What is it about?
Quantum mechanics is a very successful theory but is very hard to understand. Here we claim that its incomprehensibility derives from the fact that its state space, Hilbert Space, depends on the continuum of complex numbers. A discretisation of this continuum and hence of Hilbert Space is developed and used to create a novel theory of quantum physics: Rational Quantum Mechanics (RaQM). In RaQM the granularity of Hilbert Space is very fine, consistent with gravity being very weak. RaQM solves all of the conceptual problems of QM. An experimental test of RaQM is proposed: the quantum advantage of quantum computers will start to fail for algorithms like Shor's, in computers with more than a few hundred error-corrected qubits. RaQM suggests a novel approach to synthesising quantum and gravitational physics.
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Why is it important?
It is widely believed that quantum computers will have substantial commercial benefits once they can be scaled to a few hundred error-corrected qubits. However, this assumes that quantum mechanics is correct. RaQM, a theory of quantum physics which agrees with quantum mechanics for simple systems, deviates from quantum mechanics when more than a few hundred qubits are entangled. Although quantum computers may not have the commercial applications hoped for, they may nevertheless be a vital tool for finding new more accurate theories of physics.
Perspectives
After a PhD in general relativity theory, I spent considerable time working on the chaotic dynamics of Earth's climate. More recently I have pivoted back to more fundamental physics, bringing a lifetime's experience in nonlinear dynamics. RaQM expresses my personal conviction that nonlinear dynamics underpins quantum physics, and that the linearity of Hilbert Space is quite superficial.
Tim Palmer
University of Oxford
Read the Original
This page is a summary of: Rational quantum mechanics: Testing quantum theory with quantum computers, Proceedings of the National Academy of Sciences, March 2026, Proceedings of the National Academy of Sciences,
DOI: 10.1073/pnas.2523350123.
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