Essay: Wave/Particle Theory Revisited: In Support of de Broglie's Model

Reference & EducationCollege & University

  • Author Robert Depaolo
  • Published August 8, 2023
  • Word count 2,881


Wave/Particle Theory Revisited:

In Support of de Broglie's Model


This article offers support for Louis de Broglie's resolution to the wave/particle paradox. The argument is submitted that as de Broglie suggested, all objects in nature consist of both discrete (solid) and wave-like properties and that the confusion resulting from the double slit experiment can be resolved by simply stating that the manifestation of a wave property is a function of the mass of the entity being measured, more specifically, that as mass increases the wave property declines and is absorbed by gravity.

A fair amount of confusion was generated by Heisenberg's Principle of Uncertainty, which debunked the idea that the physical universe could be subject to precise levels of prediction. A series of explanations followed each attempt to resolve the question of why matter at the subatomic level could act like both a wave and a particle in varying circumstances. Max Planck offered resolution in his research on quantum mechanics. Yet some questions about the nature of matter remain unresolved.

In a sense it all began with research and speculation regarding the atom, long considered the fundamental unit of matter. For many years Ernest Rutherford's model of the atom was accepted, largely because it seemed to provide a perfect fit with the natural world. He believed the way planets orbited the sun (through the gravitational force) was applicable to how electrons orbited the nucleus of an atom.

Danish scientist Neils Bohr saw a problem with this model. He understood that the structure and function of the atom had to be stable, because if not, all objects in nature would eventually either fly apart or decompose. He understood that as electrons rotate around the nucleus of an atom there is an emission of radiation and subsequent loss of energy with each rotation. He realized energy had to be exerted and expended for the rotation to occur. That meant with each rotation the energy holding and supporting the orbit would decline and eventually result in the collapse of the atom – as well as the rest of the bodies that exist in the universe.

Bohr provided a model through which the activity in the atom could ensue without upsetting the cosmic apple cart. It was based on the idea that the orbit of electrons was not in a constant state but instead featured a "shifting of lanes." With each influx of energy, the electron would change its orbit and remain in that orbit until another energy influx occurred. With increased energy input the orbit would shift to a higher level, while with low energy input it would shift down to a lower level orbit. In that way constancy was established through an entropy preventing correlation between the orbit and the release of radiation and energy.

A simple way to understand this is with the example of driving a vehicle on a highway. Assume the “miles per gallon” was at 50. If the car shifted to the left lane and moved at an increasing speed to pass other vehicles more gas would be consumed. Over time, if the car remained in the left lane and maintained a high rate of speed, the 50 miles to a gallon standard would be compromised. On the other hand, if the car shifted back to the left lane intermittently there would be a net conservation of gas. By slowing down and speeding up alternately while shifting lanes the 50 miles to a gallon standard would remain intact.

The double slit experiment has invited speculation and driven research in the field of theoretical physics ever since Thomas Young first introduced scientists to the mystery of matter back in 1801. The phenomenon is well known, as demonstrated not only by their experiment but by Heisenberg's subsequent formulation of the Principle of Uncertainty. The process is by now familiar to both scientists and amateur "lay-theoreticians" like this writer. In essence, when running photons (and electrons in some instances) through a single slit that are then collected on a screen, particles appear to have a specific path and destination, but when two slits are included, rather than particle A predictably ending up "here" and particle B ending up "there" the path and destination become enmeshed. The previous and anticipated direct pathways turn into interference patterns with a smudging effect. As a result, the endpoint of the particle can only be determined probabilistically.

While there are various ways to describe this phenomenon perhaps the most lay-friendly way to explain this is to say that for some reason, with a choice involving more than one possible pathway to a destination a particle turns into a wave.

If that were the only aspect to this, interpretation might be clear. A less than sophisticated person, not versed in the math or theoretical concepts available to trained physicists might simply assume the particles bumped into each other. broke up as they crossed paths and thus ended up looking like "mushy" waves.

As it turns out that description would be wrong because when being observed the particles seem to revert to their concrete "particle-ness" - as if a collection of class clowns behaving badly when the teacher turns her back only to return to innocence when she faces the class.

Explanations have been offered to explain why there is a double standard involved in particle physics. Perhaps the most widely accepted is that all the universe is entangled; meaning that the observer/scientist is neither an observer nor a scientist (in the sense of being objectively detached from the event). Instead, his observation is really an interaction - his or her eyes submitting photons themselves which somehow add mass or discrete essence to the particle by colliding with the particle (almost as though humans are God-like in being able to create mass from wave-like energy just through visual focus.

