This post really expands my intuition from years ago; "what if no finite set of equations can fully describe the universe" https://groups.google.com/d/msg/sci.physics.research/PrlzkXUPq2o/WBdj0ThbsyoJ
But see the remainder of that discussion thread for links to opinions of others far more qualified than myself on this topic.
Some thoughts:
(1) "What does the term "Physical law?" mean?" This is a longstanding debate in philosophy, see https://plato.stanford.edu/entries/laws-of-nature/ I think you'd benefit from reading up on the literature.
(2) " It means that someone knowing that law can predict with some accuracy the state of the universe at some point in the future from its state at the time of observation." Nitpick: The present vs. future stuff is a red herring. For example, we use the laws to predict the past also.
(3) The question I'd ask about your proposal to identify laws with predictability is: What is predictability? Do you mean, the actual ratio of true to false predictions made using the law is high? Or do you mean something more robust--if the observer had made many predictions using the law, most of them would have been true? Or probably would have been true? Or what? Notice how it's hard to say what the second and third formulations mean without invoking laws. (We can use laws to ground counterfactuals, or counterfactuals to ground laws, but the hope would be to ground both of them in something less mysterious.)
The idea of a universe "without preset laws" seems strange to me. Say for example that you take your universe to be a uniform distribution over strings of length n. This "universe" might be highly chaotic, but it still has an orderly short description -- namely, as the uniform distribution. More generally, for us to even SPEAK about "a toy universe" coherently, we need to give some sort of description of that universe, which basically functions as the laws of that universe(probabilistic laws are still laws). So even if such universes "exist"(whatever that means), we couldn't speak or reason about them in any way, let alone run computer simulations of them.
if a short computation produces a random universe, then there is not going to be anything like a law of nature inside it. The existence of laws from the outside, and the observability of laws from the inside are different questions.
"exist"(whatever that means)
What are you implying here? It's clear that *we*, or at least *you* exist, in the sense that the computation of our minds is being performed and inputs are being given to it. We can also say, (with slightly less certainty) that observable external physical objects such as atoms exist because the evolution of their states from one Planck instant to the next is being performed (even when we're not observing it - if the easiest way to get from observation t1 to observation t2 is by computing all the intermediate states between t1 and t2, it's likely that the external object exists on the entire interval [t1..t2]). This is my conception of an object's existence, that the computation of an object's state is being done. What is yours?
I largely agree with your conception. That's sort of why I put scare quotes around exist -- I was talking about universes for which there is NO finite computational description, which (I think) is what the OP was talking about. I think it would basically be impossible for us to reason about such universes, so to say that they 'exist' is kind of strange.
All finite length sequences exist in any infinite random sequence. So, in the same way that all the works of shakespeare exist inside an infinite random sequence, so too does a complete representation of any finite universe.
I suppose one could argue by the anthropic principle that we happen to exist in a well ordered finite subsequence of an infinite random sequence. But it is sort of like multiverse theories where it lacks the explanatory power or verifiability of simpler theories.
All finite length sequences exist in any infinite random sequence
Yep. Fortunately, the sequences I played with are quite finite, 1024 samples, see the followup post. And I agree that musing about multiverses, while fun, has not been scientifically fruitful so far.
What sort of thing is the universe? If it is a mathematical object, then at least we have an answer to the question, and it is not clear how to answer it otherwise. This seems to me to be strong evidence that the universe is a mathematical object.
This is discussed in Appendix A of Tegmark's paper (I guess I am using "mathematical object" synonymously with "mathematical structure").
People not being able to come up with any idea but that diseases are a curse of the gods is strong evidence not for diseases being a curse of gods but for the ignorance of those people. The most likely answer to that question is either something no one will think of for centuries to come or simply that the model of separating objects into "sorts of things" is not useful for deciphering the misteries of the universe despite being an evolutionary advantage on the ancestral savanna.
So, I don't think that I would have the same kind of intuition about diseases and curses as I do about mathematical objects and existence, even if I didn't know any possible cause of disease except for curse. But of course my introspection about that could be wrong.
I don't think that I am separating objects into "sorts of things". It is more like I am asking the question "what does it mean to be a thing?" and answering it "to be a thing is to be a mathematical object".
"What kind of a thing is that existing thing" and "what is existence anyway" are rather orthogonal questions. If you reject MUH, you need to explain what breathes fire into the equations.
That began with an 'if'. If you accept the MUH, the problem you have is lack of evidence for it, or even evidence against it.
"Exists" is one of the words I tend to taboo. People usually just use it to mean "is part of the Everett branch that I am currently in" but there are also some usages that seem to derive their meaning by analogy, like the existence of mathematical objects. I'm not sure if there is a principled distinction being drawn by those kinds of usages.
