Can The Novikov Self-consistency Principle Be Reconciled With The Wheeler-DeWitt Equation In A Functional Integral Formulation Of Quantum Gravity, Specifically In The Context Of A Mini-superspace Model With A Bianchi IX Cosmology, Where The Hartle-Hawking State Is Used To Define The Wave Function Of The Universe?
The Novikov self-consistency principle can indeed be reconciled with the Wheeler-DeWitt equation in the context of a functional integral formulation of quantum gravity, specifically within a mini-superspace model using Bianchi IX cosmology and the Hartle-Hawking state. Here's how:
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Hartle-Hawking State and Path Integral: The Hartle-Hawking wave function is derived from a path integral over all possible Euclidean geometries. This formulation inherently considers all possible histories, including those with closed timelike curves (CTCs).
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Novikov Self-Consistency Principle: This principle ensures that any events involving time travel are self-consistent, avoiding paradoxes. In the path integral approach, histories that lead to paradoxes are either suppressed or excluded, as the principle is naturally enforced by the consistency requirements of the wave function.
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Wheeler-DeWitt Equation: As the wave function satisfies the Wheeler-DeWitt equation, it encapsulates the quantum dynamics of the universe in a timeless framework. The equation, combined with the Hartle-Hawking state, ensures that only self-consistent histories contribute to the wave function.
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Mini-Superspace Model: In the simplified Bianchi IX model, the analysis of CTCs and their implications is more manageable. The functional integral approach in this context likely includes mechanisms to exclude inconsistent histories, thus aligning with Novikov's principle.
In conclusion, the functional integral formulation, through the Hartle-Hawking state, ensures that the wave function of the universe respects the Novikov self-consistency principle, avoiding paradoxes and reconciling it with the Wheeler-DeWitt equation in the specified model.
Answer: Yes, the Novikov self-consistency principle can be reconciled with the Wheeler-DeWitt equation in the described quantum gravity model. The Hartle-Hawking state, derived from a functional integral, naturally enforces self-consistency, avoiding paradoxes associated with closed timelike curves.