A theorem published in 2018 proved, through rigorous mathematics, that nothing deeper than quantum mechanics could ever give rise to quantum mechanics. Physicists just broke it.
The paper, published in Physical Review A, comes from James Hefford and Matt Wilson at Université Paris-Saclay. What they found is not a refinement of quantum theory or an adjustment to an existing model. They identified a mathematical structure sitting one level above quantum mechanics, a theory where cause and effect have no fixed sequence, where two events can simultaneously precede each other with nothing in the laws of physics settling which came first, and they proved that ordinary quantum mechanics falls out of it the same way the solid everyday world falls out of quantum physics. Findings published in Physical Review A establish the precise map from that deeper structure into standard quantum theory, trace every step of the derivation, and confirm it satisfies every condition required for the result to be valid.
The deeper theory is called QBox. Nothing in it behaves the way quantum mechanics behaves, and nothing in quantum mechanics behaves the way everyday reality behaves. That stacking is not coincidence. It is the architecture of the argument. Classical reality, tables and chairs and the trajectory of a thrown ball, emerges from quantum mechanics through a process called decoherence. A quantum particle in isolation exists in superpositions, multiple states simultaneously, behaves as a wave, and changes when observed. The moment it begins interacting with its surrounding environment, air molecules, stray photons, background radiation, those quantum properties become inaccessible rather than absent, smeared into the environment beyond any practical recovery. What the observer sees looks classical. Decoherence is not a collapse of reality into something simpler. It is a filter that blocks access to the deeper layer. Hefford and Wilson are arguing that quantum mechanics itself is that same kind of filtered view, the readable surface of something far stranger underneath.
Inside QBox, causality as physicists currently understand it does not exist. In standard quantum mechanics, even at its most counterintuitive, one thing remains fixed: events have an order. A causes B, or B causes A, but one of those is true and the other is not. QBox is built on a framework called indefinite causal order, in which that constraint is abandoned entirely. Two operations can stand in a relationship where each one precedes the other simultaneously, no ordering fixed, no fact of the matter available to settle the question. This sounds like an abstract mathematical curiosity. It stopped being that around 2012, when physicists formally defined objects called process matrices that encode indefinite causal structures precisely, and it stopped being even theoretically remote when laboratory teams began building devices called quantum switches that perform two quantum operations in a genuine superposition of causal orderings. Those experiments exist, have been replicated across multiple institutions, and are published in peer-reviewed journals. The physics of indefinite causal order is not speculation. What Hefford and Wilson are doing is working with the theoretical framework those experiments point toward and asking whether quantum mechanics itself lives inside it.
The 2018 theorem by Ciarán Lee and John Selby in the Proceedings of the Royal Society was the wall standing between that question and an answer. Lee and Selby proved that recovering quantum mechanics from any deeper theory through hyper-decoherence, the second-order version of the decoherence process that produces classical from quantum, was mathematically impossible as long as the deeper theory obeyed two conditions. The first was causality: no signalling from the future back into the past. The second was unique purifications. Purification is a technical term for a specific relationship between states of incomplete information and states of complete information. For any mixed state, a state where something is unknown, there must exist a corresponding pure state, a state of total knowledge, from which it derives. Lee and Selby required that this pure state be unique up to a reversible transformation. If a theory satisfied both conditions simultaneously, they proved, it could not hyper-decohere into quantum mechanics. The theorem stood for six years and effectively closed the research programme.
QBox breaks both conditions, and the breaking is not accidental. It is the mechanism. QBox permits controlled signalling to the past because its systems are built as boxes with a past-facing component and a future-facing component, and the theory grants access to both. Strip that access away and the backwards signalling disappears. On purifications: in QBox the correct measure of purity is not borrowed from quantum mechanics but derived from the theory’s own geometry, convex extremality in the space of quantum channels. Under that definition, purifications in QBox are not unique. Hefford and Wilson prove this with an explicit construction in the paper’s appendix: two distinct unitary operations, a specific pair of states built from them, identical reduced states, no reversible transformation relating the two purifications. Non-unique purifications. Both conditions of the Lee-Selby theorem violated. The no-go no longer applies.
