Oxford's Radical Quantum Theory Challenges Hilbert Space and Shor's Algorithm

Physicists at Oxford University have proposed a radical new theory called rational quantum mechanics (RaQM). The framework challenges long-held assumptions in quantum theory while keeping its most reliable predictions. Emeritus Professor Tim Palmer, the theory's architect, argues that core concepts like infinite-dimensional Hilbert Space may not reflect reality.

RaQM discards the traditional Hilbert Space, a mathematical cornerstone of quantum mechanics since its inception. Instead, it redefines quantum states using rational observables, effectively breaking the continuous nature of the theory into discrete parts. This shift aligns with David Hilbert's own scepticism about infinity in physical reality.

The theory does not dispute the predictive success of quantum mechanics. It questions how we interpret its foundations, particularly the nature of entanglement and non-locality. RaQM offers a fresh take on Bell's Theorem, suggesting that quantum correlations arise from holistic laws rather than spooky action at a distance.

One of RaQM's boldest claims is that Shor's algorithm—a quantum method for factoring large integers—will fail when applied to systems with a few hundred error-corrected qubits. Unlike standard quantum mechanics, which allows information content to grow unboundedly with qubit count, RaQM imposes a strict limit. Professor Palmer views this predicted breakdown not as a flaw but as a potential bridge to a deeper theory unifying quantum mechanics and gravity.

No experiments have yet tested RaQM's predictions. There are currently no known research projects aimed at verifying or disproving its claims.

If Shor's algorithm fails under the conditions RaQM describes, it could mark a turning point for quantum theory. The outcome might force physicists to reconsider how quantum states store information and interact with gravity. For now, the theory remains untested—but its implications could reshape the future of physics.