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26.7 Two tests of Newton's third law by Benjamin Crowell, Light and Matter licensed under the Creative Commons Attribution-ShareAlike license.

`E=mc^2` states that a certain amount of energy `E` is equivalent to a certain amount of mass `m`. But mass pops up in physics in several different guises: the mass measured by an object's inertia, the “active” gravitational mass `m_a` that determines the gravitational forces it makes on other objects, and the “passive” gravitational mass `m_p` that measures how strongly it feels gravity. Einstein's reason for predicting the same behavior for `m_a` and `m_p` was that anything else would have violated Newton's third law for gravitational forces.

Suppose instead that an object's energy content contributes only to `mp`, not to `ma`. Atomic nuclei get something like 1% of their mass from the energy of the electric fields inside their nuclei, but this percentage varies with the number of protons, so if we have objects `m` and `M` with different chemical compositions, it follows that in this theory `M_p"/"M_a`, and in this non-Einsteinian version of relativity, Newton's third law is violated.

This was tested in a Princeton PhD-thesis experiment by Kreuzer^{11} in 1966. Kreuzer carried out an experiment, figure ar, using masses made of two different substances. The first substance was teflon. The second substance was a mixture of the liquids trichloroethylene and dibromoethane, with the proportions chosen so as to give a passive-mass density as close as possible to that of teflon, as determined by the neutral buoyancy of the teflon masses suspended inside the liquid. If the active-mass densities of these substances are not strictly proportional to their passive-mass densities, then moving the chunk of teflon back and forth in figure ar/2 would change the gravitational force acting on the nearby small sphere. No such change was observed, and the results verified `m_p"/"m_a=M_p"/"M_a` to within one part in `10^6`, in agreement with Einstein and Newton. If electrical energy had not contributed at all to active mass, then a violation of the third law would have been detected at the level of about one part in `10^2`.

The Kreuzer result was improved in 1986 by Bartlett and van Buren^{12}using data gathered by bouncing laser beams off of a mirror left behind on the moon by the Apollo astronauts, as described p. 271. Since the moon has an asymmetrical distribution of iron and aluminum, a theory with `m_p"/"m_aneM_p"/"M_a` would cause it to have an anomalous acceleration along a certain line. The lack of any such observed acceleration limits violations of Newton's third law to about one part in `10^10`.

26.7 Two tests of Newton's third law by Benjamin Crowell, Light and Matter licensed under the Creative Commons Attribution-ShareAlike license.