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The universe has a very wide variety of phenomena.

However, there is not, similarly, a zoo of physical laws. Instead, it appears that the universe is governed by a small number of laws that are valid in a wide range of conditions.

It is easy to imagine an universe in which each planet in the solar system moved in a different way: Some planets could do circles, others triangles, others squares, etc.

Instead, in reality there is a single law, the law of universal gravitation, that controls the orbits of all planets.

Why are universals like this so prevalent in the realm of physics?

EDIT: To bring what I mean closer to home, consider how we used to describe the world in newtonian physics. We used properties like heat capacity, tensile strength, refractive index, viscosity, and so on to describe a variety of materials. There were different laws for different kinds of objects.

Then, in the 20th century, quantum physics, together with Maxwell's theory of electromagnetism, unified and explained all these different properties from a few fundamental principles, making it possible (at least in principle) to derive mathematically the values of all these physical quantities.

The fact that this unification of distinct phenomina is possible is the jewel of physics: The world is much smaller and much more interconnected than what we would naïvely expect from our everyday experiences of reality.

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    There is, on the other hand, a "zoo" of chemical, biological, psychological, etc., laws. Or even physical ones, for that matter, outside of fundamental physics. Heard of Darcy's law? Fundamental physics is simply the field where we collect more or less universal laws.
    – Conifold
    Jan 26 at 21:02
  • How do we know it's the universe governed by these laws rather than asking if these are perhaps the laws humans are able to formulate? Perhaps the universe is far more complicated, and humans are too simplistic. How can you rule that out?
    – user4894
    Jan 26 at 23:19
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    The universe you describe can be imagined but it raises lots of questions. For example, the law that makes orbits triangular must be applicable locally, in the space occupied by the orbit (otherwise, it would be chaotic, not triangular). So why is this law applicable in local space but not in other places? Where is the boundary? What happens when something crosses this boundary? Are those boundaries themselves determined by an higher order, universal law? etc... we can imagine many strange things but it's hard to stand scrutiny.
    – armand
    Jan 26 at 23:50
  • @armand This is just a thought experiment. But if you demand consistency, we could consider classical mechanics (which we know is a self-consistent theory). What do you think about the edit I made to the question? Jan 29 at 14:07
  • That's a good question. I suspect that like many other questions it has something to do with the anthropic principle. That is, in a universe governed by many disparate laws it would be much more difficult for a conscious lifeform to make sense of its environment in a way that provides any evolutionary advantage, and therefore such lifeforms are extremely unlikely to evolve in the first place.
    – Ron Inbar
    Feb 23 at 21:25
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It did not start out that way. But with the passage of time, the people who thought deeply about physical laws gradually uncovered certain very general underlying principles which gave rise to heaps of separate laws- which were then understood to represent special cases of the more general underlying principles.

This process is called unification. Examples include Maxwell's laws of electrodynamics and the Weinberg/Salaam electroweak unification.

Another type of example is furnished by Noether's Theorem, which is the single general principle at the root of all the different conservation laws in physics.

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    But, why though..? ;)
    – CriglCragl
    Jan 26 at 22:32
  • @criglcragl, because the first level of "why" does not satisfy. it is natural to look for the reasons behind the reasons. Jan 26 at 23:42
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It did start that way. If, there was a start. What even is time? In General Relativity it is pictured as a dimension. But the surest thing we know about this, our theory of gravity + time, is that it doesn't fit with quantum mechanics, our theory of everything else - our best meshing so far, the Wheeler-DeWitt equation, finds time 'cancels out', it isn't a variable. So Loop Quantum Gravity & other approaches to quantum gravity, are looking at time as emergent, rather than fundamental.

What do we think a dimension is? Noether's theorem proved, dimensions are directly equivalent to local continuous symmetries - the set of conservation laws, energy momentum, &c, are the dimensions. So we can start to picture a universe with emergent dimensions: a pattern, in something fuzzy, like quantum foam, or a spin network. Like a crystal, that is organised symmetrically in some directions but not others as a liquid cools - and that is exactly the idea of Lisi's E8 theory. There was this smooth, symmetrical system, metaphorically like a liquid, and the laws of our universe 'crystalised out', with the constants it has, just one of many ways it could have gone, perhaps 'seeded' like crystals can be.

One of the deepest traits, patterns, we find is the uncertainty principle. It allows the borrowing of a little energy, for a little time, as long as the balance is restored. But we are able to observe it must apply, because if something interesting -something weird- happens in that little window, it doesn't quite go back how it was. A particle-antiparticle pair appear, say. They can re-annihilate, giving back the nice flat empty space. But, an even more weird thing can happen: in the fuzzy uncertainty window, the symmetry can get 'violated': charge-parity-time or CPT violation in particular, because that made what we see in our universe, vastly more matter than antimatter. So it's like this asymmetry, this 'violation' of things crunching back neatly, the way time is not like the other dimensions (or, CP&T aren't all quite the same), gave this vast delay in payback of the borrowed energy, in what can happen (the number of states, the size of the probability space) before the complexity will crunch back into simplicity, which we still think it will (just because, things change). So there is a deep elegance to this uncertainty principle: we find it everywhere, and it can make, everything - the laws, the particles, the dimensions, the complicated patterns of them like our big bang.

In a timeless universe, what would the 'beginning' mean? It's philosophically problematic anyway, because if time began at it, what does it mean to ask what happened before?

