A Causal Framework for Non-Linear Quantum Mechanics

Abstract

We add non-linear and state-dependent terms to quantum field theory. We show that the resulting low-energy theory, non-linear quantum mechanics, is causal, preserves probability and permits a consistent description of the process of measurement. We explore the consequences of such terms and show that non-linear quantum effects can be observed in macroscopic systems even in the presence of de-coherence. We find that current experimental bounds on these non-linearities are weak and propose several experimental methods to significantly probe these effects. The locally exploitable effects of these non-linearities have enormous technological implications. For example, they would allow large scale parallelization of computing (in fact, any other effort) and enable quantum sensing beyond the standard quantum limit. We also expose a fundamental vulnerability of any non-linear modification of quantum mechanics - these modifications are highly sensitive to cosmic history and their locally exploitable effects can dynamically disappear if the observed universe has a tiny overlap with the overall quantum state of the universe, as is predicted in conventional inflationary cosmology. We identify observables that persist in this case and discuss opportunities to detect them in cosmic ray experiments, tests of strong field general relativity and current probes of the equation of state of the universe. Non-linear quantum mechanics also enables novel gravitational phenomena and may open new directions to solve the black hole information problem and uncover the theory underlying quantum field theory and gravitation.

22 pages, 0 figures, Journal Version

References in corpus (3)

• Gravity Probe B: Final Results of a Space Experiment to Test General Relativity
• A New Method for Gravitational Wave Detection with Atomic Sensors
• Correlated Worldline theory: Structure and Consistency

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