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I don't know if how Clark retold this story is historically accurate but the details of the challenge got my cogs turning:[LIST=1][*]Even though this is a theoretical challenge, light is without mass. How could the box register a lower weight?
To answer this question one needs to note the differences between Newton's concept of gravity as opposed to Einstein's and how it impacts on "weight" and mass.
The equations describing Newton's concept of gravity are linear. From a physical viewpoint the gravitational force between 2 masses is the same as breaking up one of the the masses into pieces and adding up the individual forces between each piece and the unbroken mass. In other words the whole is equal to the sum of its parts.
From a GR perspective the equations are no longer linear, in this case one would find the whole is now less than the sum of its parts.
The "missing mass" is taken up by the binding energy required to break up the mass into pieces. This energy also contributes to the total force. In fact energy in general contributes to mass via the equation E=mc^2.
This has been experimentally confirmed. One finds for example the mass/energy of the helium atom is less than the sum of its constituent protons, neutrons and electrons.
In Einstein's example the photon carries away a certain amount of energy which is related to its wavelength hence the box will be lighter.
Regards
Steven
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