What is the difference between laws (e.g., Newton's Laws, Boyle's Law) and principles (e.g., Principle of Least Action , Heisenberg Uncertainty Principle)? As far as I know, both break down to some limit.
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4$\begingroup$ The difference is rather arbitrary and subjective, and mostly due to historical reasons. $\endgroup$– agaminonAug 3, 2022 at 22:21
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1$\begingroup$ @agaminon, though brief, isn't your comment more an answer than a comment? $\endgroup$– Alfred CentauriAug 3, 2022 at 22:36
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$\begingroup$ Possible duplicates: physics.stackexchange.com/q/68599/2451 , physics.stackexchange.com/q/44706/2451 and links therein. $\endgroup$– Qmechanic ♦Aug 4, 2022 at 2:37
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2 Answers
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On paper, a principle should be something that is postulated, while a law is proven within a given framework.
The problem is that some physics results that were principles in the past have been proven since then, but we keep calling them principles for historical reasons, out of habit:
- Heisenberg's uncertainty principle (which is neither a principle nor about uncertainty)
- Pauli exclusion principle (proven under the name spin-statistics theorem) and so on.
Also, the way "principle" is used may vary a bit from language to language. In my language (French), both laws of thermodynamics are called principles, even though it's a rather obsolete denomination for those too.
The principle of least action, as far as I'm aware, actually is a principle. It's the basic axiom we're using, coupled with Noether's theorem, to build all known theories.
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$\begingroup$ Close enough. A model is a choice of mathematical objects, and relations between them, that can be used to successfully predict the outcome of some experiments. Laws are the relations, but the model also requires objects (vector for velocity in classical mechanics, scalar field for temperature in thermodynamics…) $\endgroup$– MiyaseAug 4, 2022 at 7:19
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$\begingroup$ Yes So principles are frameworks and laws are models build from them $\endgroup$– quanityAug 4, 2022 at 7:26
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$\begingroup$ That would be "first principles". A simple principle can also be a law that hasn't been proven yet but is known to work well, typically because it's been infered from experiment. $\endgroup$– MiyaseAug 4, 2022 at 7:32
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As @agaminon mentions in his comment, the difference is rather arbitrary and subjective. To my knowledge, there has generally never been any adherence to a particular criteria for what laws or principles are supposed to be in typical physics literature.
This is of course, not the case in modern mathematical literature, even those that dabble in physics, however, the terminology is different. Math literature generally talks about these laws and principles via very precise definitions and propositions. These propositions could be axioms (these are assumed to be true and serve as starting points for deductive reasoning), lemmas (auxillary propositions that are used to prove theorems) or theorems (the big results, often named).
At the very least however, depending on the formulation of your theory you can determine using the above criteria, which physical laws or principles are axiomatic, which are definitions and which are theorems. There are of course, technicalities that I don't go into here. From the examples you mention, we have,
- Boyle's Law - Theorem (macroscopic thermodynamic laws can essentially be derived from statistics),
- Newton's Laws: 1st - Theorem (special case of the 2nd law); 2nd - Definition (of Force); 3rd - Theorem (provable using linear algebra),
- Principle of Stationary Action - Axiom or Theorem (depending upon your formulation),
- Heisenberg's Uncertainty Principle - Theorem (in most formulations).
And as @Miyase highlights, even the names can often be misleading due to historical reasons, let alone their status as a law or principle.
