First recognized in 1900 by Max Planck, it was originally the proportionality constant between the minimal increment of energy, E, of a hypothetical electrically charged oscillator in a cavity that contained black body radiation, and the frequency, f, of its associated electromagnetic wave. In 1905 the value E, the minimal energy increment of a hypothetical oscillator, was theoretically associated by Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called the photon. 

Classical statistical mechanics requires the existence of h (but does not define its value). Eventually, following upon Planck's discovery, it was recognized that physical action cannot take on an arbitrary value. Instead, it must be some multiple of a very small quantity, the "quantum of action", now called the Planck constant. Classical physics cannot explain this fact. In many cases, such as for monochromatic light or for atoms, this quantum of action also implies that only certain energy levels are allowed, and values in between are forbidden.
Who originally associated the minimal energy increment of a hypothetical oscillator with a "quantum" or minimal element of the energy of the electromagnetic wave itself?
When did he do this?
What letter is the value called?
How did the light value behave?
As opposed to what?
What was it later called?
Who was energy E originally recognized by?
What type of action can't take an arbitrary value?
What must it be instead?
What is that also known as?
Is there another name for it?
What is it?
Is this fact widely understood in physics?
What does this imply about energy levels?
What about values in between?
Einstein
theoretically associated by Einstein
In 1905
In 1905 the value E, the minimal energy increment of a hypothetical oscillator, was theoretically associated by Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself.
E
the value E
as an electrically neutral particle
The light quantum behaved in some respects as an electrically neutral particle
an electromagnetic wave
s an electrically neutral particle, as opposed to an electromagnetic wave
the photon
It was eventually called the photon. 

Max Planck
First recognized in 1900 by Max Planck, it was originally the proportionality constant between the minimal increment of energy, E,
a physical one
following upon Planck's discovery, it was recognized that physical action cannot take on an arbitrary value
some multiple of a very small quantity
 Instead, it must be some multiple of a very small quantity, the "quantum of action", now called the Planck constant
the "quantum of action"
the "quantum of action", now called the Planck constant.
yes
 now called the Planck constant.
the Planck constant
the "quantum of action", now called the Planck constant.
no
Classical physics cannot explain this fact.
only certain ones are allowed
this quantum of action also implies that only certain energy levels are allowed
they're forbidden
values in between are forbidden.