Double-slit experiment according the pilot wave model of Broglie and Bohm
The double-slit experiment is special in the way it shows the wave properties of photons and matter, because the wave is measured in two seperate slits and then compared by interference. The Copenhagen interpretation of quantum mechanics states that a photon has particle properties or wave properties, but not at the same time, depending on what is measured. In the double slit measurment an interference is visible, which is a wave property, so a wave is measured. Then there is no particle on a certain position, following a path. Only at the end, at the detector, the wave photon is absorbed and becomes a particle, while the wave disappears. The double slit measurent therefore shows some wave properties. In the pilot wave model, originally developed by Louis de Broglie and further developed by David Bohm, a photon has particle and wave properties simultaneously. The particle follows a path, togheter with a wave. The double-slit experiment shows, with simple real- and thought experiments, what the wave and particle properties would be if this assumption is made. Additional to the Quantum mechanics we now have a particle going through one slit (with its wave) and only a wave going through the second slit. It is build up in steps, starting with only a particle. The description is limited to conclusions, without explanation why.
With the standard measurement parallel monochromatic light uniformly illuminates a detector (1). When a screen with a slit is added (2), diffraction will cause scattering of the light, resulting in a wide wave on the detector. When a second slit is opened (3), the different lengths the waves travelling through both slits causes interference. At A both lengths are the same, the waves run in phase and add up to a double height peak. At B the wave from slit 1 travels longer and becomes opposite to the wave from slit 2, so extinguish each other. When light is seen as photons the effect will be the same: in time the wave in (3) will be build up with single photons.
- Suppose the experiment is repeated with one photon with a certain energy, which is the same in every measurement (although in theory impossible). Also suppose that without a screen (1a) and with one slit (2a) the photon will go to B.
- If in (2a) the slit is narrowed, the result will not change: the energy is the same. Conclusion: the energy of a photon is independent of the area of the slit. It is really a particle.
- Open slit 1 (3a). Comparison with (3) shows that no photon will arrive B. So the photon turns off and arrives somewhere else. Conclusion: something goes through slit 1, which changes the path of the photon.
What does the experiment show about the properties of this "something"?
- The interference pattern in (3) shows that it has the shape of a sine wave, giving interference when going through both slits.
- If both slits are narrowed, the result will not change: the energy and detection position of the photon are the same. Conclusion: the energy is independent of the amount of wave through the slits. So the wave does not contain energy in its volume.
- If only one slit is narrowed, the result will be a mix between (2) and (3). The photon can arrive at B, but still with a lower propability then at A. The photon still has the same energy. Conclusion: the amount of wave through the slit effects the path of the photon.
- In (3) the waves through both slits cancel each other completely in B, so are equal in size in both slits. Conclusion: the wave have the same amplitude at a distance of the photon.
- In (3b) the wave from slit 1 cancels a part of the wave which went through slit 2 at a later time. Conclusion: the wave has the same amplitude after the photon.
- If the wave from slit 2 arrives at B, it cancels fully a part of the wave which went earlier through slit 1. This is the same at zero interference more to the right of B, with differences of 1.5, 2.5 .. etc wavelengths. Conclusion: the wave exist also for the photon, with equal amplitude.
- Both conclusions taken to its extreme: the wave has the same amplitude everywhere in the universe, visually as above.
- Move the detector to the slits and note the places B where no photon arrives. These are the red lines in (3c). But how can a photon travel to A through this "forbidden" zone, the zone without photons when the detector would be placed there? Suppose the photon travels to A and crosses the red line at B'. Place the detector at B'. Now the photon will not arrive at B', so will follow a different path. Conclusion: also the distance between slits and detector, does influence the path of the photon. So the path is influenced by an object before the photon, where it not yet is, or absorbed later on.
- A photon travels between a sun and a planet. That is also a kind of slit, so has effect on the track of the photon, also after it travelled light years. The effect will be extremely small, but present.
- Place a mirror above the slits (3d). The effect will be same as (3), with a single photon equal to (3a). In a mirror a photon is not reflected, but absorbed by an atom, which transmits a new photon. The atom does not know that it is part of a mirror on a certain angle, and transmits the new photon in an arbitrary direction. How does the photon know that it has to go downwards? (3d) implies that not only the photon, but also its wave is reflected. The wave is wide and hits all atoms in the mirror. Conclusion 1: the atoms reflects also the wave of the photon. According the Huygens principle these combine again to parallel wave fronts, but now mirrored. Conclusion 2: the new wave directs its new photon, not the other way around. It is a pilot wave.
- Place detectors in slit 1 and 2, to measure through which slit the photon travels (3e). The photon will be detected in slit 1 or 2. But the interference as in (3) disappears. Conclusion: if a situation is created in which a photon is forced to become visible (detected), the wave cannot pass that.
- To be able to reach B the wave must be diffracted in slit 1. To get the result of (3), the wave must diffract all around, as in (3f). This effect is known for waves with a carrier, like a sound wave. Then every air molecule in slit 1 is struck by the incoming sound wave and radiates it all around. For this reason in the past the ether was proposed, as carrier of the light wave. However it was proven that this physical ether does not exist. But then diffraction should not be possible and one would expect the wave travels as (3g). Conclusion: there still must be "something" in split 1 which diffracts the wave. If this is true, it its likely that also outside the slit this must be the carrier of the wave, with unknown properties.
- Above explains also why in (2) the photon diffracts. Also through slit 2 comes a wave which is diffracted all around. Because the mirror shows that the photon follows the wave, the photons will also diffract in all directions.