Thus, it appears the universe is an interactive system – in other words, information-based. That is where theory comes into play and specifically why de Broglie's idea of wave/particle combinations seems to make sense.

De Broglie suggested all entities in nature have both wave and particle properties, including Elephants, humans, and bears. The reason those creatures don't exhibit visibly undulating interference patterns as they move about is because as the mass of an object increases the wave property of the entity is consumed by gravity. The idea was that since gravity is a function of mass, if an elephant could be shrunk down to the size of a photon one would be able to see wave patterns in its movement as it meandered through the Indian forest.

De Broglie felt that might explain the transformation from wave to particle and the transformation from probabilistic path to predictable, measurable path.

Other theories have been posited. Among the most notable was Richard Feynman's notion of a Sum of Histories. He suggested the reason particles' destination and momentum could not both be measured in one observation is because the particle takes all possible paths to the destination before finally ending up in one or another location. That would certainly account for the probabilistic nature of the pathways.

On the other hand, what is meant by all possible pathways? Does it mean one can determine how many destinations there are in the universe by calculating the probability of a particle ending up in a specific location at a specific time? For example, if there is a likelihood of a photon ending up in location A 50 % of the time how does that correspond to the histories of the pathways the photon traveled prior to ending up in the aperture?

Furthermore, what exactly does 'histories' mean, and does the probability of a particle ending up in a specific location at a specific time correspond directly with the number of paths it took along the way? If so, what paths? Are they infinite or finite? If the former, the particle would never arrive at any destination. If the latter, its endpoint should (as Einstein might have opined) be fixed rather than probabilistic. Still, Feynman’s theory has gained wide acceptance.

If one uses the photon as an example this might make sense. The photon travels at light speed so despite the belief that it travels at 186,00 miles per second and is therefore subject to time passage, time does not pass for the photon. Photons do not decay. They do not adhere to the law of entropy because a particle that doesn’t experience time lapse cannot run down. Consequently, a photon can theoretically pop in and out of the blue without being tethered to the constraints of "when” or "where." In that sense, Sum of Histories theory seems plausible. However, electrons do have mass and do run down. Time does lapse for them, yet they behave like photons in the double slit experiment. Therefore, one could argue that they could not run through a sum of histories series of pathways without experiencing delays and time passages.

De Broglie’s theory was rejected by most because it did not ostensibly jive with “the math.” Just why math seems to contradict de Broglie's theory is hard to figure. Sometimes it seems physicists work backwards, in that a priori math is often used to prove a theory (for example superstring theory) when the theory is observationally unprovable. It seems math is supposed to be used to prove a theory rather than being proof itself. It should not come first, but second, to be used as a means of confirming or refuting a theory with teeth. The attractive aspect of de Broglie's theory is that it does have teeth, and this is easily determined by simply looking at the fundamental nature of matter.

In a sense movement must serve as a backdrop to constancy because it is needed for the energy to both do and not do actions. Thus, in the strictest sense – from the constant activity in the nucleus of an atom to the behavior of a couch-potato, motion – as Aristotle suggested, is a constant feature of the natural world. Indeed, while most of his ideas have not passed the test of time that one might be timeless. The reason why can be found in the law of inertia, which holds that motion is endless in a vacuum and can only cease when a barrier is present to block its path. Technically speaking that means the static quality of apparently stationary objects is somewhat artificial and, in the final analysis, a dependent variable in the workings of nature.

If one applies that principle to stationary objects (those without observable de Broglian wave properties) it seems the lack of wave activity in massive objects is itself illusory and only eclipsed by an outside barrier. It suggests what one sees in a wave-like particle is the most natural manifestation of matter, and that the absence of wave properties in massive objects is the outlier.

Regarding de Broglie’s theory, a wave function is a form of movement. All the solid structures of every entity in the universe are moving at the most basic internal level. The question becomes why, if atoms and particles in the body are jostling around frenetically, do things seem to be inert?

The answer might be that as the number of atomic clusters increases an increase in the cancelling effect occurs. Waves become trapped by interactive mass. Atoms in proximity to one another have no space to exercise external movement. The congestion of atoms of course equates with mass. Thus, the greater the number of atoms within a space confined by membranes the less external movement will occur even as the movement and energy within the atom remains constant.

Not only could that imply something about the nature of gravity - which de Broglie argued is what separates entities with observable vs. implicit wave activity. It also might offer a plausible explanation of the wave particle duality, in which case de Broglie’s theory would make sense- even if the math extrapolated from it was not “elegant” enough to satisfy theoreticians who espouse other, arguably metaphysical explanations of the phenomenon.

