Are classical optics and quantum mechanics double slits fundamentally the same?

[aletheia]

TL;DR

Do the quantum and the classical wave interference pattern represent the same physical reality?

Has this question been explicitly discussed in the quantum-foundations literature?

Classical optics:
I(x) ∝ |E₁(x) + E₂(x)|²

Single-quantum case:
P(x) ∝ |ψ₁(x) + ψ₂(x)|²

What appears statistically in QM is the same interference structure from wave optics?

The most recent papers approaching this matter that I could find were:
C. J. Villas-Boas et al., “Bright and Dark States of Light: The Quantum Origin of Classical Interference,” Physical Review Letters 134, 133603 (2025).
J.-J. Cheng et al., “Quantum origin of diffraction from bright and dark states,” Physical Review A 113, 052201 (2026).

The first derives classical interference from a quantum description involving collective bright and dark states of light.

The second extends this framework to diffraction and explicitly describes it as connecting quantum and classical wave optics.

So, is there an interpretation or quantum-optical framework that explicitly addresses this issue?

References to papers or authors addressing this question would be appreciated.

 

[PeterDonis]

Do the quantum and the classical wave interference pattern represent the same physical reality?

I'm not sure what this question even means.

In actual experiments, there is no such thing as "quantum interference pattern" vs. "classical interference pattern". There is just the interference pattern which is observed. The light doesn't know whether it's "quantum" or "classical". It just does what it does.

In terms of theory, since the classical theory is simply an approximation to the quantum theory, we would expect both to make the same predictions for what we would observe, in any experiment for which the classical theory is a good approximation. This includes double slit experiments where the light intensity is high enough that we cannot distinguish individual photon impacts on the detector.

The classical theory, however, cannot explain why, when the intensity of the light source is very low, we can distinguish individual photon impacts on the detector--individual dots--that build up an interference pattern over time. For that case, the classical theory breaks down--it makes wrong predictions.

I don't know if any of this is what you mean by "represent the same physical reality". But that's the physics.

 

[DaveE]

What appears statistically in QM is the same interference structure from wave optics?

Interference is just a consequence of vector addition. You'll also see it in water waves in a harbor. Lots of things are well modeled mathematically as vectors. It sounds to me like you are seeking profundity in basic math.

 

[sophiecentaur]

It sounds to me like you are seeking profundity in basic math.

Good point here. Calculations with scalars don't seem to give the same awkwardness; we are very familiar with elementary school arithmetical operators and the idea of a=bXc but we seldom question how this simple bit of maths can relate to real world understanding. We intuitively assume linearity, I suppose. But it never is.

 

[Paul Colby]

A double slit interference pattern can be produced using sound or water waves. So interference is a wave phenomena in each of these cases. The “awe and mystery” of the optical example comes about because of the quantum mechanical nature of photons, not the interference pattern.

 

[anuttarasammyak]

I remember I had learned in junior high that not wave amplitude itself but its square matters energy. How teachers are explaining the reason?

 

[sophiecentaur]

How teachers are explaining the reason?

To measure a quantity requires Energy, which is a function of Wave Energy (power times observation time) and Power is Amplitude Squared. The amplitude (and phase) are needed to calculate the resulting interference and you can only arrive at the Energy after the vector addition. The actual details of this are complicated and involve not only the Energy of the wanted signal but the level of interference / noise. A theoretical calculation of interference can often appear 'wrong' until the practicalities of measuring the interference pattern are considered.

 

[aletheia]

Interference is just a consequence of vector addition. You'll also see it in water waves in a harbor. Lots of things are well modeled mathematically as vectors. It sounds to me like you are seeking profundity in basic math.

If you really think my problem is “basic math”, then it’s on you — for not understanding it and for this passive-aggressive argument.
What I’m actually doing is understanding where exactly might be the problem between quantum mechanics discreteness and relativistic physics continuity.
I’m also allocating some of my spare time on the mass gap Yang-Mills Clay problem — which is rather ironic seeing your comment…
However, I can’t even expose my reasoning cause it’s “off limits”, i.e., discuss physical ontology is not allowed, as I have been already warned before…

 

[aletheia]

I'm not sure what this question even means.

