Such fun to read! Like the first comment, I like physics but do not have the math skills, and yet still enjoy trying to get the gist of ideas. You really make it so interesting! Please continue to explain it as you do to some of us “five year olds” :)
I'll throw my mad hat into the ring: the indeterminism of QM and the indeterminism permitted under certain topologies in GR are not different, they are the same. QM can be derived from GR, but that's GR with nontrivial topology.
At 77 I've been a therapist for 54 years but started an Hon Physics BSC in 1966 – and frankly found it boring after a month > maths is not my cup of tea :) However, bluntly, Kurt, I followed you on your YT podcast and found you eminently flexible – with EQ to match your obvious IQ... And even in articles like the one I just struggled through you show that... In which case (unless you've already dismissed him and I hope you try again) I would dearly like to introduce you to an interview with Federico Faggin on his Quantum Information theory which he produced (with much attention to EQ + IQ as well) after an experience he had which shifted his worldview: he twists determinism into a Gordian Knot! Thx for reading... bdjspooner@gmail.comhttps://www.youtube.com/watch?v=0FUFewGHLLg
Dr Federico Faggin on Quantum Information Panpsychism Explained
Well-written article: you break it all down nicely.
It does make me wonder which precise definition of "determinism" is actually relevant in general relativity. You poke holes in a lot of them, but at the end of the day I (as an almost daily user of general relativity for many years) don't think determinism should hold much meaning beyond existence and uniqueness of solutions for a given initial value problem locally--that is, for a short time, where short time could easily mean all of human history when it comes to the actual physics. Your point that spacetimes with closed timelike loops may not even have local existence and uniqueness is a fair one technically, but in reality, we have never observed a closed timelike loop, and I don't think we ever will. Thus, "local determinism", which I claim is just determinism, is legitimate.
On the other hand, global determinism might be an oxymoron: something which makes sense in a mathematical framework (like a globally hyperbolic spacetime), but which in practice we have no reason to believe is true in reality. I suspect most people who work in GR get this. But hey, globally hyperbolic spacetimes do define a very nice category, and people like me sure like those ;)
Thanks for the piece! Would be happy to talk about this.
There are certainly many interesting aspects of this problem, but I think there is for some reason an exaggerated obsession with things having to come naturally out of the mathematics without assumptions...
When you think about how little information about our actual world goes into the EFE (like there is no relation to which matter fields actually exist, initial conditions of the universe, etc....), it's not strange in any way that they would allow for many solutions which might not be real. Of course, the physical examples that are pointed out are interesting, especially the singularities, but....see the next point
We also know for sure that the field equations are in some sense an effective theory, and if we have to assume hyperbolicity to get the full quantum description, I think that's fine (see caveat), that's what most theories of physics do, assume things that seem reasonable about our world
The caveat is that if and when we have a quantum gravity description, we have to check ourselves again and see that it closes the loopholes nicely and consistently, meaning for every physical situation we can imagine
N.B in quantum theories we always worry about unphysical solutions....but of course there is a very important difference there. We have the superposition principle, which basically makes us have to consider always the full space of solutions. The EFE, being non linear, don't have that.....
So then a complete state doesn't always predict what came before either...
showing that both the past and future are probabilistic, the only thing you could be sure of is the complete state at any one time if you knew everything in the system?
The Schwarzschild metric is "an exact solution to the Einstein field equations". The Schwarzschild metric gives nonsensical results at both extremes, in addition to the divide by zero problem. Einstein's field equations cannot accurately describe the rotations and motions of galaxies.
Therefore, both the Schwarzschild metric and Einstein's field equations are known to be approximations, giving reasonably correct answers only within certain unstated limitations.
Thanks, that was a most interesting read. As it happens, I recently created a toy model that elucidates concepts like global hyperbolicity and indeterminism. The writeup I didn't publish yet, but have uploaded it to Vixra: https://vixra.org/pdf/2504.0062v1.pdf (yes, I know, no-one reads Vixra...) ;)
Interesting -- very interesting! -- but this loses impact from being at least the third successful assault on my ingrained sense that the world is deterministic -- after QM and chaos theory (a chaotic system may be deterministic in principle. In principle I can dine in the best restaurant in Rome tomorrow. (But I'm betting my lunch will still be a sandwich in the living room.)
I guess my point boils down to why I should care. (Other than the intellectual joy of it all.)
