The Extension Of Knowledge

      Kepler had no idea why planets orbited in an ellipse; but by accurately defining the pattern, he allowed people to predict the orbits of other heavenly bodies.

      It wasn't until another one hundred years after Kepler's discovery that Sir Isaac Newton formulated his theory of gravity. It was Newton, Einstein, and others who offered explanations for why orbits are elliptical. But in many respects, the reasons are not as important as finding the pattern and thus having the ability to predict.

      During the 17th, 18th, and 19th centuries, great efforts were made to discover other patterns, develop theories and rules, and add to our predictive abilities. But the more that was learned about our universe, the more complex it became. And eventually complexity brought researchers and philosophers to the conclusion that completely deterministic laws, such as the laws of motion proposed by Sir Isaac Newton were insufficient to explain the workings of the universe. Observed uncertainty and randomness conflicted with the predictions of the classical theories. The appearance of randomness called into question our ability to ever understand.

      The quantum theory started with the German physicist Max Planck in 1900, and was further extended by Albert Einstein in 1905 and many others thereafter. The quantum theory, which initially dealt with waves, came to be combined with the atomic theory which was more focused on particles. Ernest Rutherford, James Clerk Maxwell, and Niels Henrik David Bohr worked to develop theories that explained the structure of the atom. But the success of the atomic theory, and of the Bohr theory in particular, also highlighted its deficiencies. And this is where the worth of quantum theory started to be appreciated.

      One of the things that resulted from all this research was uncertainty. When trying to define the orbit of an electron in an atom, it was found that these particles do not seem to have a single path in the space-time continuum. Instead, they seem to travel by every possible path, with a specific position only able to be postulated by probability. The American scientist Richard Feynman developed a mathematical description of this motion which depends on amplitude and cycle. Thus, what are thought of as subatomic particles, appear to be acting more like waves. Experiments confirm this observation. If a single electron is fired at an obstruction with two openings in it, we would expect that the electron would only pass through one of the openings. In fact, tests show that the single electron passes through both openings at the same time. How then do we identify the position of an electron?

      In 1925, German theoretical physicist Werner Karl Heisenberg developed a new theory of quantum mechanics called matrix mechanics. In 1927, he formulated his uncertainty principle. This principle stated in essence that the more accurately one tries to measure the position of a particle, the more one interferes with its velocity, resulting in an inability to simultaneously determine the position and momentum of a particle. The uncertainty of the position of the particle, times the uncertainty of its velocity, times its mass can never be smaller than Plank's constant. We are now faced with probability calculations replacing the exact mathematics of classical mechanics.

      If uncertainty is a fundamental condition of our universe, then this fact would seem to foil attempts to identify patterns, construct rules, and make accurate predictions. Complexity, uncertainty, chaos -- these are the issues of the day. How can we hope to understand? It is from this platform that mankind struggles to extend knowledge as we progress into the third millennium.