Incorporating the quantum of action h into classical physics

Investigate whether and how the quantum of action h can be incorporated into the framework of classical physics in a consistent manner, or otherwise ascertain the reasons such incorporation is not possible.

Background

Planck recounts that, after introducing the quantum of action h, he made repeated attempts over several years to reconcile this constant with classical physics. He explicitly states that these attempts failed, leaving open the question of whether a classical integration is possible at all.

References

For several years, I repeatedly tried to somehow incorporate the quantum of action into the system of classical physics. But I did not succeed.

— The history of the discovery of the physical quantum of action (Zur Geschichte der Auffindung des physikalischen Wirkungsquantums)  (2403.09689 - Marquet et al., 2024) in Section III (The theoretical formula for Radiation), p.159

Until now, there is no mathematical proof showing whether this classical stochastic approach can really provide an alternative approach to atomic stability, though a heuristic argument is given in .

— Hamiltonian Floer Theory for Quantum Electrodynamics up to First Order in $\hbar$  (2608.19996 - Fabert et al., 20 Aug 2026) in Section 1, Introduction; also discussed in Section 2.3, subsection “Stochastic electrodynamics”