Essentially, wave/particle duality employs the notion that an entity simultaneously possesses localized (particle) and distributed (wave) properties.
The idea has been introduced into modern physics to account for observations in which particles of matter interact to produce effects that appear to be identical to the effects that occur when waves diffract and interfere.
However, the concept of rests on an assumption. It is assumed that wave propagation mechanisms can provide the only possible explanation for scattering effects observed in experiments such as the Twin Slit experiment.
At face value, the assumption looks convincing. The French physicist, Louis de Broglie introduced the wave/particle concept into physics in the 1920s, with a brilliant prediction that particles of matter possess wave properties and act as though they were composed of propagating waves. Experimental confirmation of de Broglie's prediction (electron diffraction in crystals) has led to the theory being cemented into the foundations of modern physics.
Later, Danish physicist Neils Bohr used the wave-particle duality concept as the foundation for his well known "Copenhagen Interpretation" of quantum mechanical effects.
At the time the theories were developed, wave propagation effects were the only mechanism that people were aware of that could produce those kinds of phenomena. Consequently, the ideas became fixed and that fundamental assumption has since persisted.
My contention is that even though the assumption looks reasonable, it may not necessarily be correct.
The object of this article is to re-examine the observations and core mathematical relationships with the intention of opening up the possibility of a different mechanism that is both consistent with relativity and quantum theory.
For more detailed background and an illustrative example ->[Historicc Summary] [Twin Slit Example].
1.1 Basic Issues
By making the assumption, we can obtain a simple explanation for particle diffraction and interference but we lose the ability to make sense of particle behavior from a relativistic perspective.
Acceptance of that assumption also requires a set of "supernatural" mechanisms and behaviors that are needed to reconcile the distributed mechanism of wave propagation with the localization of particle interactions.
Two factors stand out, the need to:
The alternative is that the assumption could be mistaken and there is a different mechanism operating. The intention of the rest of this article is to explore that possibility.
Fig 1. Single slit diffraction, artificially modeled without wave propagation effects
With regard to this last point, there is a conceptual problem in relativity if you regard a photon as a propagating wave.
When you look at the "existence" of a single photon from a photon's "frame of reference", then you find that the photon retains the same phase across its whole existence, as though it is "frozen" in stasis as it propagates. In other words, the photon experiences no time when it moves from its start point to its end point.
This could mean that a photon does not oscillate when it propagates from one place to another, and may be inconsistent with wave propagation models.
Certainly, you can plot the appearance of this constant phase across an observer's reference frame and see that it projects as oscillations, (consistent with Maxwell's equations) but this is not the same thing as wave propagation. Rather, it looks to be an illusion that arises because that which is simultaneous in the photon's frame is not simultaneous in any other observer's frame of reference. It is an artifact of the way time occurs across space.
This could mean that a photon does not propagate as a wave. It may well interact in an oscillatory manner and, as a result, scatter in patterns that resemble wave propagation effects. However, this is quite distinct from the fundamental processes of interference and diffraction that require a particle to distribute its presence across a large volume of space.
The object of this section is to explore the relationship between the form of a scattering pattern and the spatial pattern in the scattering object (the slit screen). By analyzing the situation in this manner, it can be seen that the properties of the final pattern depend only on the spatial pattern of holes in the screen and do not depend
However, the question is, despite the success of the relationship, can we eliminate the wave propagation aspects and still obtain the correct answers?
Fig. 3 below shows a typical optical interference pattern as it develops. At the left, the particle distribution is well defined, it goes through some transient phases as the pattern emerges, then the distribution stabilizes into a set of well defined "rays".
What I wan to look at here, is examine the relationship between the initial pattern in the slit screen and the final "stable" pattern that the beam settles into in what is conventionally described as, the "far field".
Fig 3. Emergence of an optical twin slit diffraction pattern.
From a scattering perspective:
If particles undergo a scattering process then each deflected particle receives an impulse of momentum to produce its change of direction. Further, that impulse would need to be directed transversely, across the path of the beam, in the plane of the slits.
Starting with the first off-center line, examine the transveres momentum impulse imparted to the particles arriving at the screen. The momentum is given by a simple formula calculated by taking angle of deflection and the incident momentum to solve for the transverse momentum impulse.
