Young's double slit and determinism

Question

In Cohen-Tannoudji's QM book, pg. 6, the following was said about the Young's double slit experiment:

Moreover, as the photons arrive one by one, their impacts on the screen gradually build up the interference pattern. This implies that, for a particular photon, we are not certain in advance where it will strike the screen. Now these photons are emitted under the same conditions. Thus another classical idea has been destroyed: that the initial conditions completely determine the subsequent motion of a particle.

I don't think I agree with what the author has said here. Since we can't perform measurement on a particular emitted photon without disturbing it, there isn't a way we can measure the initial conditions of the photon after it leaves the source. Although photons are emitted under the same conditions, i.e. from the same source, each photon may travel in different directions and velocities after leaving the source. Thus each photon, although from the same source, can have differing initial conditions, which in terms affect where they strike the screen. The reason why we can't predict where the photon strikes the screen may be because we don't know the initial condition of the photon.

What do you think about my argument?

Answer 1

Although photons are emitted under the same conditions, i.e. from the same source, each photon may travel in different directions and velocities after leaving the source.

Take this experiment

Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

The classical wave from a laser pointer, considered as a plane wave, is composed of the quantum mechanical photons in a mathematically complicated way that also has the quantum mechanical indeterminacy, i.e. probability of what the track of the individual photon is. In that sense the beginning of the photon "track" can be considered within the angular opening allowed by the laser beam width and the double slits' So the "initial condition" is known within this limit.

The footprint of the single photons on the screen has distances much larger than the width of the slits, we can draw a ray from the slits to the screen. But that ray is not predictable , quantum mechanics predicts the probability that a photon footprint will hit at (x,y).

Answer 2

You are right up to a point- when the authors state that the photons are created under the same initial conditions, that is clearly an imprecise statement, as the starting position and direction of the individual photons are subject to a degree of uncertainty. However, that uncertainty is not enough to account for the results of the interference effects. Our theories suggest that even if multiple photons were to be presented to the slits in exactly the same way, they would still be detected on the screen in a dispersed diffraction pattern.

You could test the extent to which the variation in initial conditions contributed to the uncertainty in the final detected positions of the photons by moving the position of the source slightly when performing the experiment. You would find that tiny movements of the source apparatus relative to the screen would not result in major changes to the diffraction pattern, and therefore could not be the cause of the wide spread of locations at which the photons are found on the detector beyond the slits.

Answer 3

Mathematically interference usually manifests from solving the coordinate part of the Schrödinger equation (or Maxwell equations, if we talk about photons) in the whole space. On the other hand, thinking of electrons/photons being emitted one by one, implies that they are localized wave packets: mathematically these can be thought as the superpositions of the eigenmodes, existing in the whole space... but this would imply that they know about the screen even before they reach it (which, by the way, violates the relativity).

This is what the statement by Cohen-Tannouji is probably about: the interference pattern is a global property, not determined by the initial conditions, i.e., by the point where the electron/photon is emitted. On the other hand, upon emission, the electron/photon cannot have immediate knwoledge of the global properties of space.

Perhaps the discussion in this answer could be helpful as well.

Answer 4

They way we have all been initially taught about the DSE and interference is misleading. They are many virtual forces at work before a photon is even emitted from the source, an excited electron/atom can be on the excited state for quite a length of time where forces called virtual photons are emitted. All the EM forces in the environment effect the direction, as well the electron will emit in preferred directions, per Feynman/Dirac "every photon determines its own path" .... and the Feynman path integral provides a good mathematical model of what paths are most probable.

Your argument is very sound, there must be differing initial conditions ... but these are due to quantum forces not classical ones so the author has good point.