Is History a Science?

Laws as approximations

Some laws are low (or high) limits of others, more general laws (or as scientists say, of more fundamental laws). For example, Newtonian dynamics (which is based on Galilean transformations) is simply the low speed limit of laws of special relativity (simply because Galilean transformation follow from Lorentz transformation at the limit of low speed). Similar, the Newtonian gravitation law follows from general realtivity at the limit of low gravitational potential (compared to square of speed of light), and Coulomb's law follows from QED at large (compared to range of weak interactions) distances. In such cases we understandably use more simple laws-approximations instead of more accurate fundamental laws.

Those laws which are just mathematical definitions (say, fundamental law of mechanics - second Newton's law ), or uncertainty principle, or least action principle - are absolutely correct (simply by definition). Others which reflect symmetries found in Nature (say, identity of electrons or homogenuity of space and time) are constantly being checked experimentally to higher and higher degree of accuracy. The fact that they have never been seen repeatably violated does not preclude testing them at increased accuracy, which is one of main goals of science. It is always possible for them to be invalidated by repeatable, contradictory experimental evidence, should any be seen. However, fundamental changes to the laws are unlikely in the extreme, since this would imply a change to experimental facts they were derived from in the first place.

Well-established laws have indeed been invalidated in some special cases, but the new formulations created to explain the discrepancies can be said to generalize upon, rather than overthrow, the originals. That is, the invalidated laws have been found to be only close approximations (see above examples), to which other terms or factors must be added to cover previously unaccounted-for conditions, e.g., very large or very small scales of time or space, enormous speeds or masses, etc. Thus, rather than unchanging knowledge, physical laws are actually better viewed as a series of improving and more precise generalisations.