You’re referring to a piece by Curt Jaimungal (host of the Theories of Everything with Curt Jaimungal) titled “General Relativity Is NOT Deterministic (Here’s the Proof)”. The core idea comes from a subtle feature of General Relativity: under certain conditions the equations don’t uniquely determine the future, which challenges the classical idea of determinism.
Here’s the simplified argument behind what he’s pointing to.
1. What “deterministic” means in physics
A theory is deterministic if:
Given the complete state of the universe at one moment, the laws of physics determine exactly one future.
This is how classical physics (like Newtonian mechanics) is usually interpreted.
Mathematically, this means:
- The equations of motion have unique solutions given initial conditions.
2. Why GR
seems
deterministic at first
The equations of GR — the Einstein field equations — are differential equations.
If you specify:
- the geometry of space,
- the distribution of matter,
- on a special surface called a Cauchy surface,
then the equations determine how spacetime evolves.
That sounds deterministic.
3. The problem: some spacetimes break predictability
General relativity allows solutions with features like:
- Naked singularities
- Cauchy horizons
- Closed timelike curves
In these cases, the future is not uniquely determined by the past.
A famous example involves rotating black holes described by the Kerr solution.
Inside them you can encounter a Cauchy horizon where:
- multiple different future spacetime extensions are possible
- the equations no longer give a unique evolution
So the same past can lead to multiple possible futures.
4. Penrose’s “cosmic censorship” tries to fix this
To rescue determinism, physicists proposed the Cosmic Censorship Hypothesis, introduced by Roger Penrose.
The idea:
Singularities must always be hidden behind black hole horizons.
If that’s true:
- unpredictable regions can’t affect the outside universe
- determinism is preserved.
But here’s the issue:
Cosmic censorship has never been proven.
And some research suggests it might fail in certain scenarios.
5. The philosophical punchline
So the claim “GR is deterministic” is only true if cosmic censorship is always valid.
But since that’s still an open problem:
General Relativity itself does not guarantee determinism.
✅ Key takeaway
- GR’s equations are deterministic locally.
- But the theory allows spacetime geometries where the future is not uniquely determined.
- Therefore determinism in GR depends on extra assumptions (like cosmic censorship).
💡 A fascinating twist:
Many physicists suspect Quantum Mechanics or Quantum Gravity will ultimately resolve these issues.
If you want, I can also explain the actual “proof” idea Jaimungal is referencing (it involves Cauchy horizons and maximal spacetime extensions) — it’s one of the most mind-bending results in relativity.
