Once Before Time - Martin Bojowald [29]
Such data already existed before quantum theory was developed in the early twentieth century, thanks to the straightforward measurability of discrete emission and absorption spectra. Finding an explanation was a prime motivation for the first researchers of quantum theory. Excellent experimental data, unexplainable by classical physics, thus existed when quantum mechanics was developed, which is different from the situation for general relativity. Researchers found important clues as to how exactly classical physics had to change. Otherwise, quantum theory, with its strange consequences, would likely never have been found, let alone accepted.
THE CLASSICAL LIMIT AND EFFECTIVE FORCES: TEARING DOWN WAVES
Extensions of already established theories are supposed to explain new observational data, but they must not give rise to disagreements with phenomena already explained by an older theory. Achieving this consistency is no simple task, for the tremendous progress of physics since Galileo Galilei has made existing theories very successful, explaining numerous phenomena that fill whole books and even libraries. It is impossible to reevaluate every single explanation in order to show explicitly that consistency remains realized. Instead, one can often cleverly make use of the fact that extensions of a theory usually introduce a new parameter: a new constant of nature. Phenomena explained only by the new theory allow one to determine the value of such a parameter by comparing theoretical predictions with measurements. The old theory, on the other hand, can be realized as a limit of the extended theory in which the new parameter takes a certain value that is fixed but incompatible with the newly explained observations; this incompatible value is usually zero, but it may also be infinite, which is actually allowed in such a limiting process.
For relativity, the new parameter is the speed of light, implicitly assumed to be infinitely large in Newtonian physics. Thus the unwelcome action at a distance in Newton’s law of gravity: Without any upper limit for propagation velocities such as that of light, a mass can instantaneously act on other masses no matter how distant they are. In quantum theory, the new parameter is Planck’s constant, which determines the size of discrete quantum jumps of energies. (Even before the development of quantum mechanics, this constant was introduced by Max Planck in the context of black body radiation, as discussed below.) Accordingly, this parameter can be measured in the emission spectra of atoms, reflecting the discreteness of excited states. By setting Planck’s constant to zero, one would eliminate the distances between different energy levels, pushing them close to each other, and classical physics with its arbitrary energy values is obtained as a limit. Mathematically, this is a very economical way of showing that nothing of the old classical theory is lost. Statements of the latter refer only to the subset of situations in which the discreteness of energies is irrelevant anyway.
How classical behavior is approached can even be demonstrated explicitly for suitable wave functions. This is important because there are, despite quantum theory’s universal applicability, many situations in which macroscopic objects are still described very precisely by classical calculations. A goalkeeper has to pay attention to many things during a penalty kick, but need not worry that the ball, as a consequence of the uncertainty principle, will suddenly appear at a position completely different from where it was just a moment ago. Wave functions must exist