>doesn't evolve deterministically
Isn't that still debated?
Isn't that still debated?
That said, we don't have a unified theory of the universe. General relativity, the dark matter question, and quantum mechanics have not been unified into any mathematical theory. All of those theories are pretty weird, mathematically. And we have no efficient way to simulate on classical computers the models that we do have.
We don't live in a billiard ball universe. It's a CS fantasy that evaporates as soon as you start doing experiments on matter and energy in the actual universe we are in.
The universe must be inherently dynamical, ie., not mere discrete states that change by rules, but properties whose nature is to interact with the world...
This is why the abstract mathematical conception of "computer" cannot describe anything physical: mathematical objects do not have temporal properties; they do not change.
This leads to the illusion, for electric devices, that the change is extrinsic to the physics of the system since we can specify the algorithm (somewhat) abstractly. But it isnt.. your pieces of meat, are in the end, the causal power which moves the liquid crystal, electric field, etc.
On your "divine command" bit: I don't think any theory has a good claim on the ultimate ontology of reality, so I don't see how one view is better than another. It's all some kind of divine command at the moment. Computationalism at least constrains the necessary properties the divine must have.
But that's just circular logic.
It begs the question as to what is "computational" and what is "mathematical". E.g. Tegmark has good points in the "Mathematical Universe" that describe possible interpretations of what it means to be mathematical. But how is computation different than math? I'd argue that computation is primarily stateful, logical, and (mostly) deterministic with a clear flow of time, whereas mathematical models are often time-reversible (as most, if not of QM is), stateless, and not necessarily "logical" in the sense of relating finite symbolic quantities. Rather mathematical models happily relate infinite series, manifolds, surfaces, high-dimensional spaces, they talk about fields and operate on functions, etc.
The interesting bit (pun) is that this seems to be a recurring pattern. Whenever there is a intellectual revolution that establishes new ways of thinking / acting, there is a tendency to apply its toolkit to everything in sight, including "the big questions".
So it was with the industrial revolution and the hordes of related engineers: the universe was invariably seen as "a machine". With the digital revolution and the hordes of computer engineers, the universe is invariably "a computer". Effectively just a glorified version of the law of the instrument [1] "to a person with a hammer everything looks like a nail".
The controversial question (and one that cannot be dismissed easily) is whether the universe is in some broader sense "mathematical". The huge success of mathematical descriptions around certain corners of the universe makes people think there might be something to it. But maybe mathematics too, is just our hammer.
but what would be the alternative?
On the other hand it may indeed be a remarkable feature of the human mind that it can "make mathematical sense" of subsets of reality, but there is no overarching system and no reason to expect that we will be able to make simultaneous mathematical sense of "everything".
It might take a long time to collect sufficient such "metadata" to help tilt the balance.
A similar question: does time evolve in discrete steps, or is it continuous?
The passage of time can only be established by comparing with physical phenomena that evolve over time. Even if that comparison would suggest "discrete steps", that doesn't exclude the possibility of time evolving continuously, but instrument / experiment too 'crude' to see between steps.
Right up there with "are we living in a simulation?", and "does $DEITY exist?". As long as you can't break into a deeper layer (assuming that exists!), it's undecidable, and a philosophical rather than a scientific question, imho.
Yes, models. But a model doesn't need to be "real", it just models something real to a certain extent. But models tend to break down if you look close enough, and I think this may also happen to QM at some point.
Bell's Theorem doesn't rule out determinism, it only rules out hidden variables. If the universe is non-local, Bell's theorem fits well with determinism.
> We don't live in a billiard ball universe
We do - at least as long we look at clumps of matter. The billiard ball universe breaks down if we look at the constituents of matter but somehow it re-remerges if we put enough of those constituents together. It's probably the biggest riddle in Physics why this happens. But it does.
Sure, but there's absolutely nothing to suggest that it will be some kind of deterministic computation underneath.
> We do - at least as long we look at clumps of matter.
Not even. Even non-quantum clumps of matter are influenced by continuous fields and dilation effects from both special and relativity. Even without QM, our universe is not efficiently simulatable on our computational models because of general relativity.
The universe behaves very deterministically if we look at "clumps of matter". Why is it this way when this determinism isn't already part of the "base"? For me that's at least a "suggestion". Not a proof of course, but still a hint.
> ... because of general relativity.
General relativity doesn't fits together with QM, so either one is (or both are) "wrong" (in the sense that they only approximate reality to a certain degree).
I'm even sceptical about special relativity: It's a good model and works well in most occasions, but it may still be wrong on a fundamental level. Most of the assumptions under which Einstein proposed SR (no QM, static universe) don't hold anymore.
Just because a system is randomized doesn't mean it's not predictable: when measured in certain ways, it will statistically tend to clump around certain states. Suppose that every second, I flip a magic random coin and walk either 2 feet forward or 1 foot backward. Then after a million seconds, you'll quite probably find me about half a million feet from where I started. Small-scale random processes can easily create something predictable on the large scale.
Still, I wouldn't characterize "clumps of matter" as being deterministic even in our everyday lives. There are many chaotic systems in this world, e.g., the weather, which can amplify randomness on the molecular level into a completely different state. Even the orbit of the Earth becomes unpredictable after several million years.
> I'm even sceptical about special relativity: It's a good model and works well in most occasions, but it may still be wrong on a fundamental level. Most of the assumptions under which Einstein proposed SR (no QM, static universe) don't hold anymore.
Special relativity is already 'wrong' in that it doesn't predict any of our observations of general relativity. But it unavoidably has plenty of truth in it, in that it is very succesful at predicting an identical speed of light for all observers, and the effects (e.g., time dilation) that that implies. Any superseding theory has to explain the same observations, at which point special relativity will continue to act as a useful model for the large-scale effects.
