Inverseness, Complementarity, and the Wave/Particle Duality
Suppose that we are in an electronics laboratory and have before us two instruments, an oscilloscope and spectrum analyzer, which are connected to a device that makes electric sparks (like the spark plugs in your car). These two instruments give us two views of what a spark looks like electrically. The views are quite different and look something like the following:
Next we disconnect the spark generator and now connect both instruments to a source of pure sine wave voltage, such as that coming from an ordinary electrical outlet in the lab. We would see something like this:
Note that these sets of two illustrations each show complementary views of the same phenomena. Note that there are two concepts of location: time and frequency. As the phenomena in one view become more precisely localized, the same phenomena, in the other view, become more spread-out. The amount of preciseness in one view is "inverse" to the preciseness in the other. This is like the momentum-position relationship in quantum mechanics:
Dp Dx > h/4p
The more precisely we know p, the less precisely we know x. And the more precisely we know x, the less precisely we know p. The two are inversely related mathematically.
"But I am not an electronics technician, and these little pictures don't mean anything to me." Okay. Try this. Get a really cheap AM broadcast band radio and place it near something that can create electric sparks, like an ordinary light switch. First, tune the radio to a blank spot in the band (and be sure you are using the AM, not FM mode if it is a dual mode radio). Then flip the light switch on and off. You will hear a pop or a click come from the radio. This shows that the act of interrupting ordinary 60 Hertz house current (second illustration) creates additional frequency components way up into the Megahertz range, which can be received by the AM radio (first illustration). Precisely locating the electrical event in the time view, causes the "location" in the frequency view to spread out.
So when you remove something from a pure sine wave you actually create additional frequency components! This may seem counter-intuitive but that is only due to our limited view of our world. We see our ordinary world mostly in terms of particles, not waves and particles. When we throw a basket ball through a hoop, it does not spread out (diffract) into a field of "ball waves". We only see the basket ball as a "particle". Our comprehension of the quantum world, however, freely utilizes both views (wave and particle) and we must educate our intuition if we are to feel comfortable with the resulting implications.
Much has been written on this subject in the literature of quantum mechanics. It is known there as "Bohr's principle of complementarity":
"In quantum mechanics, complementarity refers to the impossibility of specifying simultaneously the wave and corpuscular attributes of a particle. (Etymologically, the wave and corpuscular attributes are both needed to give a 'complete' picture of a particle.) The wave and corpuscular properties of 'particles' are complementary in the sense that if we specify the precise value of a wavelike property we cannot simultaneously specify a corpuscular property." ( Quanta: a handbook of concepts, P. W. Atkins, 2nd ed. 1991, p. 61)
The concept can be illustrated by examining the properties of light:.
"Furthermore, in the sense of the uncertainty principle, the number of photons in a beam is complementary to the phase of the wave. That is, if the phase of a light wave is known exactly, nothing can be said about the number of photons present. This restriction is an aspect of the dual character of electromagnetic radiation: the number of photons is an intrinsically particle property and the phase of the radiation is an intrinsically wavelike property; speaking precisely in the language of one precludes speaking precisely in the language of the other." (Quanta: a handbook of concepts, P. W. Atkins, 2nd ed. 1991, p. 281)
The idea that one object, when subjected to different viewing methods, can give different appearances, is not in itself a cause for concern. Look at the picture below:
"Ribbons" by Gary W. Priester
On the surface, it appears to be something we would find in an art gallery or a wallpaper shop. But this image encodes some additional information: depth. It is called a "stereogram" and we have to stare at it (or through it) for a while before we see the "other" image. Although this is a bit out of the ordinary, there is nothing inherently baffling or self-contradictory about it.
According to the complementarity concept, a quantum mechanical entity may be seen as a wave or as a particle. This creates a problem for physicists and philosophers: if something is really particle, it cannot be a wave; conversely, if it is really a wave, it cannot be a particle. Although the views may be "complementary", they are fundamentally incompatible. The question is not "How does it look under a particular viewing method?" but instead, "What is it? What is it really?" Is there a way to get a more complete, more fundamental view of this thing? Is there a more natural view that is free of basic incompatibilities? We can get a clue to answering these questions by reviewing how the wave/particle concept developed in the first place:
"Given the historical matrix from which quantum mechanics emerged, it is not surprising that a great deal of early quantum theory was expressed in terms of wave and particle concepts. For every physicist at the turn of the century, these were ready-to-hand pieces of theoretical equipment. For sound pragmatic reasons physicists were loath to discard them. In 1900, however, with Planck's attribution of particle properties to electromagnetic waves, they began to be used in unorthodox ways; Planck's move was mirrored twenty-five years later by de Broglie's attribution of wave properties to electrons.
These episodes in the prehistory of quantum theory do not teach us to abjure a unified understanding of quantum phenomena in favor of a doctrine of epistemological complementarity, according to which we are compelled to move to and fro between two incompatible ways of picturing the world. They teach us merely that neither of these ways is fully adequate. We can draw a different conclusion than did Bohr, even while agreeing with him that "The two views on the nature of light are rather to be considered as different attempts at an interpretation of experimental evidence, in which the limitations of the classical concepts are expressed in complementary ways". (The Structure and Interpretation of Quantum Mechanics, R.I.G. Hughes, 1989, p. 231)
Here is a similar thought from a textbook:
"Actually the electron is neither a particle nor a wave. It is a fundamental entity of matter, and it cannot be described by saying it is something else more familiar. . . . Likewise, the photon is neither a particle nor a wave. It also is a fundamental entity, characterized by certain properties." ( Introduction to Electromagnetic Fields and Waves, Charles, A Holt, 1963, p. 25)
Maybe physicists have simply been asking the wrong question. Instead of asking "Is it a wave or is it a particle?" maybe they should be asking something like: "How does an inherently rotational entity appear to an observer in a linear, extensional reference system?" It turns out that it would be seen either as a particle or as a wave, depending on the experimental set up. You can read more about this in my article The Origin of Intrinsic Spin.
Also, you might want to read: Commutation and Angular Momentum
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