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.
Last edited: Sunday, 12:12 AM
aletheia said:
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.
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aletheia said:
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.
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DaveE said:
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.
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.
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I remember I had learned in junior high that not wave amplitude itself but its square matters energy. How teachers are explaining the reason?
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anuttarasammyak said:
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.
DaveE said:
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…
[Moderator's note: Off topic content deleted.]
Last edited by a moderator: Tuesday, 7:53 PM
PeterDonis said:
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.
Paul Colby said:
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”.
[Moderator's note: Off topic content deleted.]
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.
Last edited by a moderator: Tuesday, 7:54 PM
aletheia said:
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.
Paul Colby said:
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.
So, basically, we agreed on this…
aletheia said:
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?
Yes, that is the real question. It comes from the quantized nature lying at the foundation of quantum physics. This mystery has lead to the notion of a particle-wave duality. However, I think the "mystery" comes from the prevailing notion of a particle as interpreted in the classical sense.
Photons are quanta, but they are not particles in the classical sense. The key is to understand that interactions always involve the exchange of quanta. In the absence of interactions, quanta evolve according to the equations of motion. In other words, they propagate as waves. That is what allows them to interfere. When they reach the detector array, the detection process invokes interactions, which again involves the exchange of quanta. Therefore, it looks like a particle is being detected.
aletheia said:
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…
Actually, I would say your statement is filled with notions that are incorrect. A double slit interference pattern happens independent of the number of photons. It can be realized one photon event at a time. Photons are quanta of energy and momentum exchanged between the EM field and the detector. No one shoots them anywhere.
flippiefanus said:
“In the absence of interactions, quanta evolve according to the equations of motion. In other words, they propagate as waves”
While I appreciate your answer, the equations are not the physical reality themselves.
One photon is one photon.
One photon leaves one mark — not two half-marks.
As far as I know, the wave-particle duality has not yet been fully comprehended.
So, the question is still up: is it wave, is it particle, is it wave or particle, or, as I were reprimanded for asking, could it be something else?
Again: I know the math is right, I’m obviously not questioning the validity of QM or SR, however, I’m reasoning about a physical ontology that can represent mainstream physics equations.
I kinda understood so far that the forum is not for philosophy, that’s the reason why I ask for physicists or peer reviewed articles where I could be updated about or could discuss physical ontology — which in my view should be the duty of physicists rather than philosophers.
Paul Colby said:
Actually, I would say your statement is filled with notions that are incorrect. A double slit interference pattern happens independent of the number of photons. It can be realized one photon event at a time. Photons are quanta of energy and momentum exchanged between the EM field and the detector. No one shoots them anywhere.
“[…] filled with […]” — could you care to be more specific…?
“[…] No one shoots them anywhere.” — so you’re saying that… the photons don’t leave the photon emitter (i.e., the single-photon source) to reach the screen?
aletheia said:
While I appreciate your answer, the equations are not the physical reality themselves.
One photon is one photon.
One photon leaves one mark — not two half-marks.
As far as I know, the wave-particle duality has not yet been fully comprehended.
So, the question is still up: is it wave, is it particle, is it wave or particle, or, as I were reprimanded for asking, could it be something else?
Again: I know the math is right, I’m obviously not questioning the validity of QM or SR, however, I’m reasoning about a physical ontology that can represent mainstream physics equations.
I kinda understood so far that the forum is not for philosophy, that’s the reason why I ask for physicists or peer reviewed articles where I could be updated about or could discuss physical ontology — which in my view should be the duty of physicists rather than philosophers.
Physics is a science, which means that it follows the scientific method. It involves coming up with a theory, using it to make predictions and comparing those predictions against experimental results. If the comparison gives agreement, we gain confidence in the theory. Nowhere in this process did the notion of what is real enter the game. So, while we do physics to gain understanding of physical reality, what it gives us a method to do calculations. In other words, the goal and the reward don't exactly match. In the end, any discussion about what is real lies beyond the realm of physics. It is philosophy, as you are hinting. Every physicist probably have their own idea about how to interpret the results they get, but there is no reliable way to determine which interpretation is correct. In my previous response, I probably inadvertently presented my own way of interpreting the reality of what is going on. At least it matches what we see.
