B Photon Continuity in Double-Slit Experiment

[jeremyfiennes]

It doesn't make sense to say a quantum particle moves along a classical path. For photons you don't even have a position observable to begin with!

I'm not talking of paths, but of detection at specific points.

 

[A. Neumaier]

I'm not talking of paths, but of detection at specific points.

You cannot detect the same photon twice, at the slit and at the screen!

 

[jeremyfiennes]

You cannot detect the same photon twice, at the slit and at the screen!

This is a thought exercise: whether in principle the 'particle' model holds, whether a single slit photon always corresponds to a single screen photon and vice versa. In the analogous SPDC case of whether signal and idler photons are always either both found or not, this can be verified experimentally. But again "in principle", due to detection inefficiency.

 

[vanhees71]

The idea that a photon lacks a position observable is laughable, as they are regularly observed at specific points in hundreds of experiments (as both detector clicks and in other manners) exactly as predicted. What you mean to say is that field theory does not allow for a photon position observable in the same sense as other quantum particle observables.

Well, we discuss science here, not wishful thinking.

The PDC photons used in Bell-test experiments are rather send through filters that they have a rather well-defined momentum to ensure a sufficient degree of coherence to enable these very experiments, and indeed you describe it right but draw the wrong conclusions: There's a position of detection events, determined by the position of massive detectors. What's measured by photon detectors are the appropriate one- or two-photon correlation functions.

 

[jeremyfiennes]

A different slant. The Schroedinger equation gives the probability of a measurement detecting a particle (photon or electron ) at a point. These probabilities always add up to unity. In other words, one cannot predict with certainty where the particle will be found. But one can predict with certainly that it will be found. Correct?

 

[DrChinese]

... indeed you describe it right but draw the wrong conclusions: There's a position of detection events, determined by the position of massive detectors. ...

It "right" because I make reference to representative experiments where this description is "useful". Those detectors are measuring arrival times of (bi)photons traveling on precise classical paths once they are corralled. I am not drawing any conclusion past what the experimenters are doing. You should be able to see the irony of asserting photons don't have position (operator), when you can measure that position to a precision limited only by experimental setup and the usual constraints of the Heisenberg Uncertainty Principle. That it is done with a detector is irrelevant. ALL particle detection events EVERYWHERE are brought to us by some detector or film or similar - you can't just deny the obvious position for photons and accept the same evidence for anything else just because it doesn't fit with your theory. The theory is not reality, but it can be a useful representation of reality.

Generally accepted science is: Photons exist, and their future position can be accurately predicted - within obvious constraints of the actual setup. This does not mean that photons are classical particles, they aren't - and I repeatedly say that it is a mistake to think of them in that manner. However, there are certainly many times when a photon exhibits the behavior of a classical particle - and such description can be useful. Certainly it is useful when the experimenter decides where to place the apparatus.

 

[Nugatory]

A different slant. The Schroedinger equation gives the probability of a measurement detecting a particle (photon or electron ) at a point. These probabilities always add up to unity. In other words, one cannot predict with certainty where the particle will be found. But one can predict with certainly that it will be found. Correct?

With the appropriate disclaimers about detector efficiency, yes. But this thread is about photons, so the non-relativistic Schrodinger's equation in the position basis isn't so relevant. Instead you have to look at how the single-photon state evolves over time.

 

[Nugatory]

You should be able to see the irony of asserting photons don't have position (operator), when you can measure that position to a precision limited only by experimental setup and the usual constraints of the Heisenberg Uncertainty Principle.

As a moderately interested bystander... it sure looks to me as if you and @vanhees71 are just rerunning the old discussion about whether it is more correct to say "it has position x" or "a detector at point x will trigger at time t". The first includes a few micrograms of unnecessary interpretational content, is more often useful, and is (IMO) more likely to reinforce B-level misconceptions.

 

[DrChinese]

As a moderately interested bystander... it sure looks to me as if you and @vanhees71 are just rerunning the old discussion about whether it is more correct to say "it has position x" or "a detector at point x will trigger at time t". The first includes a few micrograms of unnecessary interpretational content, is more often useful, and is (IMO) more likely to reinforce B-level misconceptions.

