Is quantum interference an instantaneous consequence of superposition ?

[Husserliana97]

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?

 

[pines-demon]

Can you write some mathematical examples? You arguments use quantum jargon but in unusual ways, it is hard to get what you mean.

 

[Husserliana97]

Well, I can try, but clearly, that would be more an attempt than anything else, since I'm not a physicist per se.
So, let's provide a mathematical expression to illustrate that quantum interference is an instantaneous consequence of superposition.
Let's consider a simple scenario with two states (amplitudes), |A⟩ and |B⟩, that are in asuperposition. So the latter can be written as: Ψ = α|A⟩ + β|B⟩ (with α and β complex probability amplitudes)
Now, to demonstrate the instantaneous consequence of superposition in quantum interference, I'll consider the interference between the two states.
The interference pattern, which arises from the overlapping of the amplitudes, can be described by the probability density function denoted by |Ψ|². This function, as I understand, represents the probability of finding the system in a particular state.
In this case, il is calculated as: |Ψ|² = |α|²|A⟩⟨A| + |β|²|B⟩⟨B| + αβ*|A⟩⟨B| + α*β|B⟩⟨A|
where |A⟩⟨A| and |B⟩⟨B| are projection operators onto states |A⟩ and |B⟩, respectively, and α* and β* represent the complex conjugates of α and β.

The interference terms, αβ*|A⟩⟨B| and α*β|B⟩⟨A|, arise due to the superposition of states. These terms represent the interference between the states |A⟩ and |B| (tha could be constructive, destructive or partial).
And there, it seems clear to me that these interference terms appear instantaneously in the expression for the probability denssity function, reflecting the immediate consequence of the superposition.
Therefore, mathematically, the fact that quantum interference is an instantaneous consequence of superposition is evident in the expression for the probability density function, where the interference terms arise directly from the superposition of states and do not involve any temporal process.

 

[Husserliana97]

Now, to demonstrate mathematically that quantum interference is not a temporal process, I may examine the time evolution of the wavefunction (in non-relativistic QM, for simplicity) and the probability density function.
The Schrödinger equation describes how the wavefunction of a system changes with time, right ? Well, in the case of interference, one can analyze the time evolution of the wavefunction and observe that interference is not a temporal process. That’s my intuition, at least !

Let's consider the same scenario the before, where the system initially starts in a superposition state:
Ψ(t=0) = α|A⟩ + β|B⟩
To analyze the time evolution, we can express the wavefunction at a later time, t, as:
Ψ(t) = e^(-iHt/ℏ) (α|A⟩ + β|B⟩)
Xith e^(-iHt/ℏ) representing the time evolution operator, which is determined by the system's Hamiltonian.
Now, if we calculate the probability density function at time t, denoted by |Ψ(t)|², we find:
|Ψ(t)|² = |α|²|A⟩⟨A| + |β|²|B⟩⟨B| + αβ* e^(i(E_B - E_A)t/ℏ) |A⟩⟨B| + α*β e^(-i(E_B - E_A)t/ℏ) |B⟩⟨A|
In this expression, E_A and E_B represent the energies associated with states |A⟩ and |B⟩, respectively.

Upon analyzing the expression, we observe that the interference terms, αβ* e^(i(E_B - E_A)t/ℏ) |A⟩⟨B| and α*β e^(-i(E_B - E_A)t/ℏ) |B⟩⟨A|, depend on the energy difference (E_B - E_A) and the time t. However, these terms do not indicate a temporal process of interference!

As far as I understand : the time dependence in these interference terms arises due to the time evolution operator e^(-iHt/ℏ), iself inherent in the Schrödinger equation. It describes how the wavefunction evolves over time according to the system's Hamiltonian.
The interference itself, however, is not a temporal process. It arises from the superposition of states and the resulting overlap and interference of their wavefunctions. The interference terms in the probability density function exist "instantaneously" at any given time t, reflecting the immediate consequence of the superposition, rather than a temporal progression.
Therefore, mathematically, we can conclude that quantum interference is not a temporal process by analyzing the time evolution of the wavefunction and observing that the interference terms arise due to the superposition – and not as a result of a temporal evolution.
What do you think ?

