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What makes a law of nature a “law,” exactly?

Cover for 

Because Without Cause

Marc Lange, author of Because Without Cause, offers some thoughts:

Scientists discover laws of nature by acquiring evidence that some apparent regularity is not only never violated but also could never have been violated. For instance, when every ingenious effort to create a perpetual-motion machine turned out to fail, scientists concluded that such a machine was impossible – that energy conservation is a natural law, a rule of nature’s game rather than an accident. In drawing this conclusion, scientists adopted various counterfactual conditionals, such as that, even if they had tried a different scheme, they would have failed to create a perpetual-motion machine. That it is impossible to create such a machine (because energy conservation is a law of nature) explains why scientists failed every time they tried to create one.

Laws of nature are important scientific discoveries. Their counterfactual resilience enables them to tell us about what would have happened under a wide range of hypothetical circumstances. Their necessity means that they impose limits on what is possible. Laws of nature can explain why something failed to happen by revealing that it cannot happen – that it is impossible.

Mark Lange, “What is a law of nature?” at Psyche (March 10, 2022)
P, a perpetuum mobile is about thermodynamics, thus large populations of particles and their distributions. So, the underlying laws are those of probability/statistics constrained by yes energy conservation. That's also where the second law comes from. A single particle ideal case becomes non relevant save as perhaps an ideal thought exercise. KF PS: Generally, laws of nature are empirically grounded, objective natural regularities and/or idealisations [think, ideal gas law PV = nRT], coming from the core constraints of our particular world. SEP starts with (and goes on to debate using as pivot the difference between Au and U spheres a mile in diameter, the latter being a natural impossibility due to critical mass):
One popular answer ties being a law to deductive systems. The idea dates back to Mill (1843, 384), but has been defended in one form or another by Ramsey (1978 [f.p. 1928]), Lewis (1973, 1983, 1986, 1994), Earman (1984) and Loewer (1996). Deductive systems are individuated by their axioms. The logical consequences of the axioms are the theorems. Some true deductive systems will be stronger than others; some will be simpler than others. These two virtues, strength and simplicity, compete. (It is easy to make a system stronger by sacrificing simplicity: include all the truths as axioms. It is easy to make a system simple by sacrificing strength: have just the axiom that 2 + 2 = 4.) According to Lewis (1973, 73), the laws of nature belong to all the true deductive systems with a best combination of simplicity and strength. So, for example, the thought is that it is a law that all uranium spheres are less than a mile in diameter because it is, arguably, part of the best deductive systems; quantum theory is an excellent theory of our universe and might be part of the best systems, and it is plausible to think that quantum theory plus truths describing the nature of uranium would logically entail that there are no uranium spheres of that size (Loewer 1996, 112). It is doubtful that the generalization that all gold spheres are less than a mile in diameter would be part of the best systems. It could be added as an axiom to any system, but it would bring little or nothing of interest in terms of strength and adding it would sacrifice something in terms of simplicity. (Lewis later made significant revisions to his account in order to address problems involving physical probability (Lewis 1986, 1994) . . . .
Overthinking. The law of conservation has nothing to do with it. Perpetual motion is impossible in the real observable world because shit happens. We can imagine a single massless particle moving in a straight line forever, in a wide-open part of space with no magnetic fields and no planets or gravity. This massless particle could go on for a long time ... until it enters a more populated part of the universe. More importantly, the lonely massless particle would never be observed by anyone, so its perpetual motion would be effectively nonexistent. As soon as it enters an area where it can perturb waves, allowing us to observe it, the hysteresis of the perturbed waves would start to slow it down. polistra

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