In actual experiments, there is no such thing as "quantum interference pattern" vs. "classical interference pattern". There is just the interference pattern which is observed. The light doesn't know whether it's "quantum" or "classical". It just does what it does.

In terms of theory, since the classical theory is simply an approximation to the quantum theory, we would expect both to make the same predictions for what we would observe, in any experiment for which the classical theory is a good approximation. This includes double slit experiments where the light intensity is high enough that we cannot distinguish individual photon impacts on the detector.

The classical theory, however, cannot explain why, when the intensity of the light source is very low, we can distinguish individual photon impacts on the detector--individual dots--that build up an interference pattern over time. For that case, the classical theory breaks down--it makes wrong predictions.

I don't know if any of this is what you mean by "represent the same physical reality". But that's the physics.

Thanks.
Even if you didn’t understand my question, your answer is exactly what I was wondering about, so, I do very much appreciated your attention.
Cheers.

 

[aletheia]

A double slit interference pattern can be produced using sound or water waves. So interference is a wave phenomena in each of these cases. The “awe and mystery” of the optical example comes about because of the quantum mechanical nature of photons, not the interference pattern.

I get your point, nonetheless, what is treated as a “mystery” in the double slit experiments usually is when the “observer” (i.e., a forced physical interaction) is on, since it “break the interference pattern”.
I can’t go much further on it (else, it’d be “personal theory” — meaning: my own reasoning of the physical reality behind the numbers), but the apparatus changes the set up of the experiment, so the outcome changing shouldn’t be “mysterious”.
Nevertheless, what has come to my attention in the last couple of years is that the real “mystery” (i.e., the real hard question to be answered) of the double slit experiment is: if each photon leaves only a single dot on the screen (e.g., if you shoot only one photon you get only one point and not two half-points), if the photon can’t be divided, how could it interfere with itself?
Apparently, given the statistical distribution, it would somehow have done it.
If you flash a constant light, or if you pass through the double slits water (like in our sensorial continuous experimentation of the universe), then you’ll see the interference pattern and nobody will get mystified by that — but when the outcome is identical in the discrete QM reality, I don’t see people discussing it.
If you shoot zillions of photons at the time, you’d say that they interfered with each others — you wouldn’t say that each photon interfered with itself…
So, the math is quite the same, the outcome is the same — one is treated as “classical” (i.e., “continuum”), the other is “modern” (i.e., “quantum”)—, but the universe is the same.
The photons are the same, and neither I nor mainstream science have any reason for believing that their behavior should vary across different scales.
So, ultimately, I’m seeking physicists and peer reviewed articles from whom approach their experiments in order to fill this gap between continuity and discreetness.
Cheers.

 

[Roberto Pavani]

TL;DR: Do the quantum and the classical wave interference pattern represent the same physical reality?

Has this question been explicitly discussed in the quantum-foundations literature?

Classical optics:
I(x) ∝ |E₁(x) + E₂(x)|²

Single-quantum case:
P(x) ∝ |ψ₁(x) + ψ₂(x)|²

What appears statistically in QM is the same interference structure from wave optics?

The most recent papers approaching this matter that I could find were:
C. J. Villas-Boas et al., “Bright and Dark States of Light: The Quantum Origin of Classical Interference,” Physical Review Letters 134, 133603 (2025).
J.-J. Cheng et al., “Quantum origin of diffraction from bright and dark states,” Physical Review A 113, 052201 (2026).

The first derives classical interference from a quantum description involving collective bright and dark states of light.

The second extends this framework to diffraction and explicitly describes it as connecting quantum and classical wave optics.

So, is there an interpretation or quantum-optical framework that explicitly addresses this issue?

References to papers or authors addressing this question would be appreciated.

Are you referring to something like: https://arxiv.org/abs/2412.10661 ???

 

[Paul Colby]

what is treated as a “mystery” in the double slit experiments usually is when the “observer” (i.e., a forced physical interaction) is on, since it “break the interference pattern”.

My training is in experiment side of physics. If I turn on this "forced physical" interaction, I would have to get up from my stool and adjust the experimental apparatus. I'd block a slit, actually change some EM boundary condition, thus changing the interference pattern in some way. In fact, the only way for energy to mystically appear in a null is for an experimenter to do something to the apparatus. I don't find this mysterious in the least.