Now to some specific statements:
"One photon is one photon" Yes, but it is not a classical particle. Perhaps better to think of it as a single quantum excitation of a field; in other words, an extended object that propagates like a wave and that can experience interference. The single excitation with the interference is still just one quantum. Therefore, all of it is involved in the measurement.
"As far as I know, the wave-particle duality has not yet been fully comprehended." There may not be a general consensus, but I think it is more or less understood, thanks to the gradual gain in understanding that came to a large extent from recent work in quantum information theory.
aletheia said:
As far as I know, the wave-particle duality has not yet been fully comprehended.
It has been discarded from modern quantum physics a long time ago (even though pop-science still talks about it). It has been discussed here on PF multiple times, you can search for threads about that.
EDIT. Sorry, I see that someone has already said that to you ![]()
aletheia said:
I proposed that the photon could be “wave AND particle”, instead of “wave OR particle”.
And that means you haven't read any textbook on quantum mechanics nor quantum field theory, so you are not the right person to propose anything. Before proposing anything, please spend at least 3 years reading appropriate textbooks. You don't know physics, if you don't know its math.
aletheia said:
“[…] filled with […]” — could you care to be more specific…?
More specific? I was discussing just the quoted statement I quoted in post #15. Hard to get more specific. What is really called for is being more complete. That would require a discussion of the mathematics used to describe the EM field.
I did supply an established fact; the interference pattern is independent of the amplitude of the light source[1]. One can produce it with any photon count rate.
[1] This assumes a thermal light source. The vast majority of light sources are thermal, radio transmitters, light bulbs, LEDs, lasers etc. Discussions of non-thermal sources is beyond my pay grade.
aletheia said:
“[…] No one shoots them anywhere.” — so you’re saying that… the photons don’t leave the photon emitter (i.e., the single-photon source) to reach the screen?
Not exactly. A mathematical complete description of light propagating from source to detector using QED is complex. Too often people are reasoning on purely inferred information. I can know from experiment when a photon is detected but, I only infer when and where it was emitted from. This inference is based on the apparatus employed and a knowledge of a well established underlying theory, QED. Discussions of shooting photons and little point particles flying about are often fabrications of the imagination that don’t accurately describe the phenomena. The statement I quoted in #15 is a good example.
aletheia said:
so you’re saying that… the photons don’t leave the photon emitter (i.e., the single-photon source) to reach the screen?
For massless fields with spin 1 or more, we can't construct position operator, so one can't think about photons traveling along any path between source and screen.
Moderator's note: Thread moved to the QM interpretations and foundations subforum.
aletheia said:
One photon is one photon.
If by "photon" you mean specifically one photon detection--one mark on a detector screen--then yes.
But...
aletheia said:
the question is still up: is it wave, is it particle, is it wave or particle, or, as I were reprimanded for asking, could it be something else?
It's something else: it's the little mark on the detector screen.
The fact that when we detect light of very low intensity, we detect it one little mark at a time, does not mean we can infer that light that is traveling through free space is "made" of little particles. But that seems to be what you are trying to do.
aletheia said:
I’m reasoning about a physical ontology that can represent mainstream physics equations.
You can't reason correctly without using the correct math.
The correct math will tell you that, in the vast majority of cases (including, for example, light from a laser), light traveling through free space is not in a state that can be usefully described as "made of photons". In fact it is quite difficult to make such states (called "Fock states") at all, and requires a very specialized experimental setup, and even then your control over what comes out of the source is limited.
So any "physical ontology" that tries to claim that light is always "made of photons" is doomed to failure. The math simply does not support such an ontology.
aletheia said:
discuss physical ontology — which in my view should be the duty of physicists rather than philosophers.
We understand that this is your opinion. However, there are many working physicists who do not share it. And it's certainly not something we're going to resolve here.
Moderator's note: Two posts discussing a paper on "dark photons" have been deleted. It's not clear that that paper is even a valid reference for PF discussion to begin with; but in any case it's off topic for this thread.
