This is the first of three parts explaining, in non-technical terms, the brilliant "Theory of Elementary Waves" of Lewis Little. If you normally shy away from discussions on physics, please give this a chance - it was especially written for you. Although I love and revere mathematics, I firmly believe if you cannot explain a principle of physics in common language and terms, then you probably do not fully grasp the principle in the first place. Little's theory is extremely broad-ranging and if I can successfully communicate the highlights of his achievement I would consider that to satisfy my goal. ----------------------------------------------------------------- PART 1 ------ Quantum physics focuses primarily on the atomic and sub-atomic level, and the evolution of its mechanics spans almost a century. In 1900 Max Planck developed an empirical formula which described certain experimental observations about energy. When looking for a theoretical basis for his formula he advanced the idea that energy, which at that time was thought to be a continuous flow of waves, actually consisted of small individual pieces, called quanta. Several years later Albert Einstein conceived the idea that light was composed of both waves and particles, and later the name photon was given to that particle of light. About 1913 Niels Bohr, utilizing the idea of Planck's quanta, created a model of atomic structure. The next decade saw many physicists involved in quantum mechanics research, and in 1926 Erwin Schroedinger formulated what was to become the cornerstone of this new theory, his quantum wave equation. The decade following Schroedinger's discovery ushered in the world of nuclear physics which has continued quantum research through today. In the seven decades since the wave equation was created, the strangeness of this new field of physics has been transformed into the 'weirdness' of quantum mechanics. The standard theory is replete with effects without causes and the assertion that matter exists in an indeterminate state. The 'weird' behavior, according to the theory's interpreters, is worn as a banner of proof, as if this difference from known facts of reality should be taken as evidence to substantiate the theories. In 1996 the physicist Lewis Little published his paper "The Theory of Elementary Waves". For the first time since Planck's quanta in 1900, a rational basis for quantum mechanics has been established. The purpose of this article is to outline Little's revolutionary theory, in non-technical terms, and to identify the kinds of problems that his ideas have resolved. I will present some highlights of the theory. A full explanation requires a much more substantial analysis. The sagacious Caltech physicist, Richard Feynman, was fond of presenting essentialized models of experiments to his beginning physics students in order to illustrate basic physics principles. Feynman believed (rightfully so) that a particular kind of experiment, one called the double-slit experiment, embodied the essence of the fundamental issues in quantum mechanics. Following Feynman, we will look at a few examples of these models, keeping in mind that, in principle, the actual experiments can and have been performed. We will then explore some fundamentals of Little's theory and re-evaluate the experiments in light of what we have learned. A particle is usually understood to be an individual coherent object possessing a specific identity which can be localized in a given region of space. It is easier to grasp the actions of quantum particles by first looking at the behavior of a more familiar particle - a bullet. Figure 1 shows a gun (our 'source') that shoots a continuous stream of bullets. The source sprays bullets, in a fan-like manner towards a wall which has two slits just big enough to allow the bullets to pass through. Some distance behind the wall is a backdrop which stops the bullets as well as counts the number of bullets that impinge anywhere along its surface. Intuitively, if we think of what is the likelihood of where the bullets going through slit 1 will wind up, we can see that the maximum number of bullets will be along an angle from the source directly through slit 1 and, as the bullets bounce off the edge of the slit, the likelihood of finding bullets will decrease as we get further in each direction from the slit. The number of bullets detected having gone through slit 1 is shown as 1's. Similarly the number of bullets going through slit 2 is shown as 2's. The important point here is that the total number of bullets counted is just the sum of the bullets going through slit 1 had we closed off slit two plus the sum of those going through slit 2 had we closed off slit 1. F I G U R E 1 -------------- | 21111111| | 211111111| | 2111111111| | 21111111111| | 211111111111| -slit 1 2221111111111| 22221111111111| / - 222222111111111| / | 2222222111111111| / | 22222222211111111| source - - - | 222222222211111111| (bullet)\ | 22222222211111111| \ | 2222222221111111| \ -slit 2 222222222111111| 22222222221111| - 2222222222111| | 222222222221| | 22222222221| | 2222222221| | 222222221| | 22222221| WALL BACKDROP In contrast to particles, mechanical waves are usually understood to be a disturbance in some continuous