G1    A Strange Experimental Fact

Which is heavier - a kilogram of lead or a kilogram of feathers? [28-155] The answer to this supposed joke is actually not self-evident. Newton was perhaps the first to have wondered about the fact that inertial mass and gravitational mass are experimentally not distinguishable from each other (see the quote in A1). In a series of pendulum experiments, he personally investigated the matter and noted that the two quantities were proportional to each other. It is only a question of defining the units for mass and force in order to make this proportionality into an equality.

In section F1, we almost casually remarked that we have to deal with, in principle, three different concepts of ‘mass’:

•   Mass as ‘inertial mass’, which resists a change of momentum

•   Mass as  ‘gravitational or heavy mass’, which suffers a force in a gravitational field

•   Mass as ‘gravitating mass’, which itself generates a gravitational field

The fact that the ‘field-causing’ mass can be equated with the 'field-experiencing’ mass has never caused a stir. But that the ‘inertial’ and ‘gravitational or heavy' masses should be identical has no logical basis and was therefore repeatedly tested experimentally. The accuracy that Newton's pendulum experiments achieved was about 1:1000. Probably triggered by thoughts of Ernst Mach, the Hungarian Baron Loránd von Eötvös performed, beginning in1899, precision experiments on this issue. He improved the accuracy of Newton by many powers of ten. Another significant increase in precision was achieved in 1964 by Robert H. Dicke and his team. Given the fundamental importance of these experiments we present the data of [29-1050ff (!), called 'the phone book' ...] in a small table. I have added the drop tower in Bremen because with this experiment for the first time not just torsion forces are being measured, but also it directly examines whether all the bodies fall equally fast. Since 2005, thanks to new catapult equipment a free fall time of around 9.5 seconds is achieved. The web link is www.zarm.uni-bremen.de/index.htm .

mwho when achieved precision
mNewton ~ 1680 1 : 103
mEötvös 1889 - 1922 5 : 109
mRenner 1935 7 : 1010
mDicke et al. 1964 1 : 1011
mBraginsky and Panov 1971 1 : 1012
mDrop Tower Bremen since 1990 1 : 1012

Misner et al. [29] call this fact "the uniqueness of free fall" or "the weak equivalence principle". This experimental fact stands at the beginning of every theory of gravitation. All (small) test bodies fall in the gravitational field of a large body at exactly the same speed, regardless of their composition and mass. Newton could not answer why this is so and he would not speculate (‘hypotheses non fingo’). A good theory of gravitation must, however, provide an answer to this question.

Starting in 1906 Einstein worked on this problem - and in 1908 he realized that he could, in his typical way, best provide a solution.

(November 2007, the link is no longer active)