Twenty-Nine Fundamental Problems in Quantum Protein Physics and a Unifying Experimental Methodology: Entangled Differential Tunneling Spectroscopy

We present twenty-nine fundamental problems in quantum protein physics, organized as a structured research program inspired by Hilbert's identification of transformative challenges in mathematics. These problems span eight domains—from quantum path integrals and protein dynamics, through coherence and decoherence in biological systems, to quantum field theory unification and the biomedical implications of quantum tunneling for cancer, neurodegeneration, demyelinating disease, and chromosomal nondisjunction—and address the central question of whether evolved proteins exploit quantum mechanical effects at physiological temperatures (310 K) with a sophistication that surpasses current engineered quantum systems operating near absolute zero. We then introduce Entangled Differential Tunneling Spectroscopy (EDTS), formalized here as Problem #24, as a unifying experimental methodology that connects a significant subset of these problems to concrete laboratory protocols. EDTS exploits time-energy entangled photon pairs to perform simultaneous differential measurements on related protein systems, achieving Heisenberg-limited sensitivity to differences in quantum tunneling landscapes. The methodology is shown to provide experimental access to Problems #1, #5, #7, #10, #12, #15, #18, #19, #22, #25, #26, #27, #28, and #29, while its theoretical framework validates the instanton description central to Problem #23. The paper draws a direct intellectual lineage from the author's 1985 doctoral research at the Institut français du pétrole on hydrogen transfer in conformationally-constrained bicyclic systems—work that anticipated by decades the modern understanding that geometric constraints modulate quantum tunneling in biological contexts—through to the proposed entangled measurement paradigm. This trajectory, spanning four decades from classical catalytic chemistry through computational science to quantum biology, is offered as both a personal scientific testament and a roadmap for the next generation of researchers.