@aletheia I have deleted some comments in two of your posts complaining about what you're not allowed to post here. Any further such comments from you will receive a warning. Please be advised.
aletheia said:
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…
Perhaps you would say that, but that's not what the math says. The math says that the interference terms in the relevant wave function are independent of the intensity of the light--which means they are exactly the same even when the intensity of the light is so low that the expectation value of photon number inside the apparatus is never greater than 1. (Note carefully how I phrased that--I did not say "there is only one photon at a time inside the apparatus". The reasons why are explained in my post #22.)
Paul Colby said:
Discussions of shooting photons and little point particles flying about are often fabrications of the imagination that don’t accurately describe the phenomena.
A later energy-momentum exchange at the detector is causally conditioned by an earlier preparation at the source — that’s my point; I’m not imagining a particle flying around…
There is, nevertheless, an ordered physical process: a physical change (or excitation, or else) at the source, an intermediate electromagnetic evolution through the apparatus, and, finally, a localized absorption event at the screen.
There is a causal and energetic relation between those events.
This is not merely a semantic issue.
Energy from the Sun reaches the Earth — plants don’t use numbers in photosynthesis.
So, whether we describe the intermediate process classically as electromagnetic radiation or quantum mechanically in terms of field excitations and discrete exchanges, the physical consequence is not just a correlation between a source and an absorber. There is an actual transfer of energy-momentum from one physical system to another.
aletheia said:
There is a causal and energetic relation between those events.
Except, this sounds to me like you're infering one event, photon emition, from the photon detection. That's not how thermal sources work, at least by the mathematics. Photon numbers are neither certain nor conserved in the interaction between the source/field or the field/detector.
aletheia said:
There is an actual transfer of energy-momentum from one physical system to another.
When or how was this ever in contention?
PeterDonis said:
The fact that when we detect light of very low intensity, we detect it one little mark at a time, does not mean we can infer that light that is traveling through free space is "made" of little particles. But that seems to be what you are trying to do.
Not at all.
My reasoning comes from observation.
However, when it comes to QM, I can’t experiment at home.
While physicists worry about the measurement, Im more interested in the physical reality of the experiment, i.e., in the double slits, what is made and what is happening from the source to the screen.
PeterDonis said:
So any "physical ontology" that tries to claim that light is always "made of photons" is doomed to failure. The math simply does not support such an ontology.
Exactly — that’s why I won’t ever deny what is objectively observed, cause the math is not random: it is derived from what was measured, and what was measured is what was observed.
Nonetheless, I won’t ever ‘believe’ in someone else’s reasoning or math; I won’t ever accept someone else’s authority when the matter is science.
I use evidence based medicine at ER everyday.
In emergency medicine, the causality for the outcome is pretty straightforward.
I am trained in observation + logic and, even though I may be considered an outsider in physics, Im very well used to applying scientific knowledge on a regular basis for more than a decade…
Im not an enthusiastic of QM (or physics)… I’m not here to learn the basics…
Paul Colby said:
Except, this sounds to me like you're infering one event, photon emition, from the photon detection. That's not how thermal sources work, at least by the mathematics. Photon numbers are neither certain nor conserved in the interaction between the source/field or the field/detector.
When or how was this ever in contention?
Fine — if you’re still attached to semantics, don't call it a photon before detection.
Don't assign it a position, trajectory, a definite photon number, etc.;
What physical state of the electromagnetic system is modified by the source, reaches and interacts with the two slits, such that changing either slit changes the later probability distribution of localized energy-momentum exchanges at the detector?
Im not inferring a one-to-one photon emission event from a detection event.
Im inferring causal physical evolution from the experimentally obvious fact that changing the source or the apparatus upstream changes what is later detected downstream. Photon-number indefiniteness does not remove that causal ordering.
PeterDonis said:
Perhaps you would say that, but that's not what the math says. The math says that the interference terms in the relevant wave function are independent of the intensity of the light--which means they are exactly the same even when the intensity of the light is so low that the expectation value of photon number inside the apparatus is never greater than 1. (Note carefully how I phrased that--I did not say "there is only one photon at a time inside the apparatus". The reasons why are explained in my post #22.)
This is actually the response of the original question of this thread.
Classical optics equation describes what QM equation predicts.
Last edited: Wednesday, 11:02 PM
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