Doug Huffman said:
The difference between a (scientific) law and theory is the topic of Karl Popper's 1934, tr.1959 The Logic of Scientific Discovery and the core of Lee Smolin's thesis, as in his 2006 popularized The Trouble with Physics.
This misses the mark.
The term "law" in physics has gone out of style. Physicists still use the term for older concepts that were labeled as laws. Ohm's law, for example, is still called Ohm's law. Ohm's law is V=IR. Using a more modern lexicon, that would be better labeled as "Ohm's equation". Newton's
Principia (a theory) included a small number of underlying equations, his laws of motion and law of gravitation. Einstein's theory of general relativity also includes a small number of underlying equations. Physicists just call those equations the Einstein field equations. In days of yore, those field equations would most likely have been called Einstein's law of gravitation.
In physics, a law typically is an equation, one which may have limited applicability. Ohm's law is a good example. Batteries, capacitors, inductors, and rectifiers don't follow Ohm's law. Neither do resistors after having had too much current pushed through them. Resistors become non-ohmic once they start emitting smoke.
A scientific theory is a tested body of knowledge that typically cannot be summarized in a tweet. (In contrast, most laws can be stated in full in a single tweet on twitter.com.) Oftentimes a book (e.g., Newton's
Principia, Darwin's
On the Origin of Species) is needed to convey the concepts of a scientific theory.
Regarding Popper, his idea of falsification, while good, also misses the mark. Despite the fact that many electrical devices are markedly non-ohmic, electrical engineers still use Ohm's law to describe resistors. Despite the fact that relativity theory and quantum mechanics falsify Newtonian mechanics, civil engineers still use Newtonian mechanics in designing bridges, roads, and buildings, and aerospace engineers still use Newtonian mechanics in designing and operating spacecraft . Falsification is a naive concept. Relativity theory and quantum mechanics didn't falsify Newtonian mechanics. They instead showed that Newtonian mechanics is not universally true. It is still quite valid in a limited (but very useful) domain.
Another area where Popper's falsification fails is when a theory is shown to disagree with reality. More often than not, the theory is tweaked rather than discarded. Darwin's theory of evolution has been tweaked a number of times, first with the modern synthesis, then with genetics, and more lately with epigenetics and horizontal gene transfer. Quantum theory similarly has been tweaked a number of times. Quantum mechanics supplanted the old quantum theory, protons and neutrons moved from the class of elementary particles to composite particles with quantum chromodynamics, and quantum electrodynamics added even more weirdness to quantum theory.