Comments and Questions on the Wave/ Particle Duality:

by Robert DePaolo

Abstract

This article discusses the essential nature of matter; specifically differing ideas on whether it consists most fundamentally of waves, particles or wave driven particles ( as in pilot wave theory) in an interdependent relationship. The question is raised as to whether this can be addressed by looking at energy signatures to see if, and to what extent wave influence exists for objects with differential mass.

A Review of Theory...

Questions about the true nature of matter first arose from a paradox inherent in quantum physics, and more specifically a component called Heisenberg's Uncertainty Principle. Experiments in this area have given rise to rather complicated interpretations of the results. The typical method is the double slit experiment. In this method photons are fired through slits and collected on a gathering board to determine their path. Photons of course are the sources of light. Over time some scientists, among them Isaac Newton described light as a wave, while others such as Thomas Young and later, James Maxwell believed it consisted of discrete particles that traveled in a straight line path. it wasn't until the 20th century that Albert Einstein developed an inclusive model of light that was made up of particles but also had wave-like qualities.The confounding yet consistent results of that experiment was that light can behave as both a wave and a particle.

More specifically, when passed through a single slit (hole) in the experimental apparatus the photons behaved as though a particle - onstensibly because a single slit left them with only one possible exit point. However when photons were fired through multiple slits a funny thing happened. Rather than photons passing selectively through one slit or another, as one would expect with any object according to the laws of classical physics, there was a smearing effect. It was as though the photons were somehow ambivalent about which hole they would pass through and kept "changing their mind" with pathway do-overs. In effect, there seemed to be no directionality or sequence governing the photons' behavior. The result seemed to turn nature upside down

This result was confirmed by the fact that the gathering board displayed an interference pattern, which is typical of waves but not particles. It was confusing. In the one- slit instance, the photon acted like a bean bag tossed into one of the holes in the children's game, whereas In the multiple slit situation it acted as if a rock was tossed into water with an ensuing ripple effect.

All of this led to what came to be known as the wave-particle duality and it prompted the critical question as to the essential nature of matter. Was is fundamentally a wave or a particle?

If it was just a question of a photon's behavior, resolution might have come easily. Because photons have no mass and travel at light speed they are not bound by temporal or spatial restraints. In order for any object to be in a specific location and travel in a particular path it must have mass. That is because the word 'mass' actually means an object can encounter resistance and be influenced by forces and fields as it moves about. In that sense its movement must be in sync with, dependent on and guided by other elements, and must therefore cooperate with the ordinary laws of physics. In addition, since photons travel at light speed they do not adhere to temporality. Thus no matter how long it seems to us they are moving about time does not elapse in the usual sense for the photon. A photon is hopelessly locked in the present - it has no past or future because both concepts imply the passage of time. Moreover, photons do not decay and thus are immune to the process of entropy, which is a function of time lapse.

Since locality (the capacity to move from point A to point B) requires a temporal sequence, a photon can be anywhere it damn well pleases. As renowned physicist Richard Feynman suggested, it could have traveled to Canada, then the Sahara before exiting through the second slit in the experiment . He referred to this unlimited temporo-spatial quality as the sum of all histories theory.

Yet it turns out the wave/particle conundrum was not limited to photons The phenomenon was also observed with electrons - which do have mass and are bound by temporal restraints. Because of that theoretical models had to be revised. Some, such as Louis de Broglie and David Bohm came to believe all matter had wave properties like the photon, but that as the mass of an object increased its wave properties were reduced proportionately. That is why, many suggested the bean bag tossed at a board with several holes would not be able to travel to the Sahara and the North Pole before arriving at the hole and enabling one of the children to be declared a winner. It had too much mass. So, the wave-particle duality coaxed a multi-dimensional view of the material world.

One of the more intriguing ideas from Bohm and de Broglie came known as pilot wave theory. It proposed that photons and matter in general consists of particles but also ride on the crests of waves. The explanation of why massive objects do not exhibit discernible wave properties is because as the mass of an object increases, the collective wave features become so voluminous as to cancel each other. In other words, hyper-smearing of wave activity acts like the interaction of high and low crests of a wave which combine to result in flat water.

Conversely, as the mass of an object decreases the wave functions of an object are increasingly freed up to manifest themselves and influence motion and other physical and ergonomic factors. British scientist Roger Penrose interpreted this phenomenon by suggesting the waves collapse due to the gravitational pull that increases alongside the increasing mass of any given object. That is, waves are pulled into the object like some sort of mini-black hole.

Still, the issue remains unresolved. Indeed none of the theories on the duality have risen above valid criticism. That leaves open the question of how resolution can be found.

Perhaps one way is to discuss the wave function in terms of energy signatures. All waves, whether emanating from a photon or from a pebble tossed into water are not in themselves massive or discrete like particles. For example, water waves are not completely guided or encompassed in specific amount of electrons or atoms. Something beyond the material is involved in wave activity. While the energy within a wave includes the vibration of particles the total amount of the wave's energy does not correlate perfectly with the collective mass of the particles. Rather it is the movement of the wave itself that conveys most of its energy. The faster the wave frequency the greater its energy regardless of how many particles are encompassed in the wave-particle package.

However, while the energy within the wave supersedes the amount of energy arising from the particles' mass, interactions between the two within the wave itself should be measurable regardless of the differential contribution of mass and wave motion to the energy production.

