Probability Waves and Quantum Mechanics
|We have seen that many kinds of vibration take the
form of waves of energy of one type or other. These waves have the ability to
transmit forces and power from one region of space to another. One can
conceive, however, of other regular phenomena that in themselves do not
transport energy so simply.
Suppose one views the earth from afar, say from some vantage point far out in space. Since the earth rotates on its axis the meridian line distinguishing regions between the earth's day and night appears to move relative to earth. If one observes the surface of the earth in the vicinity of this borderline one may notice electric lights being switched on or off in buildings, people dressing or undressing and some cleaning their teeth, birds beginning to sing or roost and so on. Such natural phenomena rotate around the globe over landmasses with this borderline. It would be impossible to predict how many people would be cleaning their teeth below this line at any instant. However if one counted such events over many periods of revolution of the median line circum-navigating the globe each day a definite average number would eventually emerge. Thus one has a wave of random events and the individual events that comprise this wave do not follow laws that determine precise outcomes but rather laws that determine probabilities that lead to definite predictions for averages that can be expected if the probabilities are fixed in time.
Examples of probabilistic oscillations include the rise and fall of populations of animal species as prey and predators wax and wane, the cycles of economic prosperity as resources and market confidences fluctuate, the rise and fall of infectious diseases as biological defences are activated in response to variations in genetic mutations. In these cases one may argue that it is "potential information" rather than energy that is being propagated in space and time. The laws of "chance" that govern these phenomena are just as precise as the laws that determine the evolution of Newtonian physics. It is simply that they refer to the probabilities of the outcomes of events and predict average properties of large populations rather than properties of the events themselves.
In a dramatic discovery at the turn of the century it was found that the Newtonian laws of physics were not applicable to the dynamics of individual atomic processes and that the extrapolation of planetary dynamics to the motion of charged particles in the atom was untenable. Such a picture inevitably led to the conclusion that atoms should radiate away all their energy as electromagnetic waves of increasing frequency as they collapse. Matter itself would no longer maintain rigidity and mechanical structures would be impossible. The ability of atoms with different properties to form molecules would fail and the emergence of chemical combinations and biological structures would be impossible. This dilemma was resolved by conceiving of the atom as a collection of localised waves whose different vibrational states in space corresponded to different states of matter. Stable atoms consisted of wave configurations with the fewest oscillations in space and the lowest frequency in time. These waves were concentrated in a very small volume of space (within a cube of side about 10-8 cm) although they extended throughout all space. New dynamical laws were discovered that predicted the structure of the patterns formed by these waves in space and time. Moreover these laws were analogous to the laws of chance discussed above. For each atom one could only predict the probability of the outcome of an experiment and more strikingly the result of any experiment depended on the state of the system itself (which may have been determined as the outcome of a previous experiment). If many experiments were performed the new rules correctly accounted for the spread in the observed results and in some cases these rules made it in principle impossible to improve the accuracy of the outcome of such experiments by technological improvements. This was completely at odds with the Newtonian paradigm that conceived of experiments determining outcomes to arbitrary accuracy.
As a result of this paradigm shift elementary charged matter is sometimes observed to move in space like tiny bullets but on other occasions it behaves more like a pattern of waves spread over regions of space and capable of producing the build up of interference patterns analogous to those produced by interfering light waves. This strange behaviour is very common for atomic scale phenomena and scientists have become accustomed to the fact that atomic laws of nature determine probabilities.
Furthermore in 1940 Paul Dirac showed that the electromagnetic field should be regarded as a collection of oscillators that also obey the probabilistic laws of quantum mechanics. The electromagnetic field as conceived of by Maxwell has to be regarded as the expectation of a huge number of quantum oscillators (called photons) acting in unison. The individual quanta of the field could act alone and behave like corpuscles of light as Einstein himself had suggested in order to explain the scattering of electrons by light.
Finally even the classical mechanical vibrations of bulk materials succumbed to the laws of quantum mechanics. The classical vibrational states are composed of vast numbers of different types of quanta generically called "phonons" and they emerge as expectations predicted by the quantum probability laws. Although the underlying quantum description of phonons can be circumvented for everyday engineering applications there are many situations, particularly at ultra low temperatures, where it becomes mandatory and the development of electronic devices would have been impossible before gaining an understanding of the wave nature of electrons in matter. Without this radical re-orientation of ideas it would prove impossible to understand in Newtonian or Maxwellian terms the precise way the temperature of matter varies with heat input or the variation of the colour of a hot poker varies with its temperature.
As long as one talks in terms of probability waves then one can form mental pictures of atoms and try and understand their interaction with the electromagnetic field. Rather like the stochastic toothbrush wave that circumnavigates the globe under the influence of the sun's motion relative to the spinning earth, the electron wave in the atom can be made to circulate around the direction of an externally applied magnetic field.
Similarly just as one can make a Chaldini pattern in a vibrating plate jump from one pattern to another by a mild perturbation from outside so one can cause the standing wave electron pattern in an atom to jump to a new configuration when excited by a photon from the electromagnetic field that always bathes the atom. The combined system of atom and field is a holistic entity. The atom can de-excite, restoring the original wave pattern and exciting the electromagnetic field in the process. This is the usual mechanism for the production of light from an atom. The many billions of photons that are radiated from all the atoms in the heated filament of an incandescent light bulb unify in this fashion to form the light we observe with our eyes. This symbiotic relation between the combined electromagnetic field and collection of atoms is at the heart of all phenomena involving light and matter. Although the expectations for collections of events involving large numbers of atoms, photons and phonons often obey the classical laws of Newton and Maxwell these latter laws arise as limits of the more fundamental probabilistic laws necessary to account for phenomena on atomic scales.