Extra-Solar Appendices

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Appendix 3

The Twin-Slit Experiment

Bullets as particles

Figure 1-1. An experiment with bullets as particles passing through twin holes.

In Figure 1-1b, the curves P1 and P2 show the probabilities measured with one hole open. In Figure 1-1c the curve P12 shows the probabilities found with both holes open. The last set of probabilities is the sum of the first two. The maximum likelihood of arrival of a bullet occurs in line with the center of the two holes and falls off smoothly as distance from the holes increases.

This contrasts sharply with the behavior of circular waves in water when they pass through two holes in a barrier and hit a non-reflecting wall (Fig. 1-2). Feynman shows how circular waves are formed in a shallow trough by moving an object up and down at its center. The intensity of the wave at any location on the screen is expressed as the square of the height of the wave, measured by an adjustable detector. This represents the energy carried to that height.

water waves interfering

Figure 1-2 The pattern formed by waves passing through twin gaps.

In Figure 1-2b, the curves I1 and I2 show intensity of the waves when only one gap is open. At any setting, the energy level varies smoothly from a maximum aligned with the selected gap to a low level near the end of the screen, in a similar way to the curves P1 and P2. But in Figure 1-2c the curve I12 showing the total energy transmitted through two gaps does not decline smoothly from a maximum to a minimum in the way of the probabilities of bullets in curve P12. Instead I12 shows a series of peaks and valleys.

This is an interference pattern, formed by the interaction of two new sets of circular waves, each being generated at the exit of a gap. Together, these two sets replace the original single set. At a location on the screen where the peaks of two waves arrive together, the combined wave height (and the energy transferred) is a maxim. Where two troughs arrive together, the combined height and energy is a minimum. And there will be a smooth transition between these states across the screen.

Electrons as interfering particles

Figure 1-3 An experiment comparable to that with bullets but using electrons as particles.

These experiments with bullets and waves passing through two holes are important to the interpretation of a similar experiment carried out with elementary particles, such as photons or electrons. Feynman’s setup for electrons is shown in Figure 1-3. Today, an electron gun would fire electrons towards the screen (the backstop) of a digital camera. And the experiment is now carried out with slits rather than holes, to provide a brighter image. The camera captures the time of arrival of individual electrons and their location on its screen. These results shown here come from experiments carried out at Cambridge University, England.

Electrons after passing through slits

Figure 2. This enlargement of a piece of Figure 3 shows the pattern of arrival of individual electrons at low beam intensity.

The intensity of the electron beam is made low enough for arrival of individual electrons to be recorded on the screen. Arriving at the screen, the electrons deposit their energy in phosphor molecules that emit light as a result of their energy gain. The electrons therefore appear as dots of light (Figure2), arriving at random times and scattered randomly in space relative to the direction of the beam. Increasing the intensity of the beam increases the number of dots, not their intensity, indicating that it is a beam of particles of constant energy that is arriving, not a wave. As a result, the number of dots increases as the electrons continue to arrive.

Emergence of waves as electron flow continues

Figure 3 As the experiment continues, successive records (b,c,d,e) show the build of a density pattern in the shape of a wave. Image: Dr. Tonomura and Dr. Belsazar

As the arrival of electrons continues, a pattern of parallel waves gradually emerges, aligned with the direction of the slits (Figure 3). The pattern looks like the pattern of combined water waves after they have passed through two narrow gaps (Figure 1-2). This has led to the assumption that the electron population has the property of a wave.

However, this assumption conflicts with the initial evidence that the electron is behaving as a particle. A more plausible conclusion is that two waves, originating from the slits, formed an interference pattern that guided the waves into the pattern observed. To form an interference pattern, the two waves must be identical. This indicates they originate from a single wave arriving at the two slits. And if the two waves from the slits can guide the electrons into an interference pattern, then the single wave is likely to be involved in guiding the electrons to the slits.

The initial distribution of single electrons arriving at the camera looks random, but as more particles arrive, a greater concentration gathers where the two guiding waves would reinforce each other. Many fewer electrons gather where they would cancel out. The two guiding waves interfere constructively where peaks meet, destructively where troughs meet. The particles are responding to the sum of the energy intensities arising during wave interference, with particles being guided more effectively into regions where the intensity is highest. But randomness remains in the final pattern, indicating that the guidance before and after the slits is not successful in removing all of this randomness in the electron stream reaching the slits.

My suggestion is that the wave guiding the particles operates across the spacetime/hyperspace interface. 

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