Newton's Second Law of Motion

Newton's second law of motion, that pillar of classical physics, the formula that says the force on an object is proportional to acceleration, has now been tested, and found to be valid, at the level of 5 x 10^-14 m/s^2. This is a thousandfold improvement in precision over the best previous test, one carried out 21 years ago (Physical Review D, vol 34, p 3240, 1986). The new test was performed by physicists at the University of Washington using a swiveling torsion pendulum, a special kind of pendulum in which the restoring force is not gravity (as you would have in a hanging pendulum) but is provided by a very thin torsion fiber.

One implication of Newton’s law is that the pendulum’s frequency (its tick-tock rate) should be independent of the amplitude of its swiveling (as long as the oscillation is small). Looking for a slight departure from this expected independence the Washington researchers watched the pendulum at very small amplitudes; in fact the observed swivel was kept so small that the Brownian excitation of the pendulum was a considerable factor in interpreting the results.

Newton’s second law is expected to break down for subatomic size scales, where quantum uncertainty frustrates any precise definition of velocity. But for this experiment, where the pendulum has a mass of 70 g and consists of 10^24 atoms, quantum considerations were not important. According to one of the scientists involved, Jens Gundlach (206-616-3012, jens@phys.washington.edu), this new affirmation that force is proportional to acceleration (at least for non-relativistic speeds), might influence further discussion of two anomalies:

(1) oddities in the rotation curves for galaxies---characterizing the velocity of stars as a function of their radii from the galactic center---suggest either that extra gravitational pull in the form of the presence of as-yet-undetected dark matter is at work or that some new form of Newton’s Second Law could be operating (referred to as Modified Newtonian Dynamics, or MOND); and

(2) the ongoing mystery surrounding the unaccounted-for accelerations apparently characterizing the trajectory of the Pioneer spacecraft (see http://www.aip.org/pnu/1998/split/pnu391-1.htm). (Gundlach et al., Physical Review Letters, upcoming article)