Straight away, we see something interesting:
The same feature characterizes the rest of the bars in the interference pattern. The deflecting momentum for the peak is always in multiples of h/D.
That is to say, that for all lines on the screen, the equation for the deflecting momentum for that line is a simple function of the slit separation and Planck's constant.
By looking only at the deflecting momentum exchanged during the scattering process, we see that there are no variables that depend on the magnitude of the momentum of the incoming particles.
If particles are considered to follow a trajectory then the incident particles are acquiring a cross-wise component of momentum that is taken from a set or 'spectrum' of possible deflections that is determined by the pattern of holes in the screen.
In effect, it looks as though the far-field pattern we see is an image of a "momentum spectrum" that depends on the slit dimensions and not on the momentum of incoming particles. In other words, the form and scale of this spectrum does not change with the magnitude of the incoming particle momenta. The beam appears to passively act like a image projector for a spectrum that is inherent in the screen.
So far, we have only calculated the location of the peaks in the pattern and ignored the continuous oscillation in image density from light to dark. Even so, this result strongly indicates that the overall pattern is characterised by a cross-wise momentum spectrum that is related to the structure of the screen and is independent of the magnitude of the momentum of incoming particles.
The illustration below illustrates the extent to which the final pattern does not depend of the supposed "wavelength" of the incident particles.
The image is a composite of two twin slit diffraction patterns. The top half of the image is constructed with a wave-length that is five times longer than the lower half. To match the patterns, the horizontal axis of the lower half of the image is reduced in scale by a factor of five.
Fig 4. Combined images of two diffraction patterns. Upper half shows pattern with a wave-length five times longer than the lower half.
So what of the exact form of the final pattern of transverse momenta?
In the far field, the exact form of the pattern is a result familiar in optics, it is obtained by taking the Fourier transform of the spatial pattern made by the slits in the screen. This result is general and covers both the one and two slit cases, in fact, it holds for any pattern of slits or holes in the screen.
So how does this Fourier pattern in the scattering momentum relate to quantum theory? The answer is quite literally a textbook case.
Applying Schrödinger's equation in this manner (to the spatial pattern of holes in the screen, rather than the incident particles) gives the exact result for the required scattering momenta in both the single and twin slit cases.
Interpreting Schrödinger's equation this way opens up the possibility that the relationships discovered by De Broglie do not correspond to wave propagation effects and are no more than a curious side effect of the characteristics of a scattering process.
When one examines the context in which Schrödinger developed his mathematical model (atomic states), it becomes apparent that the equation very precisely characterizes the states that particles can adopt with respect to one another. Furthermore, in doing so, the equation characterizes the spectrum of energies that the system can exchange with other systems (e.g. atomic spectra).
In the twin slit context, the equation seems to characterise the spectrum of crosswise momenta that can be transferred to the incident particles as the space in which the particles exist opens up from a constrained pattern to a smooth state (far-field). This model has some very different features compared to the interference model:
Additionally, we no longer need to classify all particles (photons especially) under the same, restrictive, umbrella of "quantum wave/particle".
The image below illustrates the evolution of an optical twin slit interference pattern. In the far field, (to the right) the pattern settles into a set of "rays" that match those that one would expect from a random scattering of particles into a Fourier transform of the slit pattern.
However, when one examines the part of the pattern when the beam begins to emerge, one sees a fine pattern that is not consistent with an instantaneous scattering in to straight-line trajectories. Instantaneous scattering would produce a multitude of crossing trajectories that would hide the fine detail apparent in the observed pattern.
To be consistent with the observed pattern, the particle
trajectories would need to emerge downstream of the slits in some sort
of process similar to the way a toy boat may be diverted from it's course
when crossing the wake of larger craft.
The idea that particles may follow a definite trajectory through such a pattern is not new. David Bohm and Basil Hiley present an example in their book "The Undivided Universe" 1993 showing a diagram (Fig 3.1) of a set of possible electron trajectories for a situation where the particles emerge from the each slit with a Gaussian distribution. The example shows the trajectories not crossing, and flowing through the pattern rather like a laminar flow of a fluid.
