Abstract
We propose a pedagogical presentation of measurement in the de Broglie-Bohm interpretation. In this heterodox interpretation, the position of a quantum particle exists and is piloted by the phase of the wave function. We show how this position explains determinism and realism in the three most important experiments of quantum measurement: double-slit, Stern-Gerlach, and EPR-B. First, we demonstrate the conditions in which the de Broglie-Bohm interpretation can be assumed to be valid through continuity with classical mechanics. Second, we present a numerical simulation of the double-slit experiment performed by Jönsson in 1961 with electrons. It demonstrates the continuity between classical mechanics and quantum mechanics. Third, we present an analytic expression of the wave function in the Stern-Gerlach experiment. This explicit solution requires the calculation of a Pauli spinor with a spatial extension. This solution enables us to demonstrate the decoherence of the wave function and the three postulates of quantum measurement. Finally, we study the Bohm version of the Einstein-Podolsky-Rosen experiment. Its theoretical resolution in space and time shows that a causal interpretation exists where each atom has a position and a spin.
Highlights
“I saw the impossible done” [1]
The goal of the present paper is to present the BroglieBohm pilot wave through the study of the three most important experiments of quantum measurement: the double-slit experiment which is the crucial experiment of the waveparticle duality, the Stern and Gerlach experiment with the measurement of the spin, and the EPR-B experiment with the problem of nonlocality
In the de Broglie-Bohm interpretation, the impacts on the screen are the real positions of the electron as in classical mechanics and the three postulates of the measurement of quantum mechanics can be trivially explained: the position is an eigenvalue of the position operator because the position variable is identical to its operator (XΨ = xΨ), the Born postulate is satisfied with the “equivariance” property, and the reduction of the wave packet is not necessary to explain the impacts
Summary
“I saw the impossible done” [1]. This is how John Bell describes his inexpressible surprise in 1952 upon the publication of an article by Bohm [2]. More than thirty years after John Bell’s questions, the interpretation of the de Broglie-Bohm pilot wave is still ignored by both the international community and the textbooks. This explicit solution requires the calculation of a Pauli spinor with a spatial extension. We recall that a physical explanation of nonlocal influences is possible
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