Basically, I understand the difference between a "Theory" and a "Theorem" but I am quite confused when it comes to "Law", "Rule" and "Principle". Can you make the differences clear to me?
Answer
A theory is a collection of concepts, laws, and equations in science that is meant to explain some particular subset of observations. It's also used for theories describing gedanken worlds that differ from ours. There is also a related word "model" that differs by a theory by being really specific while a "theory" may leave some details adjustable, and "framework" which is on the contrary less specific than a theory and fully determines the general methods, and type of objects and arguments that are allowed in research. The boundary between the terms is not quite sharply delineated.
A theorem is a mathematical proposition, usually a hard one to prove or disprove, and usually a far-reaching and general enough, that has been proven to hold by rigorous mathematical methods. A lemma is a less important version of a theorem, usually one that is used as a step to prove full-fledged theorems.
"A rule" is usually used for some prescriptions that should be memorized and that chooses the right answer from a usually small list of possibilities. In particular, there are right hand rules that determine the sign of some quantities and/or its relationship to directions in space (this direction or opposite direction). Some of the rules define conventions – claims that could have also been chosen in the opposite way but people must understand each other so they agreed to use one particular sign etc. Hund's rules determine which angular momentum is chosen – again, the number of candidates is usually limited.
"A law" is a more substantive insight about Nature, a building block of our understand how Nature (or the society) works. It may be equivalent to one equation, one identity for continuous quantities, like Coulomb's law for the attraction or Ohm's law $U=RI$ etc. How Nature works is described by the "laws of physics".
"A principle" is more general than a law and it is usually a statement of a general type or a philosophy or a condition that good laws (explained in the previous paragraph) are supposed to satisfy. A principle is therefore an extra criterion that has been induced from the observations and the known laws and that is imposed on the new candidate laws. The principle of relativity is an example. Principles usually require more verbal, words-based descriptions to be fully formulated, as opposed to a single particular equation that may define a "law".
No comments:
Post a Comment