Importance and Range of Validity
Newton's laws were verified by experiment and observation for over 200 years, and they are excellent approximations at the scales and speeds of everyday life. Newton's laws of motion, together with his law of universal gravitation and the mathematical techniques of calculus, provided for the first time a unified quantitative explanation for a wide range of physical phenomena.
These three laws hold to a good approximation for macroscopic objects under everyday conditions. However, Newton's laws (combined with universal gravitation and classical electrodynamics) are inappropriate for use in certain circumstances, most notably at very small scales, very high speeds (in special relativity, the Lorentz factor must be included in the expression for momentum along with rest mass and velocity) or very strong gravitational fields. Therefore, the laws cannot be used to explain phenomena such as conduction of electricity in a semiconductor, optical properties of substances, errors in non-relativistically corrected GPS systems and superconductivity. Explanation of these phenomena requires more sophisticated physical theories, including general relativity and quantum field theory.
In quantum mechanics concepts such as force, momentum, and position are defined by linear operators that operate on the quantum state; at speeds that are much lower than the speed of light, Newton's laws are just as exact for these operators as they are for classical objects. At speeds comparable to the speed of light, the second law holds in the original form F = dp/dt, where F and p are four-vectors.
Read more about this topic: Newton's Laws Of Motion
Famous quotes containing the words importance and, importance, range and/or validity:
“The chimney is to some extent an independent structure, standing on the ground, and rising through the house to the heavens; even after the house is burned it still stands sometimes, and its importance and independence are apparent.”
—Henry David Thoreau (1817–1862)
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (1859–1952)
“[F]or as Socrates says that a wise man is a citizen of the world, so I thought that a wise woman was equally at liberty to range through every station or degree of men, to fix her choice wherever she pleased.”
—Sarah Fielding (1710–1768)
“Once one is caught up into the material world not one person in ten thousand finds the time to form literary taste, to examine the validity of philosophic concepts for himself, or to form what, for lack of a better phrase, I might call the wise and tragic sense of life.”
—F. Scott Fitzgerald (1896–1940)