differences AB–BA are proportional to a number measured by Max Planck

That discovery was that in order to get a satisfactory

quantum generalization of a classic theory one must

replace various

numbers in the classic theory by

actions

(operators). A key difference between

numbers and actions is that if A and B are two

actions then AB represents the action obtained by

performing the action A upon the action B. If A and

B are two different actions then generally AB is

different from BA: the order in which actions are

performed matters. But for numbers the order does

not matter: AB

ZBA.

The difference between quantum physics and its

classic approximation resides in the fact that in the

quantum case certain differences AB–BA are proportional

to a number measured by Max Planck in

1900, and called Planck’s constant. Setting those

differences to zero gives the classic approximation.

Thus quantum theory is closely connected to classic

physics, but is incompatible with it, because certain

non-zero

quantities must be replaced by zero to obtain

the classic approximation.