Resolvability of the quantum measurement problem: the von Neumann chain

Summary

Historically, two measurement problems arose – one in 1926 with the discovery of Schrödinger’s equation and Born’s rule and the second in 1935 [1].  It had initially appeared that the problem in 1926 could be resolved by an interpretation. The problem that arose in 1935 is much more serious than that of 1926 as it was found that Schrödinger’s equation predicts the measuring device plus system will become entangled whereas the measurement postulate predicts the two exist in a product state. From such arguments it is clear that a problem exists, however it has not been firmly established whether or not the problem could still be resolved strictly by an interpretation of the von Neumann postulates or whether the problem requires further experimentation and theory.  In a recent paper [2], the authors propose that the Copenhagen interpretation often characterized by the two von Neumann postulates of quantum mechanics, can only be considered either incomplete or wrong at the moment.  The resolution of the problem requires further investigation, either theoretical, experimental, or both [3]. The issue examined in this paper is whether or not von Neumann’s chain theorem precludes the experimental investigation of the conditions under which measurement occurs. It is found that von Neumann utilized an assumption that limits the class of von Neumann chain Hamiltonians in his proof. A class of tests that can constructively discriminate measurement from unitary evolution (UMDT) is put forward. It is proven that the class of UMDT tests proposed are outside the von Neumann chain class of Hamiltonians. The utility of the theorem is exemplified by application to a recent argument by Frauchiger and Renner.

[1] M. Steiner and R. Rendell, “Two Historical Problems in Quantum Measurement,” Work in Progress, 2022.
[2] M. Steiner and R. Rendell, “Incompleteness of the Copenhagen Interpretation,” Work in Progress, 2022.
[3] M. Steiner and R. Rendell, “Logical Requirements for the Resolution of the Quantum Measurement Problem.” Work in Progress, 2022.