Science (n): The process of learning about the natural universe by observation and
experiment.
At least, that's what I teach my students, usually on the first day of class. Science is, ironically, difficult to define
precisely, but this is the definition I've developed over the years. If anyone has any suggestions for improvement, let me
know. I also teach my students that if theory doesn't agree with nature, there are two choices: change the theory, or change
nature. Unfortunately, all attempts to change nature have failed. Our only choice? Change the theory. That, in a nutshell,
is why we have quantum mechanics. In this first part of a multipart series, we will review the failures of classical mechanics
that necessitated the development of a new theory of nature.
David W. Ball
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Isaac Newton first published his three laws of motion in 1687, in Principia Mathematica. Although they took some time to be accepted, ultimately it was realized that the three laws did indeed accurately describe
the motion of objects. The predictive nature of the three laws was so good that it inspired Pierre-Simon Laplace, the famed
French mathematician and astronomer, to famously remark that if we knew the position and velocity of every bit of matter,
we could predict the future of the universe.
However, as the 19th century progressed, certain experiments produced results that could not be explained in terms of the
understanding of nature that science held at that time. Here, we will review the main issues. Spectroscopy
Figure 1: One of the earliest models of spectroscope (1).
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In 1860, Robert Bunsen (of Bunsen burner fame) and Gustav Kirchhoff (of Kirchhoff's laws fame) invented the spectroscope (Figure
1). One of the noteworthy findings, noted almost immediately, was that some samples absorbed only particular colors of light.
Bunsen and Kirchhoff quickly concluded that the colors of light absorbed (or emitted, depending upon the temperature of the
sample) were specific to the elements in the sample, and less than a year later discovered the elements rubidium and cesium
by noting new colors of light not previously associated with any other known element.
Of course, there is an obvious question — why? Why do different elements absorb or emit only certain colors of light? Also,
what determines which colors of light are absorbed or emitted? Unfortunately, nothing in Newton's laws of motion, or law of
gravity, or even Maxwell's equations of electromagnetism (published in 1861) could explain why.
Figure 2: Emission spectrum of the element hydrogen. The leftmost line is in the far violet and sometimes is not detectable
by the human eye. A major issue in the late 19th century was exactly why these colors, and no others, are emitted by hydrogen.
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The element hydrogen had a particularly simple spectrum. This was arguably defensible, because it was known even then that
hydrogen was the simplest element. However, there was no theoretical explanation for the particular colors that hydrogen did
absorb or emit (Figure 2).
The simplicity of the spectrum did inspire some investigation, and in 1885, Swiss mathematician Johann Jakob Balmer announced
that the wavelengths of the lines of light emitted or absorbed by hydrogen could be predicted by the following formula:
where x was 3, 4, 5, and 6 for the lines going from red to violet, respectively. This formula is more well known in its reciprocal
form as
Collectively, these four lines of light are called the Balmer series of hydrogen, in Balmer's honor. Three years later, a
Swiss physicist, Johannes Rydberg, generalized Balmer's formula to include light emitted in other regions of the spectrum;
his formula is
