Two Historical Problems in Quantum Measurement

Summary

There has been and currently still is substantial debate and misconception regarding the definition of the quantum measurement problem.  At a recent conference [1] attended by notable scientists many who have actively worked on the problem, it is stated as a fact in the call for papers that MWI solves the quantum measurement problem: “The Many-worlds interpretation of quantum mechanics solves the measurement problem, avoids action at a distance and indeterminism and does not contradict empirical evidence. Why, then, it is not in the consensus?”  Moreover, Maudlin [2] and separately Lewis [3] wrote that Bohm’s theory solves the Measurement Problem. Mermin very recently wrote a paper [4] in which he claims that there is no quantum measurement problem. It appears that many are under the false impression that all that is needed to resolve the QMP is to produce an interpretation that explains the two postulates.  We examine two separate measurement problems that historically arose. The first in 1926 arose due to the proposed necessity of having to resort to a dual description of Nature. Schrödinger’s equation was proposed to suffice to explain microscopic phenomenon and it was deemed by Bohr that a statistical rule would be necessary to explain the quantum postulate for which quantum phenomenon reveal their nature through measurement.  Born’s rule was proposed as the statistical rule which later became the measurement postulate as proposed by von Neumann. The first problem arose to explain further what happens in the process of measurement, given that a measurement occurs. At this point, there was no clear indication if Schrödinger’s equation fails to give the correct predictions, or whether there was a fundamental epistemological limitation in obtaining the result. Such a limitation was claimed by Bohr to exist due to an uncontrollable interaction during measurement which made one of two conjugate variables uncertain so that a classical space-time accounting whereby one knows precisely both conjugate variables could not be had.  The second quantum measurement problem arose in 1935 when Schrödinger showed that his equation made the prediction of entanglement between measuring device and particle [5]. Experiments beginning in the 1970’s and refined over the years subsequently led to the confirmation of these entanglement predictions. This latter problem is much more serious than the first problem, as it implies that Schrödinger’s equation makes an incorrect quantum state prediction when measurement occurs [6, Ch. 3]. The logical requirements for resolution of this second problem are examined further in an upcoming paper [7].

[1] “The Many-worlds interpretation of quantum mechanics: current status and relation to other interpretations,” https://philevents.org/event/show/96009, Oct. 18, 2022.
[2] T. Maudlin, “Why Bohm’s Theory Solves the Measurement Problem,” Philos Sci, vol. 62, pp. 479–483, 1995.
[3] P. J. Lewis, “How Bohm’s Theory Solves the Measurement Problem,” Philos Sci, vol. 74, pp. 749–760, 2007.
[4] N. D. Mermin, “There is no quantum measurement problem,” Phys Today, vol. 75, no. 6, pp. 62–63, Jun. 2022, doi: 10.1063/PT.3.5027.
[5] E. Schrödinger, “The present situation in quantum mechanics,” Naturwissenshaften (English translation in Proceedings of the American Philosophical Society vol 124), vol. 23, pp. 802–812, 1935.
[6] M. Steiner and R. Rendell, The Quantum Measurement Problem. Inspire Institute, 2018.
[7] M. Steiner and R. Rendell, “Logical Requirements for the Resolution of the Quantum Measurement Problem.” Work in Progress, 2022.