My own preference is to avoid limiting options. As it appears there exists opposites for everything (call it the apogee and perigee of the waves) I always leave open the possibility for something that I am missing. I consider laws not only erroneous and overly constraining, but also impediments to growth in knowledge. Knowledge comes from resolving paradoxes or another way to look at it would be to find the opposite and from that comes new ideas. The does not appear to be an end to this process.

As for my own understanding, the Copenhagen Interpretation is rather muddy, inconclusive, and unsatisfying - by choice. But the Interpretation is simply that and since it is metaphysical in nature is free to make these claims, despite its limitations. Metaphysics is all about intuition, imagery, and finding patterns. There needs to be a distinction between this, e.g. quantum interpretations, and quantum equations, which are quite limited in their nature.

As soon as you break the symmetry of a circle - put a nick or a mark on its circumference - immediately you can see (from this imperfection) that it has some relative rate of motion (or rest). — apokrisis

OK, but the issue was whether or not it is possible to have a perfect circle, such that you could not tell its rate of spinning, or even whether or not it is spinning. And if there is such a perfect circle, the perfect symmetry, which would be impossible to determine whether it's spinning or not, wouldn't it be nonsensical to speak about it as if it is spinning? That's what I am trying to get at, the nonsensicalness of this notion of spinning, which appears to be totally incompatible with the pure symmetry of a circle.

OK, but the issue was whether or not it is possible to have a perfect circle, such that you could not tell its rate of spinning, or even whether or not it is spinning. — Metaphysician Undercover

Why is that not what I was discussing?

That's what I am trying to get at, the nonsensicalness of this notion of spinning, which appears to be totally incompatible with the pure symmetry of a circle. — Metaphysician Undercover

You see a featureless disc. How do you tell if it is spinning or not? Would you see anything different if a stopped disc started to move, or a moving disc stopped?

The difference between a spinning vs motionless triangle, pentagon or - most especially - any irregular shape is always going to be obvious to the eye. And yet a circle is an unbroken symmetry in that regard. So that is a mathematically important and distinct property - hardly a nonsensical one.

And then - surprise, surprise - rotational symmetry is one of physics foundational facts. Nature can't prevent what it cannot see. And so rotation is built in as an inertial property. Any object - in the absence of impressed forces - will continue to spin at the same rate forever, in just the same way as it will move in a straight line forever due to translational symmetry.

So again, the notion is hardly nonsensical. The theorem linking the maths to the physics is pretty famous - https://en.wikipedia.org/wiki/Noether's_theorem

I am not suggesting limiting options, though. I am all for thinking of every possibility we can imagine, and then working out how we logically conceive of each one. The thing is I don't see how something like whether there are laws of nature or not is discoverable by science. Science itself operates on the assumption that there are invariant laws of nature; and it's not clear how it could function without that assumption.

Some scientists make this assumption others are much more careful. Here is one such discussion about laws and you will easily notice the widely held views on the subject, among scientists and philosophers. Many scientists will readily admit that the equations they rely on are simply useful approximations and therefore should not be considered immutable laws of nature. Without consensus at any level, it is difficult to use a term such as laws of nature or scientific laws. Best just discuss the specific subject and about the ambiguous and undefined general term.

https://blogs.scientificamerican.com/observations/deep-in-thought-what-is-a-law-of-physics-anyway/

My views on scientific laws are closely aligned with this view:

http://www.iep.utm.edu/lawofnat/

"In 1959, at the annual meeting of the American Association for the Advancement of Sciences, Michael Scriven read a paper that implicitly distinguished between Laws of Nature and Laws of Science. Laws of Science (what he at that time called "physical laws") – with few exceptions – are inaccurate, are at best approximations of the truth, and are of limited range of application. The theme has since been picked up and advanced by Nancy Cartwright."

Well what I mean is that scientists expect chemicals for example to behave the same tomorrow as they did today. Or when hypothesizing about, for example geological formations, they assume that materials behaved the same millions of years ago as they do today. Or when they are hypothesizing about galaxy formation or even what would have happened just after the Big Bang, they assume that different elements, particles and materials would have behaved as expected in the hypothesized conditions.Without such assumptions science could never get started.