medium; the disturbance propagates through the medium. Water waves and sound waves are two common examples of this simple wave phenomenon. We can perform the same double-slit experiment using a wave for a source instead of the bullets. Figure 2 shows a similar experimental setup where now the source makes circular water waves. The backdrop, instead of counting the bullets as before, now has the ability to measure the intensity of the wave impinging on its surface. If we cover slit 2 and measure the intensity of the waves coming through slit 1, and then cover slit 1 and measure the intensity of the waves coming through slit 2, we get a distribution that looks very much like the count distribution for the bullets in Figure 1. However, when we measure the intensity with both slits open, unlike the case with the bullets, the total intensity does not equal the sum of the intensities from slit 1 and slit 2 alone. In fact, we get a total intensity which sometimes is more than and sometimes less than the sum of the intensities from slits 1 and 2. This difference of wave behavior as compared to particle behavior is a consequence of the interaction of the waves coming through each of the slits. This is actually a very common wave occurrence which you can see if you watch the waves that result from the passing of two boats. If the waves meet when both are at their crest the resultant wave of their combination is larger than the sum of the originals. On the other hand, if one wave is at its crest and the other at its trough, the waves cancel each other and you can observe relatively smooth water. This interaction of two waves is called, in physics, interference. Constructive interference is the additive process when the two waves are 'in phase' with each other; destructive interference is the subtractive process when the waves are 'out of phase'. F I G U R E 2 -------------- | 211111| | 2111111| |) 211111| | ) 2111| ) | ) 21| ) - slit 1 211| ) ) ) ) 21111| ) ) - ) ) 2211111| ) ) | ) 222111111| ) ) ) | ) 22221111111| source-)- -)- -)| ) ) 222222111111| (water ) ) ) | )) 22222221111| wave) ) ) | )) 222222111| ) ) - ) ) 2222211| ) ) ) 22221| ) - ) 221| ) | slit 2 21| | ) 2221| | ) 222221| | 2222221| | 222221| WALL BACKDROP Now that we have seen how classical objects like particle-bullets and water waves respond to the double-slit experiment, the next step is to investigate the response of quantum mechanical particles. All we need do is to use as a source an electron (a charged particle) or a photon (a quantum of light). When we perform the double-slit experiment using photon particles, the result is _not_ like the bullets in Figure 1. In fact, the interference pattern seen in the wave source of Figure 2 is observed. The experiment seems to be telling us that the photon particle acts like a wave. How we don't know, just somehow. This observation has led quantum mechanic theorists to use the ideas of particle-wave, or wave-particle. The connotation of this is that a photon is a particle with wave-like properties, but it is completely unclear what this means in reality other than pointing to the results of the experiment. It is possible to detect that the photons are arriving as discrete packets, so it seems reasonable to assume a particle goes through either slit 1 or slit 2. But, if we block off slit 2 we just get the same distribution for slit 1 as we got for the counting of bullets. Likewise for closing off slit 1. Only by keeping both slits open do we get the interference pattern. Clearly there is some kind of wave interaction. If we try to 'peek' and see which slit each particle is going through (a particle is always detected as going through slit 1 or slit 2), the results of the experiment are again just like the counting of bullets. So the theorists conclude that we cannot definitely say that the particle goes through either slit 1 or slit 2, since the act of determining that fact changes the outcome. When speaking about the experiment, the standard theory treats probability as if it had physical characteristics. There is a certain probability of the particle going through either hole, and probability interference (somehow acting like real wave interference) is what causes the wave-like result. If you can detect a particular particle, that changes the probability pattern. So there is a ghost-like quality to the actions of these particles, where probability replaces a real existent. In fact, the standard theory is saying that the very act of observing forces a particular probability and it is then that something _becomes_ real. It is this ghost-like quality which leads us to the Schroedinger wave equation. The solution to the equation is known as the wave function; it gives the probability of locating a particle at a particular place and at a particular time. The Schroedinger equation, then, associates a wave with a particle. A characteristic of the equation is that if you have separate solutions, they can be combined together - a process known as superposition. Think of a particle at the source vanishing and being replaced by a host of ghost particles that follow different paths to the backdrop. These ghost-like particles somehow interfere with each other, which results in the pattern