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B.  The implication

According to Maxwell's theory, when charged particles vibrate and stir up waves in the electromagnetic force fields around them, energy from the particles' vibration should pass into the waves gradually.  Furthermore, when electromagnetic waves run into charged particles and set the particles to vibrating (or alter their existing vibration), the energy transfer from the waves to the charged particles should also be gradual.  The theory also-crucially-implies that such energy transfers in either direction could involve any amount of energy whatsoever, corresponding to how long the transfer took.

Planck's formula, on the other hand, fit all the known facts about light in a high-temperature enclosure, but the formula would only make sense if the energy transferred always came in exact multiples of a certain definite amount and only that amount.  It was as though, for any given frequency, the light waves' energy came in some kind of indivisible "atoms" of its own, with the atoms' size in direct proportion to the waves' frequency.  Such "atoms of energy" had no obvious relation to the continual energy flow expected of Maxwellian light waves.  Despite this, Planck published his formula in October 1900, and published its interpretation in terms of energy "atoms" (or quanta) in December 1900.

Planck himself supposed that although the energy of the light might be emitted and absorbed as definite quanta, the energy would be spread smoothly throughout the light waves as they moved through space, as Maxwell's equations suggested.  But Albert Einstein gave these energy quanta a great deal of thought, and by 1905 had found reasons to suspect that energy was not spread smoothly throughout the light waves, but that it traveled through space as isolated points of energy instead.

How could that be, given that Maxwell's equations seemed so well confirmed by experiments?  Einstein offered one possibility.  As of 1905, physicists had never observed anything about light's electromagnetic force fields beyond their average behavior over intervals of time.  Even in one microsecond, a Maxwellian visible-light wave should undergo millions of vibrations.  But what a real light wave actually did during any single vibration had never been resolved by experiments.  Einstein thought that the energy of a light wave might in fact move in discrete units, but in such a way that the units' average distribution over short durations would look smooth in the types of experiments that had been done at the time.  It would take new experiments to reveal the units' nonuniform distribution.

So what were Einstein's reasons for thinking the energy of light traveled through space in such units?  Some evidence came from Planck's law itself.  Einstein saw that this law suggested that light quanta act a lot like molecules of a gas.     (.....continued)

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