Wave Particle Duality:

This duality is “put in our face” by the dual split experiment.  I think a λ-hopping viewpoint can provide some clarity on how the electron (or photon) never goes thru one slit not to mention two slits and the many slits of diffraction gratings.

Before I continue here are a few links that are worth looking at:

1. I cannot say enough good things about the Khan Academy. This video explains Huygen’s wave propagation mechanics and points out that light propagates as an interference phenomena even before it reaches the aperture.

Each point on the wavefront acts as a circular radiator, and the reason the wave propagates straight ahead is interference. Even though this video looks at light waves it is still valid for electrons in that the deBroglie equation λ = h/mv applies for both electrons and light.

For electrons the equation is  λ = h/mv.

For light the equation is λ = h/p where p momentum of the light.

This You-tube video very clearly shows the problem created by the two slit experiment for light.

Here is the problem: If we fire a single photon at a time at the two slits we get an interference pattern as shown in the video, however, our analysis via Huygen’s interference theory requires a photon at each slit to create an interference pattern. A single photon at a time has no mechanism to create a interference pattern. So,how can a single photon or electron at a time create an interference pattern.

The solution that peer reviewed physics agrees on is that we need to forget about getting a physical visualization of what is going on. The only way to understand this phenomena is via the equations of quantum mechanics. So, shut up and calculate!

The video on the left is the classic where Feynman insists that a solitary electron must either go through one slit or the other. His logic is perfect for his hypothesis.

However, from the viewpoint of DWT (this website), the hypothesis is bogus. The electron does not go through either slit. An electron does not move by going thru, it λ-hops over (see section 11).

Click on the picture at left to see how standard quantum mechanics uses uncertainty and the Schrodinger wave equation to determine wave amplitudes and probabilities.

This is the standard approach to physics as of 2017. It gets excellent results, but leaves us yearning for a model where we can visualize what is happening.

Is there a better way to visualize how an interference pattern appears even if each electron is fired one at a time in the indiscriminate way indicated in the above diagram?
Answer: YES, think of the two slits as a crude lens in front of the advancing electron. When this electron has hopped to within a wavelength of either slit, it takes a momentary breather, and on its next hop it jumps (λ-hops) over the two slit barrier (the lens). The lens effect of the barrier and the electron’s position and velocity before the jump over the barrier determines its trajectory angle toward the detector. This vector (arrow to the detector) is unique for every electron that arrives because each electron approaches the slits differently. It is these electron trajectories that form the interference pattern. The Huygen’s two vector approach is not needed to get the interference pattern. Even for a single electron both slits are involved in causing the interference pattern.

OK. I have introduced the magic of λ-hopping. I can hear my reader say “come on man, the electron just walks thru the door without opening it?” .....”Is this some kind of mystical event?”

I grin a little and say: OK laugh at me, but this λ-hopping explanation is better than Feynman’s explanation that we can never know how an electron goes thru both slits at the same time, so shut up and calculate!

Is there any merit to the concept of λ-hopping beside being a theory that has both particle and wave integrated as part of its description?
Answer: YES, Using this theory it is possible to: 1. Give a visualization of how a single electron at a time can produce an interference pattern. 2. Account for dark matter and dark energy 3. Account for an accelerating expansion of the universe 4. Explain gravity as a quantum mechanical phenomena involving gravitons (cousins to photons). 5. Show how gravitons acting as dark matter is causing the precession of Mercury’s orbit around the Sun. See sections 17, 19, 20, 21 . 6. Explain why Foucault’s Pendulum and all gyroscopes rotate with respect to the background of stars.

A Note about the Uncertainty Principle:

A modified dual slit experiment is called for in which each electron is precisely placed before the slits with precise velocities (wavelengths). If we can do this, I believe the interference pattern will go away because all the electron trajectories to the detector will be the same. If not, I may need to pet Schrodinger's cat.