Bohm and Hiley's choice of "Gaussian" slits may be deliberately chosen to produce a "laminar" pattern. The Fourier transform of a Gaussian curve is a Gaussian curve. Hence the single slit component of the pattern will remain static from the the slits out to the far field. In the text, Bohm and Hiley use the example to illustrate a concept of a wave-like quantum field that accompanies each particle and determines its path by providing "information" that guides the particle according to the "form" of the field rather than it's strength.
Examination of the early stages of an optical interference pattern generated by "rectangular" slits shows beams of particles coming off either side of each of the two main beam (as in the fig 5 below) and judging from appearance, parts of each beam do look to cross each other.
First, Rutherford, for discovering that atoms were largely "empty" space; each consisting of a small positively charged nucleus "orbited" by one or more negatively charged electrons.
From this point, I suggest a diversion from the orthodox interpretation of this behavior. Most orthodox interpretations involve making the assumption that the observed frequency is a property of the photons being emitted because it was assumed that light is a wave and displays interference. This may be an unwarranted assumption;
As a result, I propose that the implications of Planck and Bohr's discoveries can be restated, along the lines of:
In terms of the classical electromagnetic fields, when particles adopt states that fulfill certain constraints then the combined field pattern of the charges becomes 'stable' so that no radiation occurs. Precisely why, I have no idea. And, as far as I can tell, neither does anyone else.
The effect of this behavior is that certain specific states of motion are the only ones that can persist in matter. Furthermore, anything that perturbs such states will almost immediately resolve itself into radiation (photons) plus a new set of 'stable' states.
In summary, when charged particles get together to occupy space as "matter" then that matter consists almost entirely of periodic states of motion that fit criteria outlined in the equations of QED.
It is commonly accepted that this effect is the source
of atomic spectra. Electrons can only adopt a restricted set of "orbits"
around a nucleus; those orbits that satisfy Schrödinger's equation.
(Note: There are other criteria relating to angular momentum and degeneracy
of states that add to the complexity of the solutions, even so, the core
relationship is obeyed in all cases).
Because it is conventionally assumed that a particle propagates as a wave, Psi is normally taken to be a mathematical representation of the simultaneous superposition of states available to the particle. While this may seem reasonable if the particle is taken to be wave-like and non local, such an interpretation does not work in a context where a particle does not propagate in space as a wave.
As an alternative, I suggest a different interpretation. That Psi represents the statistical superposition of the states present and/or available in the system that the particle is part of/interacting with.
If that is the case then we can take the spatial structure of the slit screen (single slit or twin slit) to represent the expectation function for the distribution of 'position' for the 'sea' of states. From there, as explained above (2.2), it is a textbook case to find the momentum spectrum of such a population.
Two important examples are:-
I acknowledge that such effects do not "prove" my case, they do however establish that this alternate approach is viable across a wide range of quantum effects. I also argue that the model is conceptually simpler in that it does not require the support of "mystical" effects that have no description or representation in the theory; For example, the purported "wave function collapse" or perhaps the "determination of reality" via the act of observation.
In one twin slit version of the experiment, a shielded magnetic field runs along the central bar between the slits. It runs parallel to the slits and the surface of the screen so that no transmitted particles (electrons) actually cross any magnetic potential.
In another version, the screen is made of insulating material and the "slits" are holes made with conducting (metal) cylinders. A Voltage is applied so that the two cylinders are at different potentials. An electron traveling through each cylinder will not 'feel' an electric potential.
In interference based interpretations of these experiments, the observed displacement in the pattern is taken to provide more evidence for "quantum non-locality" because it is assumed that the particles are propagating as waves and produce the effects by somehow "sensing" the shielded fields.
However, if you take the approach that the pattern is an "image" of a momentum spectrum that can be exchanged between the slits and the incident particle then a different kind interpretation becomes possible.
Why? The quantum exchanges between the slit screen and the incident particles involve quantum states in the slit screen that propagate transversely, through the "shielded magnetic/electric field" in question and are directly affected by it. The spectrum of available excitations that have dimensions that traverse the field, (i.e.. those responsible for the twin slit component of the pattern), become shifted and the single slit component does not, as observed in the experiments.
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