Did any "classical era" physicist foresee that a theory such as Quantum Mechanics is logically inescapable?

Question

I am interested in knowing if in the era preceding the observations that lead to the advent of Quantum Mechanics, anyone foresaw logically that a theory such as Quantum Mechanics is in a sense, "unavoidable".

I am not referring to a prediction of any of the technical details of the QM theory we have today, that of course is unlikely. I rather mean some prediction with regards to the particular and central feature of QM as a theory where the process of measurement is very central, both formally and conceptually, and as one which is deeply incorporated into the theory.

The motivation for the question, is that it seems possible that someone had postulated as a logical necessity, even before QM was "forced" on us, some future time when the very act of measurement itself has to be taken into account as a significant physical interaction that changes the state of the system, when the system is of a small enough scale. On that note, I need to clarify that I am not referring to techniques for handling various types of measurement uncertainties, clearly those were well known prior to QM and are not really referring to the same concept I am describing.

Please note I am not here debating whether that "logical" step of predicting a QM-like theory in the past is in itself valid or not -- it may very well be criticized and shown to be erroneous. I am only highlighting the point that it seems to me not impossible that someone may have thought along those lines, and hence I'm curious if anyone in fact did. Also note, while my title is asking for physicists who speculated along those lines, it will be also interesting to know if any philosopher wrote something about it. However, I am most interested to know if any of the famous physicists such as Newton, Maxwell, Hamilton, etc. ever wrote something pertaining to this idea.

Answer 1

The following is far from "foreseeing" a "logical inescapability" of quantum mechanics, but I think it's quite interesting.

Bernhard Riemann (not a physicist) is generally credited with founding the mathematics of curved space ("Riemannian Geometry") which some decades later provided the mathematical framework of General Relativity. It is less known that near the end (III §3) of his famous habilitation lecture Ueber die Hypothesen, welche der Geometrie zu Grunde liegen (held June 10, 1854, first published in 1868) he writes

Die Fragen über das Unmessbargrosse sind für die Naturerklärung müssige Fragen. Anders verhält es sich aber mit den Fragen über das Unmessbarkleine. Auf der Genauigkeit, mit welcher wir die Erscheinungen in's Unendlichkleine verfolgen, beruht wesentlich die Erkenntniss ihres Causalzusammenhangs.

[...]

Nun scheinen aber die empirischen Begriffe, in welchen die räumlichen Massbestimmungen gegründet sind, der Begriff des festen Körpers und des Lichtstrahls, im Unendlichkleinen ihre Gültigkeit zu verlieren; es ist also sehr wohl denkbar, dass die Massverhältnisse des Raumes im Unendlichkleinen den Voraussetzungen der Geometrie nicht gemäss sind, und dies würde man in der That annehmen müssen, sobald sich dadurch die Erscheinungen auf einfachere Weise erklären liessen.

Die Frage über die Gültigkeit der Voraussetzungen der Geometrie im Unendlichkleinen hängt zusammen mit der Frage nach dem innern Grunde der Massverhältnisse des Raumes. Bei dieser Frage, welche wohl noch zur Lehre vom Raume gerechnet werden darf, kommt die obige Bemerkung zur Anwendung, dass bei einer discreten Mannigfaltigkeit das Princip der Massverhältnisse schon in dem Begriffe dieser Mannigfaltigkeit enthalten ist, bei einer stetigen aber anders woher hinzukommen muss. Es muss also entweder das dem Raume zu Grunde liegende Wirkliche eine discrete Mannigfaltigkeit bilden, oder der Grund der Massverhältnisse ausserhalb, in darauf wirkenden bindenen Kräften, gesucht werden.

Translation (based on the one by William Cifford)

The questions about the immeasurably great are for the interpretation of nature useless questions. But this is not the case with the questions about the immeasurably small. It is upon the exactness with which we follow phenomena into the infinitely small that our knowledge of their causal relations essentially depends.

[...]

Now it seems that the empirical notions on which the metrical determinations of space are founded, the notion of a solid body and of a ray of light, cease to be valid for the infinitely small. We are therefore quite at liberty to suppose that the metric relations of space in the infinitely small do not conform to the hypotheses of geometry; and we ought in fact to suppose it, if we can thereby obtain a simpler explanation of phenomena.

The question of the validity of the hypotheses of geometry in the infinitely small is bound up with the question of the ground of the metric relations of space. In this last question, which we may still regard as belonging to the doctrine of space, is found the application of the remark made above; that in a discrete manifoldness, the ground of its metric relations is given in the notion of it, while in a continuous manifoldness, this ground must come from outside. Either therefore the reality which underlies space must form a discrete manifoldness, or we must seek the ground of its metric relations outside it, in binding forces which act upon it.