[Paper Review] Causality Violation and Nonlinear Quantum Mechanics

Jacques Pienaar|arXiv (Cornell University)|Dec 31, 2013

Quantum Mechanics and Applications43 references3 citations

TL;DR

This paper proposes a consistent operational framework for nonlinear quantum mechanics that allows causality violation via closed timelike curves (CTCs), using Deutsch's model as a foundation. It demonstrates that such models can avoid superluminal signalling and verify predictions operationally, while showing that even non-interacting CTCs can violate the uncertainty principle in quantum optics, enabling perfect cloning of coherent states.

ABSTRACT

It is currently unknown whether the laws of physics permit time travel into the past. While general relativity indicates the theoretical possibility of causality violation, it is now widely accepted that a theory of quantum gravity must play an essential role in such cases. As a striking example, the logical paradoxes usually associated with causality violation can be resolved by quantum effects. We ask whether the explicit construction of a theory that allows causality violation might in turn teach us something about quantum gravity. Taking the toy model of Deutsch as a starting point, in Part I we argue that, despite being a nonlinear modification of quantum mechanics, the model does not imply superluminal signalling and its predictions can be operationally verified by experimenters within an appropriate ontological setting. In Part II we show that the model can be directly applied to scalar quantum fields, provided the fields are sent back in time by an amount much larger than the coherence time of the wavepackets. We propose a generalisation of the model that lifts this constraint and recovers the predictions of standard quantum field theory when the size of the temporal jump is much smaller than the coherence time of the wavepackets. Finally, we discuss an extension of the model to ordinary gravitational time dilation. The resulting model generalises and extends earlier work on the topic and can be tested experimentally using current technology.

Motivation & Objective

• To assess whether Deutsch's model of causality violation in quantum mechanics is operationally consistent and free from superluminal signalling.
• To extend Deutsch's model to relativistic quantum fields, particularly quantum optics, to study CTC effects in high-energy regimes.
• To generalize the model to wavepackets with temporal extent comparable to CTC size, recovering standard quantum optics in the zero-delay limit.
• To explore connections between CTCs and gravitational time-dilation, proposing testable predictions in Earth's gravitational field.
• To investigate whether causality-violating models can be unitary and consistent with energy conservation, and to assess implications for quantum gravity.

Proposed method

• Models CTCs as nonlinear quantum operations using the formalism of 'nonlinear boxes' to analyze signalling and verifiability.
• Applies relativistic quantum field theory and quantum optics formalisms to describe bosonic scalar fields interacting with CTCs.
• Derives conditions under which CTCs can violate Heisenberg's uncertainty principle, particularly for coherent states.
• Generalizes the model to wavepackets with arbitrary spacetime extent relative to the CTC, ensuring smooth recovery of standard quantum optics in the limit of vanishing CTC size.
• Compares the formalism to event operators in curved spacetime, suggesting a physical interpretation for CTCs as gravitational time-dilation effects.
• Uses unitary purification to show that the model can be made unitary at the cost of introducing multiple copies of the input state.

Experimental results

Research questions

• RQ1 Can a nonlinear quantum mechanics model that allows causality violation be operationally consistent and free from superluminal signalling?
• RQ2 Can CTCs in quantum field theory lead to violations of the uncertainty principle, even without direct interaction?
• RQ3 How can Deutsch's model be generalized to fields with finite temporal extent relative to the CTC size?
• RQ4 Is there a physical correspondence between CTCs and gravitational time-dilation, and can this be tested experimentally?
• RQ5 To what extent can causality-violating models preserve unitarity and energy conservation?

Key findings

• Deutsch’s model of CTCs is non-signalling and operationally verifiable when interpreted within an appropriate ontological model.
• Even in the absence of interactions, a CTC can be used to clone coherent states perfectly, violating Heisenberg’s uncertainty principle in quantum optics.
• The generalized model smoothly recovers standard quantum optics in the limit where the CTC size becomes negligible compared to the wavepacket coherence time.
• The model’s predictions are consistent with the event operator formalism proposed in earlier literature, suggesting a physical link between CTCs and gravitational time-dilation.
• While energy conservation holds on average, it can be violated in individual experimental runs, indicating a potential relaxation of energy conservation in CTC-affected processes.
• The model admits a unitary purification, though it requires multiple copies of the input state, raising questions about the physical reality of such copies.