There are implications deriving from de Broglie’s theory. One is that the original/primal state of the universe is not static, i.e. consisting of mass, but kinetic. In other words, motion is the essential state of the universe. That might explain why, despite gravity, the universe continues to expand at an increasing rate of acceleration. It would also obviate the need for a big bang to get things rolling. Rather than a universe of nearly infinite mass reaching some sort of boiling point and exploding, it could be that the primal universal entity was just that - universal and constant – essentially adhering to the law of inertia. Only when mass arose through an increase in information content in the universe could there be a juxtaposition of motion and mass that led to clustering and separation of one element of matter from others, thereby creating the potential for inter-material collisions and ultimately universal expansion.

The wave properties of atoms are relevant points of discussion – especially as pertains to Schrodinger’s notion of stationary and continuous waves within the nucleus of an atom. For example, when waves oppose each other there is a cancellation effect. Interference of one with the other leads to apparent stationary status, whereas waves traveling in the same direction will facilitate movement and continuity of motion. However, in either case the motion is constant. Otherwise, even with interference patterns motion and energy are required to produce cancellation. In other words, work is necessary to produce any sort of effect. The question is whether interference and apparent stationary status corresponds to mass and clustering.

Another possible facet of a primal-motion model with explanatory potential is that while mass clumps together based on differentials from one object to another motion has a wave-like flow and dispersion. Just as light waves do not clump together but are in a sense united by an overriding frequency and amplitude, so could this explain the relatively even dispersion of matter across the universe without need of Inflation Theory.

One argument against this idea is that an atom has wave activity because components within it (neutrons. protons, and electrons are active features. However, while all bodies in nature are composed of atoms, that does not address the question of why the behavior of subatomic particles has a particle/wave duality. One answer to that question might be that all particles contain and manifest energy and to do so they must somehow be in motion.

A second potential problem with the de Broglie model lies in the fact that while each atom and/or particle has wave properties that does not resolve the question of whether separate atoms and particles could interact in a way to produce apparent collective wave/particle transformations. In part, the double slit experiment - while not answering why that could happen, seems to confirm that it does happen. The various particles run through slits in that experiment do interact to produce interference patterns and merge into a wave/particle singularity. In that context it would appear separate atoms and particles can somehow transfer their wave/particle duality to one another. – entanglement? If true it raises the possibility that the cancellation effect can be somehow contagious, or able to innervate the membrane of other particles in their path.

While these ideas are highly speculative, and not nearly as precisely defined as de Broglie’s concepts it seems possible that since the fundamental nature of the atom is motion, the universe and all the creatures in it are implicitly kinetic and only slow down to a state of apparent inactivity due to a cancellation effect resulting from the accumulation of mass within each structure. Thus, elephants, lions, tigers, bears, and humans can be described as inherently motile mechanisms capable of standing in line at the supermarket, dozing off in the savanna and hibernating in winter only because their primary wave properties cancel each other out due to wave negation and underlying gravitational effects.

This rather fanciful notion raises the interesting chicken/egg question of which came first, energy or mass. If the proto-universe had no movement and “began” in a fixed state of intense heat and mass before expanding that would give preeminence to mass. On the other hand, it is also possible the universe was in a state of movement from the outset - in other words, displayed kinetic constancy, and that expansion resulted from the accumulation of mass as movement patterns slowed down due to mass cancellation effects. In either case it seems de Broglie’s hypothesis merits perhaps more respect and consideration than has been granted by the math models.


De Broglie. L. (1964) The Current Interpretation of Wave Mechanics; A Critical Study. Amsterdam, Elsevier.

Planck. M. (1915) Eight Lectures on Theoretical Physics. Dover Publications

Rutherford. E. (1911) The Scattering of alpha and beta particles by matter on the structure of the atom. The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science series 6, 21 (125) 669-688

Bohr, N. (1922) The Theory of Spectra and Atomic Constitution Three Essays, Cambridge. Cambridge University Press

Thomas Young’s Experiment www. Archived from the original 3/31/2.

Schrodinger, E. (1926 An Undulatory Theory of f the Mechanics of Atoms and Molecules. Physical Review 28 (6) 1049-1070

Robert DePaolo M,S, Clinical Psychology, retired practitioner in the fields of clinical, educational and neuropsychology. Former adjunct professor of psychology N.H. University System, author of six books and many articles on science, education, psychology, politics and true crime.

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