Popper's criticism and his alternative proposals once more reveal the strong points of the Copenhagen philosophy, and especially of the ideas of Niels Bohr. Today it is very difficult to find a satisfactory account of these ideas.INTRODUCTION In his essay ‘Quantum Mechanics Without “the Observer”’ (in [20], 7–44), Popper criticizes the Copenhagen Interpretation and suggests construing the quantum theory as a ‘generalization of classical statistical mechanics’ ([20], 16). The uncertainty relations, he says, set ‘limits to the statistical dispersion … of the results of sequences of experiments’ ([20], 20) and not to what can be said about individual systems. Some strange features of orthodox microphysics are due either to a misinterpretation of probability, involving some ‘very simple mistakes’ ([20], 42); or else they are a straightforward consequence of the fact that the quantum theory is a statistical theory. For example, ‘the reduction of the wave packet … has nothing to do with quantum theory: it is a trivial feature of probability theory’ ([20], 37). The idea of probability that is presupposed in all these arguments, however, is Popper's propensity interpretation. Adopting this interpretation suffices for making clear what the quantum theory really is: a ‘generalization of classical statistical mechanics’ ([20], 16). This is Popper's position as I understand it. This position, it seems to me, is attractive enough as long as one does not carry the analysis too far. But it breaks down when confronted with all the facts which Bohr wanted to take into account. Altogether Popper's criticism and his alternative proposals once more reveal the strong points of the Copenhagen philosophy, and especially of the ideas of Niels Bohr. Today it is very difficult to find a satisfactory account of these ideas.

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ψ

is equal to or less than the diameter of the atom? What is the position-space wave function of two finite volume massive bosons if we take contact interaction into account? How a photon produce electron-positron pair with finite volume concentrate rest masses? What are the charges of the electron-positron pairs forming loops in the vacuum? How two particles with three-momentums

k_1, k_2

(k_1 \neq k_2)

produced to form a loop at a space-time point always arrive at another spacial point simultaneously? What is the microscopic explanation in terms of particle exchanges of the force in the Casimir effect? What is the mechanism of the collapse of the momentum-space wave function of a particle knocking out an elctron from an atom? What is meant by

|Ψ> = {c_1 (t)}|Ψ_{U^{238}}> + {c_2 (t)}|Ψ_{Th^{234}}> ~?

Quantum mechanically the region between the rigid walls (which is equiprobable in classical mechanics) is non-homogeneous for a particle in a rigid box. A photon can not reproduce Maxwell's equations apart from moving with velocity

c

. How can a process involving only a few photons be described starting from the Maxwell's equations? The large scale structure of the Universe is homogeneous. What is the screen in our brains to view objects, as they are, of sizes larger than our brains?

ψ

k_1, k_2

(k_1 \neq k_2)

|Ψ> = {c_1 (t)}|Ψ_{U^{238}}> + {c_2 (t)}|Ψ_{Th^{234}}> ~?

Quantum mechanically the region between the rigid walls (which is equiprobable in classical mechanics) is non-homogeneous for a particle in a rigid box ! The large scale structure of the Universe is homogeneous.