The hyper-decoherence map is precise and its physical meaning is worth understanding directly. Every system in QBox has two halves. The top half faces the future. The bottom half faces the past. The hyper-decoherence map takes the bottom half and applies a completely depolarising operation to it: all information in the past-facing component gets replaced with maximal noise, erased, rendered inaccessible. The top half is left exactly as it was. What comes out is a completely positive, trace-preserving map, which is the exact mathematical object that describes every allowed transformation in standard quantum mechanics. Collect every result of this operation across the full structure of QBox and what you have is provably equivalent to quantum theory as physicists have used it for a century.
The physical interpretation of that process is the part that should not be moved past quickly. In ordinary decoherence, an observer loses access to quantum behaviour because the system cannot be isolated from its environment. The quantum information is still there. It has dispersed into the surrounding environment beyond reach. In hyper-decoherence from QBox, what the observer loses access to is the past-facing half of every system. The deeper theory contains both temporal directions simultaneously, past and future, as live and accessible components of physical reality. Hyper-decoherence does not destroy that structure. It imposes a constraint on the observer: they can only reach the future-facing half. The past component is cut off. Standard quantum mechanics is what physics looks like when access to the past direction of reality has been removed. In that framing, the past is not gone. At the level of QBox it is still there, encoded in the bottom half of every box in the theory. The observer simply cannot reach it.
The connection to quantum gravity has been building in the theoretical physics community since at least 2007, when Lucien Hardy proposed that any successful theory unifying quantum mechanics with general relativity would need to accommodate non-fixed causal structures. General relativity allows spacetime to warp and curve depending on the distribution of mass and energy, which means the ordering of events is not absolute but depends on geometry, and that geometry is dynamic and changes. In regions of extreme gravitational curvature, near a black hole’s event horizon or in the conditions immediately following the Big Bang, the causal structure of spacetime is not a fixed background but a variable determined by the physics itself. Hardy argued that a genuine quantum theory of gravity therefore cannot treat causality as a given. QBox, built precisely on the abandonment of fixed causal order, fits that requirement. The hyper-decoherence from QBox to quantum mechanics is a concrete toy model of the mechanism by which ordinary quantum physics might emerge from a quantum gravitational theory where spacetime itself, and therefore causality, is not predetermined.
Hefford and Wilson do not claim QBox is physically real, and the paper states two competing interpretations without resolving between them. The first: the existence of a valid hyper-decoherence map is evidence that something structurally similar to QBox genuinely underlies quantum mechanics in nature, and hyper-decoherence is a real process that explains why observers at the quantum level perceive fixed causal order rather than the indefinite structure beneath it. The second: the map works by discarding an entire temporal dimension, which is a more drastic operation than anything in standard decoherence, and that may mean the axioms used to define valid hyper-decoherence are not strict enough. The authors note that requiring hyper-decoherence to preserve the number of degrees of freedom rather than eliminating a temporal direction wholesale would likely invalidate their construction. Whether anything survives under that tighter requirement is an open question the paper explicitly leaves for future work.
What is not open is the status of the Lee-Selby theorem. It has been bypassed. A post-quantum theory satisfying a precise formal definition now exists, and standard quantum mechanics is recoverable from it. The theory is QBox. The recovery is the hyper-decoherence map in Physical Review A. The question physicists are now carrying is whether that map describes something physically real or exposes a gap in the current mathematical framework for post-quantum theories. Either answer changes the picture. If QBox is real, quantum mechanics is not the ground floor of nature. If the axioms need rewriting, the search for what does sit beneath quantum mechanics now has a new constraint to work with, one purchased by finding out exactly where the current framework breaks.
Source:
Hefford, J. & Wilson, M. (2025). Decoherence to quantum theory from a causally-indefinite post-quantum theory. Physical Review A. https://doi.org/10.1103/kmmy-3dy3