Without such assumptions science could never get started. — John

However, you're overlooking the fact that:

I habitually wake up in the morning, however the time I awake constantly changes, and yes it is possible that I will not awake at all. — Rich

So, we all should be grateful that Rich remembered to get up today, and consequently that the solar system continues to exist. X-)

Incidentally, Nancy Cartwright's PDF is here, and worth reading in this context.

The fact that laws of nature have limited application doesn't detract from their usefulness within that domain.

Again, I say the only real question is 'why are there laws', and that whatever this question is, is not a scientific question, but a meta-scientific question.

The circle simply illustrates the basic principle that a symmetry is defined by differences not making a difference.

Yes, I got that. The point I was trying make is that I do not see how unregulated chaos can produce anything other than … unregulated chaos. ‘Symmetry’ implies repetitive patterns, which are, as I envision it, absent in chaos.

Unlawfulness comes in once we start talking about symmetry in the sense of dynamical equilibrium states - or broken symmetries that can't get more broken and so ... become effective or emergent symmetries again.
And this is better illustrated by a gas of particles. At equilibrium, every particle is as likely going forward as going backward. So all action settles to a collective average.

Such phenomena can only take place in a stable orderly lawful universe. If instead our starting point is utter unlawfulness/chaos, we would not know what to expect. Given unlawfulness, particles could pop out of existence for no reason at all. The collection of particles could turn into anti-matter and/or form a conglomerate. During observation the cosmological constant could shift followed by an instant implosion of the universe. And so forth. Thorough unlawfulness all the way down is completely unpredictable.

... The ground state becomes a new effective symmetry - the ball rolling around in the circle of the trough - which the world then reads off quantumly as a new degree of freedom or an actual particle.

What you are talking about are events and laws that result from more fundamental laws. I have no problem with that idea, as long as it not offered as an "explanation" of laws at the fundamental level.

Are you talking about laws or constants? Or laws with different constants? That is, do you have a clear story on how they are the same or different kinds of things?

I am talking about laws and their constituents.

I am not suggesting limiting options, though. I am all for thinking of every possibility we can imagine, and then working out how we logically conceive of each one. The thing is I don't see how something like whether there are laws of nature or not is discoverable by science. Science itself operates on the assumption that there are invariant laws of nature; and it's not clear how it could function without that assumption. — John

I think you might have gone a bit too far. Humans will try to explain Reality whether there are varying or non-varying laws. Science does not assume invariant laws, but the existence of laws that vary more slowly than the extent of our experience certainly makes science more tractable. Our experience only encompasses approximately 14 billion years back to the surface of last scattering!

‘Symmetry’ implies repetitive patterns, which are, as I envision it, absent in chaos. — Querius

Chaos is more subtle than that. It does have characteristic organisation. The primary symmetry of "chaos" is the fractal or powerlaw pattern that is scale symmetry. In a fractal system, you have fluctuations over all scales and thus a state without any average size of fluctuation.

So chaos as an absence of constraint still has a strict kind of patterned order. It has a wildness that mathematically regular.

Given unlawfulness, particles could pop out of existence for no reason at all. The collection of particles could turn into anti-matter and/or form a conglomerate — Querius

So you say. Yet the forment of the quantum vacuum generates particles with a spontaneity that is also completely statistically predictable. What we observe in nature is thus a spontaneity that can't help also being ordered.

Just to have an energetic event you have to have spatiotemporal separation. And to maximise the randomness of the spacing of the events itself is an imposition of an organisation. There is a limit on even making things as unpredictable as physically possible. Go past the point of effective randomness and you start getting back towards the overly orderly.

Again the ideal gas illustrates the issue. Low entropy or order would be all the particles gathered in one corner of a flask. So therefore maximum disorder ought to be every particle as spread out as possible, right? But then that would put every particle spaced out an even distance on a grid. So now we are back into a state of high order that won't last long.

It's another version of the sphere packing story and why effective physics rules.

