Giorgio wrote:
So, suppose that the light wave has travelled across half our galaxy and, undisturbed by the galaxy boundary, has now reached us in a coherent state (on this I can agree in principle). This wave should now have a cross section thousand of times the starting wave.
When this wave encounter our boundary (a telescope, an interferometer, other), will it have to collapse over itself to regain it's original (starting) cross section before interacting with the boundary?
If your answer is yes, how do you solve this mathematically?
Excellent question: You have gone for the jugular! You did, however, not specify whether the wave has the energy of a single quantum or is an entanglement of quantum waves. I assume that you imply a photon being spread over such a large area.
Let us first consider a special double-slit experiment where we send through single photons one-at-a-time. Then, according to what I postulate, each photon moves through both slits and the two lobes spread out and interfere with each other. Thus when this spread-out wave front reaches the screen, this front will cover a large area of the screen. Within the screen there are an array of atomic-sized absorbers which are resonating owing to Heisenberg's uncertainty relationship for energy and time. When the expanded photon-wave resonates with such an absorber, it collapses in size and becomes absorbed by this absorbing point. Thus you still have to accept that the wave can collapse or inflate when its boundary conditions change. The only difference is that it is a real wave that collapses not a probability distribution.
In other words when the photon impinges into the slits it encounters new boundary conditions which forces it to morph into two parts (which stay in immediate contact with each other) and which then interfere and spread out on the other side. When it reaches the screen it collapses to form a point. Since there are many points on the screen at which such a wave can collapse, a large number of identical photons moving through the slits must generate the intensity of the diffracted wave fronts in pixel-format.
When now training two detectors on the slits to see through which slit the photon came, the photon-wave will collapse into the detector with which it resonates first. We then conclude that the photon came through a single slit. But this change in boundary conditions forced the diffracted wave to collapse: There can then be no diffracted-interfered wave front reaching the screen. Thus after many photons have passed through the slits roughly 50% would have collapsed into one detector and 50% into the other. We conclude from this that the photons could not have moved through both slits at once.
But there is now no diffraction pattern on the screen anymore. This is compelling evidence that our measurements on the slits destroyed the wave that has moved through both slits. If the diffraction pattern remained: THEN YES we will have Copenhagen-magic!
Now to return to your question of a light wave that has a wave front of millions of kilometers: Assuming that it has the energy of a single photon and extrapolating from the double-slit experiment above, the conclusion has to be that it will collapse near-instantaneously. However, we have never observed a single photon producing star yet. But my inclination is that this is what would happen.
Now you asked how do I handle this mathematically: I suppose you mean how would it be possible for such a large light wave to collapse at a speed faster than light speed. Consider it as follows: The shape and size of ANY wave are determined by its boundary conditions. When the boundary conditions change suddenly, is the wave going to wait for Einstein's permission to morph and adjust? I do not think so. I expand on this aspect in my book. What it really implies is that a photon wave (and thus alo an electron-wave) is in immediate contact with itself. If it is spread out over light years and you tickle it on one side, the other side will know immediately. The same for a single wave formed by the entanglement of photons (or electrons).
Note that "instantaneous morphing" also explains so-called "quantum jumps". When an electron wave around a nucleus absorbs energy, it cannot fit the boundary conditions which held it stable before absorbing the light energy. It then has to morph "instantaneously" in shape and size. The wave "jump-morphs": There is not a "particle" involved.
