Doesn't Even Show Up to the Table (Einstein)
Audio Brief
Show transcript
This episode explores whether Einsteins theory of general relativity is truly deterministic.
There are three key takeaways. First, general relativity is not monolithically deterministic. Second, local predictability does not guarantee global certainty. Third, global determinism requires a geometric property called global hyperbolicity, which many valid cosmic solutions lack.
While Einsteins equations function locally, global predictability often breaks down in the wider universe. Therefore, determinism is a localized feature depending on ones specific coordinate in spacetime rather than a blanket property of the theory. In these models, the past does not always uniquely dictate the future.
This shift forces physicists to view cosmic predictability as a regional variable rather than an absolute rule.
Episode Overview
- This episode addresses the fundamental question of whether Einstein's Theory of General Relativity (GR) is deterministic or not.
- It explores the strict definition of determinism—where the past uniquely entails the future—and explains why GR does not fit neatly into this category.
- The discussion highlights the complexity of GR's solution space, which contains both deterministic and non-deterministic equations.
- It introduces key physics concepts like local determinism, global determinism, and global hyperbolicity to clarify how predictability works in spacetime.
Key Concepts
- The Dual Nature of GR's Equations: General relativity is not a monolithically deterministic theory. Its mathematical solution space is diverse, containing both deterministic equations (where the future is predictable) and non-deterministic equations (where it is not).
- Local vs. Global Determinism: While the Einstein equations are locally deterministic, achieving global determinism requires a specific geometric property known as "global hyperbolicity."
- The Limit of Global Hyperbolicity: Many physically interesting and mathematically valid solutions in general relativity lack global hyperbolicity. This means that even within a valid universe described by GR, global predictability can break down.
- Determinism as a Localized Property: Rather than viewing determinism as a property of the entire theory, it is more accurate to view it as a property of specific solutions. In a GR-governed universe, whether your future is determined can depend entirely on your specific location in spacetime.
Quotes
- At 0:00 - "My view is that by the strict definition of what a deterministic theory is, namely that we always have the future being entailed uniquely by the past, then the answer is no. GR is not a deterministic theory as such." - explaining why general relativity fails the strictest definition of physical determinism.
- At 0:46 - "1. The Einstein equations are locally deterministic. 2. Global determinism requires global hyperbolicity. And number 3, many physically interesting solutions, perfectly valid, lack global hyperbolicity." - summarizing the three core mathematical realities that define predictability in general relativity.
- At 1:18 - "Turns out in Einstein's own theory, God sometimes doesn't even show up to the table." - contrasting Einstein's famous philosophical stance ("God does not play dice") with the actual mathematical consequences of his equations.
Takeaways
- Shift your evaluation of physical theories by treating determinism as a property of specific solutions (or regions of spacetime) rather than an all-or-nothing property of the theory itself.
- Apply the concept of global hyperbolicity when trying to determine if a cosmic model or spacetime solution allows for absolute predictability from past to future.
- Avoid the common pitfall of assuming local physical laws guarantee global predictability, as local determinism in GR does not automatically prevent global indeterminism.