What you are talking about are events and laws that result from more fundamental laws. I have no problem with that idea, as long as it not offered as an "explanation" of laws at the fundamental level. — Querius

I don't follow. But anyway, the Goldstone mechanism started out as a mathematical curiosity, then an explanation of macrostates and quasiparticles, now it explains the Higgs and effective mass. So it is working its way down towards the "fundamental" quite nicely.

I am talking about laws and their constituents. — Querius

What do you mean by constituents? Laws certainly relate variables.

How a system behaves is dependent not only on its constituent parts but also on the organization of these parts, which creates a causal web/network in which general behavior arises. — darthbarracuda

Also, in many cases (i.e. many ontological domains, including the objects of quantum physics) the very nature and existence of the material parts causally and/or constitutively depends on properties of the system of which they are proper parts. This can include boundary conditions, topological properties of space-time, etc. George Ellis argues for this in his recent book on the topic of top-down causation. This general point also has been argued by Michel Bitbol in some of his papers on emergence and on the foundation of quantum mechanics.

Ellis's and Bitbol's arguments are quite general, not very controversial, and free of the obscure and speculative quantum woo-woo that sometimes permeates the discussions of natural scientists when they turn to the topic of the mind. This ontological dependence of parts on whole also had been argued by John Haugeland in Pattern and Being and in Truth and Rule Following (both collected in his Having Tought: Essays in the Metaphysics of Mind). Haugeland's ontological points are quite general but Ellis's and Bitbol's discussion show that physics, even so called fundamental physics, is no exception and affords no refuge to the reductionist.

even so-called fundamental physics...affords no refuge to the reductionist. — Pierre-Normand

How times have changed.

And then - surprise, surprise - rotational symmetry is one of physics foundational facts. — apokrisis

That's the point I was getting at. What a surprise. This incoherency is considered by some to be "one of physics foundational facts".

You see what happened to the assumed eternal circular motions which Aristotle assigned to the orbits of the planets. It turned out that they weren't actually circular, nor were they eternal. You are repeating the very same mistake with your "rotational symmetry".

Yet the forment of the quantum vacuum generates particles with a spontaneity that is also completely statistically predictable. — apokrisis

The "forment" of the quantum vacuum? I assume you mean foment, but that still doesn't make any sense. Nor does the claim that the quantum vacuum generates particles with a spontaneity that is "completely statistically predictable". I think that the very opposite of this is actually what is the case.

But these particles of energy within the so-called "quantum vacuum" are just very clear evidence that quantum field theory is unacceptable. That's the real problem here, quantum field theory just hides the realities of existence behind some artificial, and incoherent, symmetries.

Well what I mean is that scientists expect chemicals for example to behave the same tomorrow as they did today. Or when hypothesizing about, for example geological formations, they assume that materials behaved the same millions of years ago as they do today. Or when they are hypothesizing about galaxy formation or even what would have happened just after the Big Bang, they assume that different elements, particles and materials would have behaved as expected in the hypothesized conditions.Without such assumptions science could never get started — John

Science depends upon mathematical equations that describe repetitious events that are approximately the same, enough so that they can be used for practical purposes. That Newton's Equations are imprecise does not mean that they are impractical. In some cases they may be impractical in which case other equations are used.

The concept of laws of nature is not only unnecessary in science, it is totally misleading.

In philosophy it is only needed by determinists who use this generality for want of specifics. It is more of a desire than anything concrete.

Science depends upon mathematical equations that describe repetitious events that are approximately the same, enough so that they can be used for practical purposes. That Newton's Equations are imprecise does not mean that they are impractical. In some cases they may be in which case other v equations are used.

The concept of laws of nature is not only unnecessary in science, it is totally misleading. — Rich

Schrödinger published his famous equation in 1926. In 1935 it was noticed by Einstein et al that his equation implied that pairs of particles prepared in a certain way, would exhibit the surprising and unexpected phenomenon of quantum entanglement. In 1981 conclusive experiments were performed proving that this feature of reality was in fact present.