we have seen for wave-like behavior. These ghosts relate to the wave function which is a solution to Schroedinger's equation. When we observe the particle, all of the probability waves disappear except for the one associated with the real object. This is the act you may have heard described as the 'collapse of the wave function'. Nothing is real, until we look at it. This is pure Kantianism. Let me try to succinctly sum up what we have learned about the standard theory. Experiment shows that quantum particles seem to behave sometimes like particles and sometimes like waves. This 'weirdness' is enshrined in an anti- concept of particle-wave (or wave-particle) which refers to nothing in reality. Real objects are replaced by probability functions which somehow govern the overall wave-like behavior that results in the patterns seen in experiments. There is absolutely no attempt to establish a causal basis; in fact this lack is proudly offered as proof of the theory since 'why should we think quantum reality is anything like what happens on a larger scale'. In one sense this is true, in that quantum behavior is uniquely defined, but does that mean we must abandon all pretense of causality and maintain a ghost-like existence of matter in some indeterminate state? Yes, says the standard theory. No, says Lewis Little's Theory of Elementary Waves. In one sense the Theory of Elementary Waves (TEW) is very profound and requires a detailed technical analysis to see how it operates and how it applies to quantum phenomena. In another sense, though, it is quite simple, in that it identifies and integrates some very fundamental parts of reality. As a starting point to understand his approach, consider some of Little's thinking regarding the double-slit experiment. Although standard theory is hesitant to even pronounce judgment as to which slit a particle goes through, Little realizes that each particle must go through a single slit and that it must follow a specific trajectory while doing so. At the outset he rejects the effect without cause of standard theory. Figure 3 shows the double-slit setup with a set of supposed trajectories for each particle. Little now argues that if we moved the target to another position, B, then as the particles follow the same trajectories they would intersect the detector at different points than before and, therefore, would not show the standard pattern. However, experiment shows that in fact the pattern occurs _wherever_ the target is placed. This experimental fact cannot be explained by the standard theory if we are to simultaneously maintain cause and effect. It can be explained, however, if you consider the experiment as evidence that there is motion _from_ the target _to_ the particle source. This is exactly opposite to the way of thinking in the standard theory. F I G U R E 3 -------------- (B) | | | | | x| | x x| | | x x | | | x x | | slit 1 -x x | | x x y x | | x - x y x | | x | x x y | | x | x x y | | source x | x | y| (photon x | x x y | | particle) x | x x y | | x - x y x | | x x y x | | slit 2 -x x | | l x x | | | x x | | | x x| | | | x| | | | WALL target What is it, then, that moves from the detector to the source. Little's theory states that it is the quantum wave that moves in this reverse direction. But, as we saw before, a wave is thought of as a disturbance of some medium and the wave propagates through the medium. What is the medium in this quantum case, and what is the cause of the disturbance? It is in answer to this question that Little breaks with tradition and establishes a base on which to explain the 'weirdness' of quantum mechanics. It is not a wave in the usual sense at all - it is an elementary wave - a _fundamental constituent of reality_. In effect, it _is_ the medium. I cannot stress strongly enough the importance of this idea. Little's theory identifies the most basic 'stuff' of existence. This is not just the mathematical representation of a phenomenon, this is a _real_ wave. The elementary wave cannot be understood by appealing to anything more basic to explain it - there is nothing more basic. The elementary waves have a structure and the effects of the changes in that structure are all we can know about them. So the ghost-like packets of waves in the standard theory have been replaced by a real existent, and the behavior of that wave is contrary to standard interpretation - the wave moves in reverse, from the target, or more generally from the detector, towards the source. In a way, Little's elementary wave is less like a traditional wave and closer to the idea of the elusive ether, in that it is like a flow, or a flux of material, while realizing that it makes no sense to talk about what kind of material it is - it just is. Twenty-five hundred years ago Parmenides said (and more recently, as Leonard Peikoff is fond of saying) the universe is a "plenum". That is, there are no gaps, no voids, no place where there is nothing. That is what Little's theory has identified, the elementary waves are what fill the universe - they are omnipresent. According to Little's theory the waves exist for every possible quantum state, for every variable parameter that is possible. Before we can revisit the double-slit experiment in the light