Instead I would talk about whether we can sensibly talk about something. And I can imagine people trying to talk about something, and not making any sense, but it doesn't seem to mean that there is a "thing" they are talking about that "doesn't exist".
People usually just use it to mean “is part of the Everett branch that I am currently in”
Not when they are asserting the existence of other branches. And most people have never heard of Everett branches.
“Exists” is one of the words I tend to taboo.
Consitently tabooing it and all its synonyms is pretty difficult, and you are not succeeding, since your said "“to be a thing is to be a mathematical object”.
You are coming to a pretty contentious conclusion, and doing so based on inconsistent tabooing -- allowing yourself to use words like "be" when expressing what you believe, but insisting on tabooing when challenged or asked to explain yourself.
or simply that the model of separating objects into “sorts of things” is not useful for deciphering the misteries of the universe
It's problematic when applied to the universe , because "universe" is a very broad category. If you are going to say it is some specific thing chosen from an even broader category, then you have to explain why that thing and not something else -- the more specific your model of the universe, the more bits of information are unaccounted for.
Inspired by http://backreaction.blogspot.com/2018/06/physicist-concludes-there-are-no-laws.html, which dissed this article: https://www.quantamagazine.org/there-are-no-laws-of-physics-theres-only-the-landscape-20180604.
Epistemic status: very raw, likely discussed elsewhere, though in different terms, but feels like has a kernel of usefulness in it.
What does it mean for the universe to be governed by physical laws? What does the term physical law mean? It means that someone knowing that law can predict with some accuracy the state of the universe at some point in the future from its state at the time of observation. Actually, a qualifier is in order. Can predict the observed state of the universe at some point in the future from its observed state at the time of observation. So
laws => predictability
This is more than a one-directional implication, however. What does it mean for something to be predictable? Again, it means that, by observing the state of the universe at some point in time the observer can make a reasonably accurate prediction of the observed state of the universe at some point in the future. Notice the qualifier "observed" again. How can an observer make this prediction? They must have a model of the observed universe ("map of the territory") inside, and use this model ("trace the map") to predict the observed state of the universe at some point in the future. This model can be very simple, "Raarg hold rock. Raarg let go. Rock fall", or more complicated, "In absence of other forces all objects accelerate downward at 9.81 meters per second squared", or even more abstract, "The stress-energy tensor is proportional to the spacetime curvature." But it is a model nonetheless.
When is a model promoted to the status of a law? When it is useful for more than a single case. When the prediction can be made repeatedly in similar but slightly different circumstances using the same model. There is a lot of complexity hiding under the surface of this "simple" statement, but at the end of the day, models are only useful if they can be reused, and thus become patterns, templates for the observers to predict the universe. Thus we have the implication in the other direction:
predictability => laws
Thus the two terms are equivalent, at least in this framework:
predictability <=> laws
Let's restate the definitions, which are admittedly only the first approximation, and may not looks standard:
Predictability: an observer inside the universe can infer the state of the universe at some future point in time, with the accuracy acceptable to the observer.
Physical (or other) laws: reusable models of the universe that are part of the observer and let the universe appear predictable to the observer.
I have been trying really hard to avoid, or at least to minimize, the mind projection fallacy, such as stating that the physical laws are the objective laws of the universe. They might well be, but that would be a next step in modeling the universe, potentially useful, but not minimal.
Returning to the title of this post, "Physics has laws, the Universe might not," what I mean by it is that Physics is one of the sciences that we humans, "observers" call a collection some of those reusable models, and so is in itself an aggregate model. The laws of Physics are the constituent models. On the other hand, the Universe, or "the territory" may or may not have something that Stephen Hawking once phrased as a question:
"What is it that breathes fire into the equations and makes a universe for them to describe?"
The minimal answer might be that the cause and effect are reversed here: the universe just exists (assuming it does), and is somewhat predictable, and the equations are those physical laws inside the observers' minds.
Now, the above is, of course, another (meta-)model. And models are not very useful if they do not result in better predictions. Or, in the language of this site, the beliefs must pay rent. So, what does this one predict? Well, for example, if the universe has no "internal" laws, according to this model, then one could potentially generate a "toy universe," possibly with some form of predictability but without any preset laws and see if anything that could be called (toy) laws would "emerge" in this toy universe, and under what conditions. It would be interesting to explore this approach further, but it requires a fair amount of decomposition and analysis to make sense in more than a handwavy way. Here are some questions that come to mind:
Should an experiment like that worked out, it would lend some credence to the above conjecture, that the physical laws are not some inherent property of the Universe, but a human attempt to make sense of it by creating reusable templates inside themselves.