# About quantum interference: space and time

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• Husserliana97
Husserliana97
Hello to all,
Questions that I hope are not completely devoid of physical meaning.

Firstly, about space. Let be a Hilbert space, in which we can by definition establish the existence of complete and orthonormal vector bases; and a Psi vector (state) that we write as a linear combination (a "superposition") of these base vectors. Here we can define a notion of distance, because this space is provided with a scalar product; for example, the distance between two vectors in the combination; but this 'distance', if I understand correctly, is only a measure of the similarity/dissimilarity between these two vectors (and cannot therefore be interpreted as a Euclidean distance).
So my first question is: what role does this distance play in interference? Or, more specifically, is a large distance (and therefore a large dissimilarity between vectors/amplitudes) an obstruction to the fact that they interfere? Which also raises the question, I think, of whether the angle matters for interference, and not just the phase ratio.

Now to time. I'll put my question like this: is quantum interference a process that takes place over time (and is therefore a 'process' in the strict sense), or an instantaneous consequence of superposition?
A physicist (I'm not a physicist by profession, as you'll have gathered) told me, without being more specific, that interference is not an 'interaction' in the strict sense of the word, in other words in the physical sense of the term. I can only guess at what is meant by this (but perhaps you'll disabuse me of the notion): an interaction would be a process during which two 'entities' (in this case two Psi amplitudes) act on each other and therefore exchange energy, impulse and, more generally, information. So interference would be nothing of the sort. But why? I can only make the following assumptions:

1) Quantum interference does not involve the exchange of forces between probability amplitudes. The amplitudes are simply superimposed and interfere without exerting any force on each other.
2) It does not require the transmission of information between them. The interference pattern is determined by the superposition of the amplitudes themselves, not by any communication between them.
3) Finally, it can be considered an instantaneous process, occurring at the same time as the superposition of the states/amplitudes. There is no propagation of influence in time.

And it's this last point that interests me. Doesn't quantum interference emerge instantaneously (so to speak) from superposition? It is, so to speak, the logical consequence, without us being able to speak of a succession (the superposition's anteriority would just be logical, not chronological).
I have in mind an analogy with quantum entanglement. In the same way that entanglement does not imply an interraction at a distance (no transmission of a signal or information) between two quantum systems, but translates the simple fact of their non-separability (the superposition of correlations between their respective states), in the same way, there would be no interaction and therefore no spatio-temporal process involved in interference; but because at least two states are superimposed, it 'follows' (logically) that they interfere, and do so differently according to their phase ratios (and their angles, then ?).
Does this hypothesis, and the analogy with entanglement, simply make sense?

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