There are several other features of the Schrödinger equation, that revealed surprising, unexpected and technologically important aspects of Reality.

So, if as you claim, physical laws merely describe repetitious events, rather than capture and reveal the structure of Reality, then please explain how it is possible that these laws reveal novel features of Reality.

The intuition of possible meanins is not in the equations in is in the minds that create the possibilities. It all begins with Schrodinger's intuition that quanta phenomenon may be described by a wave equation. Similarly, Einstein and his associates looked for possible contradictions in the meaning of the equations. It is the always the mind's intuition that is driving science into new creative directions. The equations themselves may act as an enabler or an inhibitor. It all depends.

The intuition of possible meanins is not in the equations in is in the minds that create the possibilities. It all begins with Schrodinger's intuition that quanta phenomenon may be described by a wave equation. Similarly, Einstein and his associates looked for possible contradictions in the meaning of the equations. It is the always the mind's intuition that is driving science into new creative directions. The equations themselves may act as an enabler or an inhibitor. It all depends. — Rich

The discovery of entanglement refutes your claim that "science depends on mathematical equations that describe repetitious events".

Entanglement is repetitious. That is how it is confirmed. Scientific experiments confirm this.

The discovery itself is the result of human intuition and creativity which one can put under the umbrella of science of one wishes. Are you suggesting that sciencific discoveries are the result of human intuition! I'm on board with this.

Entanglement is repetitious. — Rich

How many times did it repeat in the 50 years between its discovery and the first time it was observed?

The fact that laws of nature have limited application doesn't detract from their usefulness within that domain.

Again, I say the only real question is 'why are there laws', and that whatever this question is, is not a scientific question, but a meta-scientific question. — Wayfarer

I agree that laws of nature, whatever we might think they are, or whatever we might think their ontological implications to be, are indispensable within the domain of science and even everyday life.

The question as to why there are laws, I guess could be answered in terms of any ontological framework; in terms of realism, idealism or pragmatism; the one standpoint they seem to be inexplicable in relation to would be nominalism.

How many times did it repeat in the 50 years between its discovery and the first time it was observed? — tom

I don't know. Do you have an exact number or an approximation?

If there are not rigidly deterministic laws of nature then there must be statistical or probabilistic laws, such that, for example, chemical elements have always been observed to combine predictably, and electronic circuits can be relied upon to an incredibly high degree, given their complexity.

All of the equations and observations are always approximate and subject to change. It was the discrepancies in physics and chemistry experiments that drove scientists to a new understanding of nuclear and quantum physics, which is also changing.

There is no need for the concept in science and I actually never read a scientific paper that called upon the notion of laws to make its presentation. Laws of nature is just an ambiguous term without any concrete value that is called upon by some metaphysical viewpoints. I have yet to have such enumerated. I guess it is more convenient to suggest they exist without any need for a concrete definition. The article I presented earlier is but one example of how disorganized and messy the topic gets if philosophers or scientists are actually called upon to provide a concrete example with definitions.

I'm afraid I have no idea what you are talking about, Rich.

OK. Define what is a law of nature and enumerate them. Then we'll have something concrete to talk about. My first comment on this thread is that it is impossible to discuss a term without a clear definition and concrete examples. It's like talking about God. Do you have a definition?

I don't know. Do you have an exact number or an approximation? — Rich

You're the one claiming that there were "repetitious events" being "described".

While entanglement was a particularly striking example of a feature of reality discovered, not by observing repetitious events, but by analysing a physical law, there are many others. Each one refutes your misconception.

The road to entanglement had nothing to do with analyzing some lifeless equations. It was the result of extraordinary intuition by Bohm and Bell followed by some fascinating creativity by Aspect which ultimately resulted in confirmation experiments by Aspect and others. The equations are simply some symbolic representations of the quality of the minds of these scientists and are confirmed by repetition.

If you wish to claim that creative intuition is the heart and soul of scientific discovery, then I would agree.

It is generally accepted by science that all the laws of nature are reducible to the laws that define the four fundamental forces or interactions; gravitational, electromagnetic, nuclear-weak and nuclear-strong.