That raises several questions. One of which has to do with Einstein's notion of matter/energy equivalence. According to that principle all the energy in a wave should be represented in material aspects of the wave. It clearly isn't. The second problem is that according to Newton's third law of motion, every action should lead to an equal and opposite reaction. This pertains to objects interacting with other objects and to what are called thrust reactions. This is exemplified by the counter force from the ground in launching a space shuttle. The third law involves reciprocity. A fuel-driven thrust backward pushes a vehicle forward with the same amount of force. Then as the vehicle ascends, a backward force emits a tail end reaction in response to its forward thrust. This is especially true when there is a change in momentum, i.e. when the object/vehicle changes speeds along the way.

Any object, whether a shuttle craft or a bullet fired from a rifle moving through air requires the exertion of a force. As soon as that occurs the action/reaction process kicks in. That's where the theory of the wave/particle duality comes into the picture.

If de Broglie and Bohm were right and all things consists of both waves and particles then the counterforce reaction should include the energy resulting from both the third law principle and from the motion generated by the wave component.

At face value that would make it hard to tell whether an energy signature at the tail end or surround (current theories do not specify where the wave aspect of matter would be; whether it is a "pull", a "push" or a "surround") of a object's movement was reflective of wave activity as per the pilot wave model, or Newtonian reactive energy in response to the initial thrust. If there could be some way to parse those two factors it might be possible to not only confirm the pilot wave concept but to measure it ergonomically in proportion to an object's mass.

One possible way to do this might be through mathematics. If the mass of an object is known, one should be able to predict its tail end energy emission resulting from its momentum. That of course is another way of stating the energy conservation principle. For example if we can measure the mass of a bullet and the speed of its forward thrust after firing, then we might be able to determine what the counter force should be. Any excess energy emissions beyond that could be assumed to result from a hidden factor; for example the wave/energy function. There is a potential paradox involved, however. Since the mass of an object increases as it speeds up that would suggest (even if in minute quantities) that trying to measure the wave function after a thrust might involve a kind of apportioning process.

Nonetheless, if such observations could be made, a couple of interesting outcomes might ensue. One would be that the predicted energy emitted from the reaction phase would be greater than the mass and momentum of the object. That extra energy could indicate the presence of a secondary aspect of the energy in the object in the form of wave activity. A second possibility would be that the energy reaction would be exactly as expected from the object's mass and momentum, which would contradict pilot/wave theory. A third, possibly intriguing result would be that the energy reaction described by Newton is actually the result of the wave component- that the third law of motion proves the existence of pilot wave theory. (While Newton described the "what" of his third law he did not describe the "why" - could it be he was actually describing the wave component in his third law of motion?

If true that would bring the third law of motion in line with the pilot wave theory and perhaps offer an additional insight on the nature of matter.

A similar idea - much more mathematically and theoretically precise - was offered by Roger Penrose and it does seem to offer food for thought with respect to the relation between waves and particles, matter and energy and the interaction between classical and quantum physics.

NOTES

Light as a particle...

Isaac Newton believed light consisted of particles because it appeared to him to travel in a straight line. He was possibly unaware that light could bend due to gravitational attractions.

Light as a wave...

One of the first to conceive of light as a wave was British scientist Thomas Young who proved in experiments that light did bend and refract in response to its interactions with obstacles. Young also created the experimental design for the double slit experiment

James Maxwell also supported the notion of light as a wave but his devotee, Albert Einstein created a partial reversion back to particle theory, albeit with the idea that waves and particles were woven together functionally; the particles (photons) carrying the energy for light itself.

de Broglie on pilot wave theory...

French scientist Louis de Broglie sought a resolution to the wave particle duality by proposing matter consisted of both, in a way analogous to Einstein's concept. In his model particles ride on the crest of waves. This idea was championed (with some revisions) by American theoretical physicist David Bohm.

When questions arose about the internal consistency of pilot wave theory...

British scientist Roger Penrose developed a mathematical and theoretical model of matter as strictly a wave function. He contended that at some point waves would become so voluminous and energized as to collapse into a state resembling a particle topography. (This is somewhat reminiscent of superstring theory). Part of Penrose's objection to pilot wave theory was that it assumed waves affected the movement of particles without describing the particles' reciprocal energy impact on the wave - a requirement of the physics of energy conservation.

In trying to explain the double slit experimental results...

American scientist Richard Feynman proposed that the pathways of photons were scattered and unpredictable other than in terms of probabilities because being devoid of time and position constraints, photons (which have no mass, thus no not typically encounter resistance to regulate their path) can be anywhere at any time. Thus what is really measured as per their position and momentum is the sum (average?) of all the places and times they've traveled in a space-time instance. In other words, the time duration observed by the experimenter is not the same as the time duration for the photon. The latter has neither a past nor a future because light speed is a universal gauge and cannot be exceeded. Ironically, it creates time by being timeless - a process analogous to the cosmic force Aristotle referred to as 'The Unmoved Mover.'

On Newton's third law of motion and its relation to the particle-wave duality...

it holds that energy is constant and that movement is characterized by opposing forces of energy...a push forward creates a counter reaction backward and vice versa. That is the basis for asking if a less massive moving object might have a greater tail end proportionate energy signature than a more massive object. In other words, if wave qualities are more pervasive in less massive objects due to reduced wave-collapse, should measurement of their wave-influenced after-effect during movement point to a greater degree of energy refuse than for more massive objects?