*This World Wide Web page written by
Dan Styer,
Oberlin College Physics Department;
http://www.oberlin.edu/physics/dstyer/StrangeQM/intro.html;
copyright © Daniel F. Styer 1999*

In 1905, Albert Einstein realized that
these ideas didn't apply to objects moving at
high speeds (that is, at speeds near the speed of light) and he developed
an alternative body of ideas called *relativistic mechanics*.
Classical mechanics is wrong in principle, but it is
a good approximation to relativistic mechanics when applied to
objects moving at low speeds.

At about the same time, several experiments led physicists to
realize that the classical ideas also didn't apply to very
small objects, such as atoms. Over the period 1900-1927
a number of physicists
(Planck, Bohr, Einstein, Heisenberg, de Broglie, Schrödinger,
and others) developed an alternative *quantum mechanics*.
Classical mechanics is wrong in
principle, but it is a good approximation to quantum mechanics when
applied to large objects.

Einstein's theory of relativity is often (and correctly) described as strange and counterintuitive. Yet, according to a widely used graduate level text,

[the theory of relativity] is a modification of the structure of mechanics which must not be confused with the far more violent recasting required by quantum theory. |

Nobody feels perfectly comfortable with it. |

I can safely say that nobody understands quantum mechanics. |

One strange aspect of quantum mechanics concerns
predictability. Classical mechanics is
*deterministic* -- that is, if you know exactly the
situation as it is now, then you can predict exactly what it will be at any
moment in the future. Chance plays no role in classical mechanics.
Of course, it might happen that the prediction is very difficult to perform,
or it might happen that it is very difficult to find exactly the current
situation, so such a prediction might not be a practical possibility.
(This is the case when you flip a coin.)
But in principle any such barriers can be surmounted by sufficient work
and care. Relativistic mechanics is also deterministic.
In contrast, quantum mechanics is *probabilistic* -- that is,
even in the presence of exact knowledge of the current situation, it
is impossible to predict its future exactly, regardless of how much
work and care one invests in such a prediction.

Even stranger, however, is quantum mechanical *interference*.
I cannot describe this phenomenon
in a single paragraph -- that is a major job of this
entire book -- but I can give an example. Suppose a box is
divided in half by a barrier with a hole drilled through it,
and suppose an atom
moves from point P in one half of the box to point Q in the other half.
Now suppose a second hole is drilled through the barrier and then
the experiment is repeated. The
second hole increases the number of possible ways to move
from P to Q, so it is natural to guess that its presence
will increase the probability of making this move.
But in fact -- and in accord with the predictions of quantum mechanics -- a second hole drilled
at certain locations will *decrease* that probability.

The fact that quantum mechanics is strange does not mean that quantum mechanics is unsuccessful. On the contrary, quantum mechanics is the most successful theory that humanity has ever developed; the brightest jewel in our intellectual crown. Quantum mechanics underlies our understanding of atoms, molecules, solids, and nuclei. It is vital for explaining aspects of stellar evolution, chemical reactions, and the interaction of light with matter. It underlies the operation of lasers, transistors, magnets, and superconductors. I could cite reams of evidence backing up these assertions, but I will content myself by describing a single measurement. One electron will be stripped away from a helium atom that is exposed to ultraviolet light below a certain wavelength. This threshold wavelength can be determined experimentally to very high accuracy: it is

50.425 929 9 ± 0.000 000 4 nanometers. |

50.425 931 0 ± 0.000 002 0 nanometers. |

One can popularize the quantum theory [only] at the price of gross oversimplification and distortion, ending up with an uneasy compromise between what the facts dictate and what it is possible to convey in ordinary language. |

Indeed, can any fundamental theory be highly mathematical? Electrons know how to obey quantum mechanics, and electrons can neither add nor subtract, much less solve partial differential equations! If something as simple-minded as an electron can understand quantum mechanics, then certainly something as wonderfully complex as the reader of this book can understand it too.