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"In 1900 Max Planck discovered a formula that describes the blackbody \
radiation curve (see Figure 1). He did this first by taking the measured \
points and forcing a curve to fit those points (a process called curve \
fitting that leads to a kind of formula based directly on observation or \
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"). Once he had the empirical formula he proved rigorously that it was \
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\[CloseCurlyQuote]t like them. Why didn\[CloseCurlyQuote]t he like them? \
Because the only way to produce the curve was to force the energy that \
produced it into discrete chunks.\n\tWhat is so bad about discrete chucks? In \
fact, what does it mean to have energy in discrete chunks? To cover this we \
need to go back into history. A long time ago, back with the ancient Greeks \
we knew only the counting numbers, what we call ",
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". A world with only natural numbers is a jagged world of boxes. We see \
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can always add another point. This is a property of the real numbers. \
Distances and most other quantities of the physical world in classical \
physics are smooth, what we call continuous. Natural numbers are discrete, \
real numbers are continuous. The discovery that the only way to produce the \
nice continuous curve of Figure 1 is the requirement that light energy comes \
in discrete chucks was quite a blow! Planck came up with a name for the \
chunks of light, ",
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".\n\tThis was a nice idea, but few people believed it. After all, a model \
must make a prediction; what predictions did this new idea make? Albert \
Einstein, in the year that he discovered special relativity, also explained a \
puzzling phenomen using the new quantum theory. In the same year he also \
proved the existence of atoms and explained the curious jiggling motion \
discovered by Brown, called Brownian motion. The phenomen he explained using \
quantum theory was one where shining unltraviolet light onto a sheet of metal \
causes an electric current to occur in discrete jumps of current. This is \
called the ",
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".\n\tMany puzzling effects and ideas came out, and the result was the new \
model of the atom based discrete levels of energy for different atoms. Many \
people have a solar system-like atom with the nucleus at its center and \
electrons orbiting like planets. This model has created many \
misunderstandings among writers suggesting that atoms could actually be \
miniature solar systems, leading to infinite regressions of levels of \
reality. In reality, the best way to think of it is a set of nested shells of \
indeterminate thickness, into which there are an integer number of electrons \
somewhere in the shell. The specific locations of the electrons are \
uncertain. Niels Bohr developed a model that was correct for Hydrogen, but \
there were problems with other atoms. It took the combined efforts of many \
famous physicists to figure out the physics of the quantum world. Werner \
Heisenberg developed a highly abstract theory that seemed to be correct. \
Erwin Schr\[ODoubleDot]dinger developed a less abstract theory that was based \
on a wave equation. Paul Dirac showed that the two approaches are, in fact, \
equivalent. Thus was born quantum mechanics."
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