That's of course true (In fact I tend to also believe in a non-deterministic universe "at the core").
But if determinism falls out in the end, it's still a hint that there may also be deterministic effects at the root. Current observation can't rule that out, it's just our model which assumes pure randomness. But there are lot's of possibilities how randomness can sneak in into QM which doesn't contradict obserservation.
And unless we solve the measurement problem in QM (by finding a unified theory from which both Schoedingers equations and Borns rule can be derived), it's still an open question. So considering it solved today is quite premature.
> ... chaotic systems ...
That's still deterministic. Sure, there may be some influence from quantum effects which then are amplified, but the dynamic of the chaotic system itself is still deterministic.
> (SR) ... predicting an identical speed of light for all observers
That's not really true. "identical speed of light for all observers" is an observation which was replicated quite often. SR is a way to explain this observation, but there before SR Lorenz already had a different model explaining it too. SR won, because Lorenz used an (at the time) unobservable "ether" and Einstein argued that its better to use Occams Razor and throw this "ether" away.
But Einstein didn't now about QFT, the Big-Bang and the microwave-background - which all contradict Einsteins assumptions: QFT uses an "ether-like" vacuum, the Big-Bang created a "T=0" for the universe and with the microwave-background also an absolute reference frame for an absolute time. This in all contradicts SR, so maybe SR is really wrong on a global level.
Which in turn would allow a non-local, realistic interpretation of quantum measurements because without SR simultaneity could be back on the table.
What I'm saying is that it's a hint of absolutely nothing. Deterministic systems can very easily produce deterministic large-scale behavior, and randomized systems can also very easily produce deterministic large-scale behavior. Since the large-scale behavior is the same either way, it gives us no predictive power over its ultimate cause, in the Bayesian sense.
> That's still deterministic. Sure, there may be some influence from quantum effects which then are amplified, but the dynamic of the chaotic system itself is still deterministic.
Your argument is that because we see "determinism falling out in the end", we should also expect "determinism at the root". But I argue that in the real world, we don't even see "determinism falling out in the end". On short timescales, computers appear to simulate finite-state machines, and the Earth appears to move in a steady pattern around the sun. But looking further out, the computer ultimately turns to dust, and the Earth wobbles out of its current path, thanks to the chaotic dynamics of the solar system. That doesn't sound very deterministic to me, unless we baselessly assume a priori that they have a deterministic cause.
What determinism do you argue does truly fall out in the end?
> That's not really true. "identical speed of light for all observers" is an observation which was replicated quite often. SR is a way to explain this observation, but there before SR Lorenz already had a different model explaining it too. SR won, because Lorenz used an (at the time) unobservable "ether" and Einstein argued that its better to use Occams Razor and throw this "ether" away.
In that case, we have two different interpetations that yield the exact same outcomes. Thus, I'd say that they're really just two different descriptions of the same model: they're equally correct, and Lorenz's description is just dispreferred due to being more difficult to work with.
> This in all contradicts SR, so maybe SR is really wrong on a global level.
There's nothing in SR that says that "most" matter can't follow the same reference frame. It just says that your reference frame has no bearing on the laws of physics you perceive, contrary to older models of the ether.
As I said, we already know that SR is wrong in that it doesn't predict any of the effects from GR, cosmology, etc. It's not an end-all-be-all theory of everything. But it doesn't stop it from giving good predictions for most places in the universe.
> Which in turn would allow a non-local, realistic interpretation of quantum measurements because without SR simultaneity could be back on the table.
You can do all that today, by specifying a reference frame that you want to consider. After all, that's how QFT does it, since it's mostly concerned about local effects. But you won't get different results from what SR predicts (in particular, the physics won't change if you look at the same system in a different reference frame), except in the circumstances where we already know it's incomplete.
Mechanics is fully deterministic. The question is if there is some kind of "QM random generator" which mixes into this, making things nondeterministic in the end. But it's possible to separate both and the "big clumps of matter" part is fully deterministic then because decoherence generally happens so fast that it doesn't matter. You need to prepare systems quite carefully to mix quantum randomness into it (like in Schroedingers cat for example).
> In that case, we have two different interpetations that yield the exact same outcomes
Only for "harmless cases". SR allows lots of strange stuff, especially if combined with gravity. Closed timelike curves for example.
But if time is absolute and only slowed down for objects moving against this background, then closed timelike curves couldn't exit. Also the trick with Kruskal–Szekeres coordinates wouldn't work anymore because switching time and space would by unphysical. This way we wouldn't have to care about the singularity (at least in Schwarzschild BHs) anymore, because space would cease to exists behind the horizon of a BH and there would be no Singularity.
> You can do all that today, by specifying a reference frame that you want to consider
But that wouldn't work with measurement of entangled object, because there would be no way to define an absolute frame in which the change of the wave-function into an eigenstate happens, it would always depends on the frame of the observer. QM requires that the change happens simultaneously, but SR doesn't allow simultaneous events.
Of course the problem with all of this is, that in the moment I can't see a way to do experiments which decides if there is absolute time or if the SR is correct.
There are deterministic models which "escape" Bell's theorem's assumptions. In particular you can assume superdeterminism (which makes it very hard to do physics) or alternatively Everettian "many worlds" quantum mechanics is completely consistent with Bell's theorem.
This makes it really hard to do physics because we usually assume you can choose to measure whatever the hell you want independent of the state of the system.
Say we have some toy physical system which changes color reguarly, for 10 seconds it's red and for the next 10 seconds it's green and so on. We assume that we'll be able to gain physical understanding of such thing by measuring it whenever we like, but in a superdeterministic universe our choice to do the experiment can be correlated with the system, so we might be "forced" to only measure it when it happens to be red. We'll only ever see it be red and we will end up framing an incorrect "law of physics" that says the thing is red.