Doesn't Even Show Up to the Table (Einstein)

Why It Matters

Understanding whether GR guarantees determinism shapes expectations for predictability in cosmology and informs the search for a quantum theory of gravity, where causal structure may be even more nuanced.

Key Takeaways

• GR's equations are locally deterministic but not globally guaranteed.
• Global determinism requires spacetime to be globally hyperbolic.
• Many valid GR solutions lack global hyperbolicity, allowing indeterminism.
• Determinism may be a property of specific solutions, not the theory.
• Einstein’s “God doesn’t play dice” contrasts with GR’s indeterminate regions.

Summary

The video tackles a classic question in physics: is general relativity (GR) a deterministic theory? By invoking the strict definition—future uniquely entailed by past—the speaker argues that GR cannot be labeled universally deterministic. Instead, the theory’s solution space contains both deterministic and non‑deterministic equations, leaving the empirical status of the latter unsettled.

Three technical points dominate the discussion. First, Einstein’s field equations are locally deterministic: given appropriate initial data on a small region, the future evolution is fixed. Second, global determinism hinges on the spacetime being globally hyperbolic, a condition that guarantees a well‑posed initial‑value problem across the entire manifold. Third, many mathematically valid GR solutions—such as those containing closed timelike curves or naked singularities—fail to meet global hyperbolicity, opening the door to genuine indeterminism.

The speaker cites Manchak’s work on the ambiguity of defining a “complete state” in GR and highlights Einstein’s famous dictum, “God does not play dice,” as an ironic backdrop. The paradox lies in the fact that within Einstein’s own framework, there exist regions where the future is not uniquely prescribed, effectively rendering “God” absent from the causal tapestry.

The implication is profound: determinism may not be a property of the theory itself but of particular spacetime solutions. For physicists and philosophers, this reframes debates about predictability, the nature of time, and the limits of scientific inference in cosmology and quantum gravity. It suggests that where an observer resides in the universe could dictate whether their future is mathematically fixed or fundamentally open.

Original Description

Einstein's theory of General Relativity: deterministic or not? While equations are locally deterministic, global determinism hinges on 'global hyperbolicity.' Many valid solutions lack this, suggesting your future might depend on spacetime location. #GeneralRelativity #Physics #Einstein #Determinism #Spacetime Full video with Curt Jaimungal: https://youtu.be/tJsghrZQaYU