Such fun to read! Like the first comment, I like physics but do not have the math skills, and yet still enjoy trying to get the gist of ideas. You really make it so interesting! Please continue to explain it as you do to some of us “five year olds” :)
I'll throw my mad hat into the ring: the indeterminism of QM and the indeterminism permitted under certain topologies in GR are not different, they are the same. QM can be derived from GR, but that's GR with nontrivial topology.
At 77 I've been a therapist for 54 years but started an Hon Physics BSC in 1966 – and frankly found it boring after a month > maths is not my cup of tea :) However, bluntly, Kurt, I followed you on your YT podcast and found you eminently flexible – with EQ to match your obvious IQ... And even in articles like the one I just struggled through you show that... In which case (unless you've already dismissed him and I hope you try again) I would dearly like to introduce you to an interview with Federico Faggin on his Quantum Information theory which he produced (with much attention to EQ + IQ as well) after an experience he had which shifted his worldview: he twists determinism into a Gordian Knot! Thx for reading... bdjspooner@gmail.com https://www.youtube.com/watch?v=0FUFewGHLLg
Dr Federico Faggin on Quantum Information Panpsychism Explained
Well-written article: you break it all down nicely.
It does make me wonder which precise definition of "determinism" is actually relevant in general relativity. You poke holes in a lot of them, but at the end of the day I (as an almost daily user of general relativity for many years) don't think determinism should hold much meaning beyond existence and uniqueness of solutions for a given initial value problem locally--that is, for a short time, where short time could easily mean all of human history when it comes to the actual physics. Your point that spacetimes with closed timelike loops may not even have local existence and uniqueness is a fair one technically, but in reality, we have never observed a closed timelike loop, and I don't think we ever will. Thus, "local determinism", which I claim is just determinism, is legitimate.
On the other hand, global determinism might be an oxymoron: something which makes sense in a mathematical framework (like a globally hyperbolic spacetime), but which in practice we have no reason to believe is true in reality. I suspect most people who work in GR get this. But hey, globally hyperbolic spacetimes do define a very nice category, and people like me sure like those ;)
Thanks for the piece! Would be happy to talk about this.
There are certainly many interesting aspects of this problem, but I think there is for some reason an exaggerated obsession with things having to come naturally out of the mathematics without assumptions...
When you think about how little information about our actual world goes into the EFE (like there is no relation to which matter fields actually exist, initial conditions of the universe, etc....), it's not strange in any way that they would allow for many solutions which might not be real. Of course, the physical examples that are pointed out are interesting, especially the singularities, but....see the next point
We also know for sure that the field equations are in some sense an effective theory, and if we have to assume hyperbolicity to get the full quantum description, I think that's fine (see caveat), that's what most theories of physics do, assume things that seem reasonable about our world
The caveat is that if and when we have a quantum gravity description, we have to check ourselves again and see that it closes the loopholes nicely and consistently, meaning for every physical situation we can imagine
N.B in quantum theories we always worry about unphysical solutions....but of course there is a very important difference there. We have the superposition principle, which basically makes us have to consider always the full space of solutions. The EFE, being non linear, don't have that.....
So then a complete state doesn't always predict what came before either...
showing that both the past and future are probabilistic, the only thing you could be sure of is the complete state at any one time if you knew everything in the system?
The Schwarzschild metric is "an exact solution to the Einstein field equations". The Schwarzschild metric gives nonsensical results at both extremes, in addition to the divide by zero problem. Einstein's field equations cannot accurately describe the rotations and motions of galaxies.
Therefore, both the Schwarzschild metric and Einstein's field equations are known to be approximations, giving reasonably correct answers only within certain unstated limitations.
https://substack.com/@ryanlaneuctit/note/p-169832185?r=62kent
Thanks, that was a most interesting read. As it happens, I recently created a toy model that elucidates concepts like global hyperbolicity and indeterminism. The writeup I didn't publish yet, but have uploaded it to Vixra: https://vixra.org/pdf/2504.0062v1.pdf (yes, I know, no-one reads Vixra...) ;)
https://open.substack.com/pub/eliamraell/p/the-theory-of-nothing-isnt-too-hard?r=5pb4rx&selection=b0834e88-8638-4ed7-9dd2-58f1d52aa69e&utm_campaign=post-share-selection&utm_medium=web&aspectRatio=square&textColor=%23ffffff
Interesting -- very interesting! -- but this loses impact from being at least the third successful assault on my ingrained sense that the world is deterministic -- after QM and chaos theory (a chaotic system may be deterministic in principle. In principle I can dine in the best restaurant in Rome tomorrow. (But I'm betting my lunch will still be a sandwich in the living room.)
I guess my point boils down to why I should care. (Other than the intellectual joy of it all.)