of elementary waves, we first need to understand what a particle is in this new theory. In Little's view the elementary waves are primary in the sense that they carry dynamic quantities such as mass, momentum, energy, etc. It is the wave that triggers the emission of the particle at the source; the state of that particle, the dynamics of its motion, is determined by the particular wave that stimulates, or induces, the emission. The particle then follows the path of the wave; thus the wave moves from the detector to the source and the particle travels from the source to the detector. We should keep in mind that these are _elementary_ waves, not waves in some medium. The wave itself is moving from the detector to the source; no dynamic information propagates through the wave; the wave carries the information as it moves. That is why, as mentioned above, the elementary waves may be best understood as being a flux or a flow. As a general statement then, a particle will follow the straight line motion opposite to its elementary wave, and will continue such motion unless there is some interaction with another particle which can change its direction. As in the case with Little's elementary waves, Little's particles are not ghost-like, they are real. There is no 'collapse of the wave function' which selects from an array of probability waves a packet of waves which describe a 'real' photon. In the TEW, _all_ of the elementary waves and _all_ of the particles are real existents. Now we can look back at the quantum double-slit experiment and try to make sense of the experiment using TEW as a guide. We understand that there are elementary waves, which correspond to all possible quantum states, that exist as real objects filling the space around us. Further, think of coherence as a certain likeness of waves which can then combine by one rule, and incoherence a certain dissimilarity in waves which can then combine by another rule. When the target, or detector, is placed in position, the particles of which the detector consists impose an 'organization' or coherence upon the existing waves. From every point on the detector flows a complete set of waves that uniquely reflect the state of the particle which imposed the organization on the wave and they are all coherent with each other; but they are incoherent with the waves flowing from other points. So for any given point on the detector, the reverse waves travel back towards the wall with the two slits, through the slits and continue onwards to the particle source. These are real waves which will interfere with each other; so, in some cases there will be constructive interference and in others destructive interference. The resulting intensity of the wave, after interference, determines, at the particle source, the likelihood of inducing the emission of a particle. The particle then follows the path of the wave back to the detector. Therefore, the pattern we see at the detector _is_ a consequence of the interference of waves and the transmission of particles; but, these are real waves and real particles and the pattern occurs due to real processes. It is the intensity of the elementary wave as seen at the source that determines the number of particles that are induced. The pattern at the detector, then, is due to the particles that follow the path of each wave back from the source. In addition, all of the usual quantum mechanical mathematics remains essentially the same - this new theory, however, explains _why_ the mathematics works. To see the dramatic contrast between the standard theory and the TEW, we can summarize as follows: The standard theory creates a wave-particle (or particle-wave) out of thin air. It is a nebulous concept without referents in reality. In opposition to the standard theory, the TEW identifies the existence of elementary waves, which are real, primary, fundamental constituents of reality, and it logically asserts, also in opposition to the standard theory, the existence of real, fundamental particles. These real, elementary waves are what interfere with each other, accounting for the observed interference pattern on the detector. While standard theory is unable to state that particles go through either one of the slits, the TEW unequivocally does so state and gives the mechanism by which it is accomplished - the particle following the path of the reverse wave. While standard theory has ghost-like objects that disappear with 'wave collapse' in order to give birth, so to speak, to a 'real' object, the TEW always deals with real objects that do not 'disappear' when the experiment is done. So, unlike the standard theory, the TEW establishes a causal basis for the actions of real entities, and completely contravenes the theory of the existence of matter in some indeterminate state. This is why I stated above: For the first time, the TEW has established, a rational basis for quantum mechanics. In Part 2 we will look at the famous 'uncertainty principle' in light of what we have learned so far about the TEW, as well as delve a little deeper into the mechanics of the TEW by discussing additional experiments. sjs@compbio.caltech.edu Copyright (C) 1998 Stephen Speicher

California Institute of Technology, Pasadena, CA 91125.