Curt Jaimungal: General Relativity Is NOT Deterministic (Here's the Proof)
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Why is Einstein’s general relativity not truly deterministic?
You've probably heard that Einstein's theory of general relativity, the theory of gravity, is a deterministic theory. Technically speaking, this is false. The reason is quite subtle, but many physicists like Penrose and others that have spoken to know about this intimately. There's a severe failure of determinism in general relativity that cannot be taken lightly. Einstein's general theory of relativity is not a deterministic theory. There is a lack of predictability. And these go on and on, as you'll see and hear over the next few minutes. Today we'll learn what precisely is GR, so general relativity, beyond the bowling ball on a rubber sheet, which is actually a circular argument, if you think about it.
We'll also learn what is determinism precisely, which also has two subclasses, a local and a global determinism. And then also what is this global hyperbolicity that you've heard about or may have heard about? It's not just overscrupulous, abstruse math, it's actually extremely important, and we'll talk about what these three have to do with one another, of course.
General relativity allows closed timeline curves, and you could say in some sense circumstances it even encourages them to happen.
So I'll speak at two levels simultaneously. One is for the person who wants a rigorous technical definition, that's where all the sources come in. And another is for those who just want the crux of the argument. For that latter person, you also have to keep in mind that almost any claim, when simplified, is replete with nuances that challenge it. That's why on this podcast I attempt to be as technical and rigorous as I can to ameliorate some of the predicaments of this compressed message. I'll put a link on screen about my opinions against this whole, hey, explain it like I'm five, bro, or you don't understand it. So why the heck is saying general relativity is Deterministic is technically a false claim that needs to be caveated.
And I'm not speaking about false in some punctilious sense that only philosophers care about. I mean false in that there exist perfectly valid solutions to Einstein's field equations, where specifying the complete state at one time doesn't uniquely determine the future. I'm not talking about singularities, although there's that as well. I'm talking about regular, smooth regions of space-time where your future simply isn't determined yet. I find this super interesting because unlike quantum mechanics, where you at least get probabilities, in some sense the indeterminism in gravity and gr is worse. You've heard of Einstein's field equations, but what is the relationship between that and GR? Well, GR, general relativity, is a five-fold package.
It comprises some theoretical principles, like the equivalence principle.
What are local vs. global determinism and how do they differ in GR?
You may have heard it stated informally that physics in a free-falling frame is locally going to be reduced to special relativity. Or that physics doesn't depend on your coordinate choice. Another is the mathematical scaffolding of certain types of Roman geometry called pseudo-Romannian geometry on a four manifold. And of course there's the field equations of Einstein, and then a geodesic equation that talks about how free particles move in that straightest possible path you've heard of in curved spacetime. And then there's also the physical interpretation that curvature of spacetime is gravity. Not that gravity causes curvature, but that they're identical. This is why that Wheeler statement is a bit misleading that space-time tells matter how to move and matter tells space-time how to curve, because it gives the sense that there is some causal path that ticks forward.
But actually, as you can see, these are dynamically coupled equations. It's not like they're time steps of causation here. But anyhow, these form a package deal. This is all part of general relativity. You're not just referring to one element here. I have substack notes on this here, which is what you're seeing on screen, and this is the coordinate free notation, one that I prefer because I don't like my physics with arbitrary choices, and not these coordinate index gymnastics.
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Chapters
8 chapters
1
Why is Einstein’s general relativity not truly deterministic?
0:00–2:46
2
What are local vs. global determinism and how do they differ in GR?
2:46–5:14
3
How does global hyperbolicity enable (or fail to enable) a well‑posed initial‑value problem?
5:14–7:15
4
Which physically interesting spacetimes (e.g., charged or rotating black holes) break global hyperbolicity?
7:15–9:25
5
What are Cauchy horizons and why do they cause a loss of predictability?
9:25–11:32
6
How do closed timelike curves make even local determinism suspect?
11:32–13:44
7
Why can’t we simply label non‑deterministic solutions as “pathological”?
13:44–15:39
8
What does this indeterminism imply for attempts to quantize gravity?
15:39–18:35
Speakers
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