Self-Interference

Now that we have constructed the Matter and Light waves, I would explain a phenomenon where they behave in the same way....i.e. Self-interference. If you send individual photons to a double slit, you will get an interference pattern. An interference phenomenon entitles destructive and constructive interference. When the valley of one wave coincides with the crest of the other (destruction) and when two crests coincide (construction).

The latest self interference experiment makes a weak-measurement of a single photon several times. The average trajectory of the photon can be detected. Please read "Observing the Average Trajectories of Single Photons in a Two Slits Interferometer"(https://materias.df.uba.ar/labo5Aa2012c2/files/2012/10/Weak-measurement.pdf) Figure 1 shows the average trajectories of Single photons. You can see that in three occasions, two trajectories merge from the slits and get together toward the center of the figure. This produces the central maximum in the pattern. The rest of the trajectories diverge towards other maxima, but they don't merge. This means that there is no interference as described in the previous paragraph.

Figure 1 Average trajectories of a single photon

These results are very similar to Ashfar's experiment (https://en.wikipedia.org/wiki/Afshar_experiment). He puts a grit of wires at the dark fringes, which in Figure 1 are the spots with lower density of trajectories. Ashfar did not find a significant reduction in the interference pattern with or without the grit! This means that there are regions that the photon avoids, i.e. there is no destructive interference.

Back to Figure 1, at the slit position 0 mm, two trajectories merge toward the center of the figure. This occurs several times, at the distances 3500, 5500 and 6000 mm. At each side of the central trajectories, there are no trajectories. These are the places where the dark fringes occur. The rest of the trajectories diverge from the center, move somewhat sinusoidal and aim toward other maxima.

Every single photon was divided in two at the slits. Thus, every two trajectories belong to a single photon. If there would be constructive and destructive interference, every two trajectories should merge at the screen This is not happening. Besides the central trajectories, the divided photon continues being divided as it travels toward the screen.

Also, the trajectories deviate from a straight line and correct its optical paths. It looks that the photon is trying to reach a maximum in the interference pattern. Hence, to reach a minima is forbidden. It is not that its probability is very low!

Every single photon reaching the screen, is still in two places at the same time. Upon arrival to the screen, the central maximum will have a 100 % chance for the photon to arrive there. However, at the second maximum the photon still has the probability to collapse in one of the two second maximum spots. This last process will be stochastic and the photon will leave a mark at either place of landing. Therefore, this will occur with a probability of 50 %.

As discussed there is no Self-interference. This is because the photon is just following to complete its optical path. These results support a model where the components to produce maxima and minima are internal to the particle.  Thus, no merge of the trajectories between slits are required.

On next figures, I will show Self-Interference for a Light and a Matter wave respectively.

Figure 2 Light wave Self-interference. Photon # 1 reached the first maximum with a 100 % probability to land there. Photon # 2 reached the second maximum with 50 % chance to land at either positions.

Figure 3 Matter wave Self-interference. Electron # 1 reached the first maximum with a 100 % probability to land there. Electron # 2 reached the second maximum with 50 % chance to land at either positions.

Richard Feynman called this experiment the most mysterious experiment which encapsulates the soul of Quantum Mechanics. This is because it is impossible to describe it in any classical way! As you can see that is true. You need a 4 dimensional vision to understand Self-interference.