Roger Penrose, who's exceptionally long and varied path in physics finally won him a well deserved Nobel Prize recently, has this nice idea of Conformal Cyclic Cosmology. We know black holes will eventually evaporate, we think protons likely decay, and the reverse of what turned the 'smooth' early universe into lumps of particles, will reverse. Just a soup of photons, which we think can't decay - and, Penrose pointed out, which don't experience time. So we have a smooth flat state again of the simplest things, like that metaphor for a liquid. And CCC suggests, that is just like the big bang, which we know explodes! It's not important here whether CCC is correct, my point is, what happens if we ask about 'before' the big bang, and, that clever people have ideas. It's a better answer than to say time just appeared out of nowhere.

So, without time, what we really have is a complicated pattern, a dot expanding & contracting, bouncing around in the vast imaginary space of all possible universes, of ways the crystal cools, and warms, gets complicated, and gets simple. When is it easiest to understand? When it's closest to a dot, the closest to total simplicity: one unified force, one kind of particle, one force carrier. Then what do we want to know? The vast space, of all probabilities, is always rapidly unmanageable to examine. In physics we call that place the Hilbert Space, but we can only really work with that where the particle numbers in it are small, and the interactions very limited. However, with our universe we have a 'cheat': we know where we ended up, which set of the 20-or-so fundamental constants the state chose. It's like trying to grapple with all the possible sounds a guitar string could ever make, vs analysing one particular tone. And that tone can tell us all about how we got from the simple place, the 'unplucked string', to this particular complicated place. That can tell us about the 'plucking', or what echo this note is resonating from (eg, 'before' the big bang), and about how this echo will die away: a Great Rip, smooth heat death, lots of options. And maybe, like in CCC, that 'final' pattern of photons can feed into the next universe, maybe like that each universe can get a little more complex, 'seed' a different set of constants, and that is how we got to this vast complex universe we see. And like, we are part of the universe studying itself, in order to work towards a final state, that will generate even more complexity - a giant music score, each entire universes timeline, a note. Like when the laws got just complex enough, universe timelines have minds in, and they make things more complex.

In this picture it's not really true to say complexity is 'from' or made out of simplicity. It's just all the states are always connected, a multidimensional sculpture of everything that was or will be, and something 'rolls around'; awareness, 'now', state-information, ripples around the pattern, borrowing from itself, and paying itself back. This is the view that everything, never stops being nothing (within the bounds of uncertainty). And nothing, can't help but make everything.

When you have a set of things, and you iterate what they are, like shaking a tray of dice or coins, you will get more outcomes of the simpler cases. For the universe to get into such an 'unusual' state, needing 20-ish fundamental constants to explain what can happen in the uncertainty window, means a vast Hilbert space. So the crystal must have cooled a lot of times with less complexity, the string had less complex echoes. The 'simple' laws, tell us about a vast array of other ways the universe could have been. Like a Hilbert space, each interaction vastly increases the intractability. There might be patterns, but we could never see them. And looking to the Anthropic Principle, there are patterns, and we are here and do see them, so it had to be that the fundamental interactions were few enough, that for simple interactions, they would be tractable. Other possible universe states, minds could not make headway. For that we need it simple enough to grasp the rules with a finite lump of matter, but complex enough to build something like our universe, then there will be minds, and they can make the next universe more complex (but still tractable to minds in it, or the feedback ends).

Apologies for not being more concise. And for remaining jargon, I trued to use as little as I could. I hope you feel this at least points towards what kind of form an answer might take, when we have better answers to fill the hand-wavey bits.

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It seems to me one has to be very careful about mixing up the state of the universe, and objective reality about it (or rather our perception of it), with our understanding of it. To be more clear, statements like "the universe is governed by a small number of laws.." or "there is a single law, the law of universal gravitation, that controls the orbits of all planets" are, honestly, kind of meaningless to me.

The "law" is nothing but our mathematical description of something, while it may rest on more foundational principles, it is simply the way humans have managed to describe, predict, explain to themselves certain phenomena in which they have detected some regularity. Newton's or Einstein's laws of gravitation are just descriptions, models if you will, they don't make the planets move around a certain way, they just help us describe and predict that behavior.

Questions like "why are there a few laws that describe reality" are then to me are much more questions about how human minds work than questions about the physical universe. What I think is we have brains evolved to prefer dealing with high levels of abstraction, plus the ability to build abstractions on top of abstractions. Once we have that, it only takes a sense of aesthetics/economics of thought to get us the cleanest possible explanations, in the most elegant terms, with the fewest assumptions possible, etc. for any particular phenomena.

TL;DR: It's not the universe prefers few laws, it's that our minds do. The universe is how it is, regardless of how clever we are at describing it.

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  • The point is that these laws, be it an object in our minds or not, reveal a long-term (and long-distance) regularity in the laws of physics. To the point that we can look at a different star, in a different galaxy, and be able to guess its chemical composition. Another example is how we can know the trajectory of a cannon ball wirthout actually performing the experiment. In situations where quantum mechanical effects are not big enough to matter, pretty much every future proposition about the world can be deduced from some initial data. That's how rigid the laws of physics are. Feb 8 at 18:22
  • It could be that the laws of physics were not so regular, in which case we would need to actually perform experiments every time to know the outcome. Instead, we can generalize from previous experiments, due to the symmetry in the laws. The question is: Why are the laws so symmetric? Why is the universe so predictable? Feb 8 at 18:25

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