 

[pines-demon]

Well, I can try, but clearly, that would be more an attempt than anything else, since I'm not a physicist per se.
So, let's provide a mathematical expression to illustrate that quantum interference is an instantaneous consequence of superposition.
Let's consider a simple scenario with two states (amplitudes), |A⟩ and |B⟩, that are in asuperposition. So the latter can be written as: Ψ = α|A⟩ + β|B⟩ (with α and β complex probability amplitudes)
Now, to demonstrate the instantaneous consequence of superposition in quantum interference, I'll consider the interference between the two states.
The interference pattern, which arises from the overlapping of the amplitudes, can be described by the probability density function denoted by |Ψ|². This function, as I understand, represents the probability of finding the system in a particular state.
In this case, il is calculated as: |Ψ|² = |α|²|A⟩⟨A| + |β|²|B⟩⟨B| + αβ*|A⟩⟨B| + α*β|B⟩⟨A|
where |A⟩⟨A| and |B⟩⟨B| are projection operators onto states |A⟩ and |B⟩, respectively, and α* and β* represent the complex conjugates of α and β.

The interference terms, αβ*|A⟩⟨B| and α*β|B⟩⟨A|, arise due to the superposition of states. These terms represent the interference between the states |A⟩ and |B| (tha could be constructive, destructive or partial).
And there, it seems clear to me that these interference terms appear instantaneously in the expression for the probability denssity function, reflecting the immediate consequence of the superposition.
Therefore, mathematically, the fact that quantum interference is an instantaneous consequence of superposition is evident in the expression for the probability density function, where the interference terms arise directly from the superposition of states and do not involve any temporal process.

This is mostly ok. But I wonder why do you need to involve time at all. Why are you trying that there is no relation between time and interference, when nobody is arguing for that. What you are trying to prove something obvious.

Note that classical waves have also interference terms.

 

[gentzen]

In this case, il is calculated as: |Ψ|² = |α|²|A⟩⟨A| + |β|²|B⟩⟨B| + αβ*|A⟩⟨B| + α*β|B⟩⟨A|
where |A⟩⟨A| and |B⟩⟨B| are projection operators onto states |A⟩ and |B⟩, respectively, and α* and β* represent the complex conjugates of α and β.

This is mostly ok. But I wonder why do you need to involve time at all. Why are you trying that there is no relation between time and interference, when nobody is arguing for that. What you are trying to prove something obvious.

You could have explicitly pointed out that it should have been
|Ψ|² = |α|²⟨A|A⟩ + |β|²⟨B|B⟩ + αβ*⟨B|A⟩ + α*β⟨A|B⟩
where ⟨A|A⟩, ⟨B|B⟩, ⟨B|A⟩, and ⟨A|B⟩ are scalar products between the states |A⟩ and |B⟩.

 

[pines-demon]

You could have explicitly pointed out that it should have been
|Ψ|² = |α|²⟨A|A⟩ + |β|²⟨B|B⟩ + αβ*⟨B|A⟩ + α*β⟨A|B⟩
where ⟨A|A⟩, ⟨B|B⟩, ⟨B|A⟩, and ⟨A|B⟩ are scalar products between the states |A⟩ and |B⟩.

That's the only issue you see in this thread?

 

[gentzen]

That's the only issue you see in this thread?

Well, I would have "liked" that post, if that issue were absent.

If you do see more issues with this thread, feel free to point them out explicitly.

 

[PeroK]

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?

You can't understand QM with words in this way. Interference is a consequence of the mathematics of QM, where a single particle is described by a complex wavefunction.

Here's a homework problem, where you can see interference emerge naturally from the wave mechanics:

https://www.physicsforums.com/threa...half-of-a-rectangular-potential-well.1060387/

 

[pines-demon]

Well, I would have "liked" that post, if that issue were absent.

If you do see more issues with this thread, feel free to point them out explicitly.

Please consider addressing what the author of the threads is saying directly to him/her. No need to fixate on the likeability of my comments

 

[gentzen]

Please consider addressing what the author of the threads is saying directly to him/her. No need to fixate on the likeability of my comments

You misunderstood: I would have pressed the "like" button below his post, not the one below yours. This was a direct and honest answer to your question to me.

My initial comment was of course directed to both of you: To him in order to inform him about his mistake, and to you in order to encourage you to be explicit.

 

[PeterDonis]

A physicist (I'm not a physicist by profession, as you'll have gathered) told me

This is not a valid reference. If your physicist can't point you to a valid reference (textbook or peer-reviewed paper) that expounds the point he is making and that you can point us to, we can't discuss it here.

 

[PeterDonis]

Thread closed for moderation. @Husserliana97 if you can get a valid reference, PM it to me and I will take a look and reopen the thread if it looks like a valid basis for discussion.