Young's Double Slit Experiment and single Photon Interference

See Also The Euclidean Representation Theorem

Diagram 12(b), shows the space-time situation. Let us consider a cross-section of the set up at right angles to the slits. Along the past light cone from position A at time T0 two paths, one through each slit, are drawn to the source. The paths intersect the source at T1 and T2. In the illustrated case T1 and T2 are separated by one wavelength along the world line of the source. The proper interval locality of T1 and T2 with T0, produce two super-positioned presences of the source at T0 at position A. Since, both presences have the same phase they will positively reinforce each other. Any quantum entity at position A will be able to sense these positively reinforced super-positioned presences and will have an enhanced probability of an interaction with a source atom. If the paths had intersected the world-line of source at events separated by half a wave-length then the super-positioned presences would destructively interfere making it very unlikely that interactions would occur between atoms in the source and those at point A on the screen. For any experimental set-up we can calculate for all positioned on the screen the relative phases and intensities of the super-positioned presences of a source atom and determine the probability distribution for the likelihood of interaction anywhere on the screen. The relative phases of the super-position presences of a source atom on the screen will depend on the path lengths from any given position to the slits

The mathematical the form of the resulting intensity distribution over the screen will be identical to that determined by the standard wave theory. Now however we are not describing how energy is continuously distributed over the screen by a wave but a probability function that determines the chances of an interaction occurring within any specific region on the screen.

In our illustration the source atom interacts with the screen at position A and time T0. However. Event T0 is properly local to both event T1 and T2, since T1 occurs before T2 and the atom is still excited at T2 then the interaction must occur at event T2 from the point of view of the donor atom. It would appear that the earlier point of locality reinforces the wave-function but cannot take part in the actual interaction.

Note

To illustrate the development of the light wave-function in the double-slit experiment we have simplified the situation by only looking at two paths between an event on the screen and the world-line of the source atom. In any practical set-up there will be many paths between any given position on the screen and the source atom. To fully determine the wave function for the double slit experiment for each point on the screen we need to superposition the localised presences of the source atoms via all possible zero interval paths.

The form of the wave-function in the double slit experiment will be radically different if only one slit is open compared to both slits being open. So even for a single interaction the likely position of an interaction on the screen depends on whether both slits are open or not.

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