Maybe. This is the quantum forum, so it is always useful to add a caveat at the beginning of a discussion precisely to insure that such misconceptions are not propagated. I try to do that (and I think most are pretty good about that too, including @vanhees71). And once the OP acknowledges that, we should be able to describe the general case, and occasionally throw in an alternative scenario. On the other hand: we can also take things so far that there is no statement that can be made that is completely true in all cases. Hard to get a useful message across when every answer is "that's wrong" - which I sometimes see more often than "that's correct". I don't think every caveat is needed in a B level discussion as long as the key points are being made.

In scientific papers: I see "it has position x" statements about 10 times as often as a statement with caveat such as "a detector at point x will trigger at time t". Ditto in textbooks and the like. The exceptions and caveats should be brought in as the general rule gets into better focus, and there is relevance. That's my take, anyway.

 

[DarMM]

As a moderately interested bystander... it sure looks to me as if you and @vanhees71 are just rerunning the old discussion about whether it is more correct to say "it has position x" or "a detector at point x will trigger at time t". The first includes a few micrograms of unnecessary interpretational content, is more often useful, and is (IMO) more likely to reinforce B-level misconceptions.

Maybe. This is the quantum forum, so it is always useful to add a caveat at the beginning of a discussion precisely to insure that such misconceptions are not propagated. I try to do that (and I think most are pretty good about that too, including @vanhees71). And once the OP acknowledges that, we should be able to describe the general case, and occasionally throw in an alternative scenario. On the other hand: we can also take things so far that there is no statement that can be made that is completely true in all cases. Hard to get a useful message across when every answer is "that's wrong" - which I sometimes see more often than "that's correct". I don't think every caveat is needed in a B level discussion as long as the key points are being made.

I think both sides here are very understandable. On the one hand one wishes to be correct, on the other completely correct QM almost nullifies conversation.

What's a particle? Well according to fully general Quantum Field Theory a "particle" is a quantum state that at very late or very early times will "probably" make a certain type of experimental probe click once.

Why probably? Well no state will definitely make a detector click due to the Reeh-Schleider theorem.

Well at least we can always speak of properties like angular momentum etc right? Well no, most POVMs cannot be read as quantizations of classical properties. Thus the observable some pieces of equipment are measuring when they "click" are simply the observable representing that piece of equipment clicking! https://arxiv.org/pdf/quant-ph/0207020.pdf
As Peres says in that paper most quantum observables don't even have names in our vocabulary.

There's just preparations and clicks! No picture like classical mechanics. However people are used to talking about objects like photons etc

Hard to know what to do.

 

[A. Neumaier]

The Schroedinger equation gives the probability of a measurement detecting a particle (photon or electron ) at a point.

No. Phoons and electrons are not described by a Schrödinger equation but by the free Maxwell and Drac equation, respectively. Solutions of the Maxwell equations don't hve a probabilistic interpretation as probability density.

 

[vanhees71]

It "right" because I make reference to representative experiments where this description is "useful". Those detectors are measuring arrival times of (bi)photons traveling on precise classical paths once they are corralled. I am not drawing any conclusion past what the experimenters are doing. You should be able to see the irony of asserting photons don't have position (operator), when you can measure that position to a precision limited only by experimental setup and the usual constraints of the Heisenberg Uncertainty Principle. That it is done with a detector is irrelevant. ALL particle detection events EVERYWHERE are brought to us by some detector or film or similar - you can't just deny the obvious position for photons and accept the same evidence for anything else just because it doesn't fit with your theory. The theory is not reality, but it can be a useful representation of reality.

Generally accepted science is: Photons exist, and their future position can be accurately predicted - within obvious constraints of the actual setup. This does not mean that photons are classical particles, they aren't - and I repeatedly say that it is a mistake to think of them in that manner. However, there are certainly many times when a photon exhibits the behavior of a classical particle - and such description can be useful. Certainly it is useful when the experimenter decides where to place the apparatus.

A WRONG description is never useful. Physics is an exact science, and we should do our best to describe it correctly. Again: You cannot define the position of a photon (to some extent maybe you can define "transverse position" somehow). All you can define are probability distributions for a photo-detector, placed at some position (which is well-defined, because as a massive object you can always define a position observable for it). As it turns out from a quite straight-forward analysis of the detection process in terms of, e.g., the photoeffect (i.e., an electromagnetic wave kicks out an electron from a bound state to the continuum) the detection probability distributions of various kinds (usually 1- or 2-photon detection probabilities as function of time(s) and position(s)) can be calculated from autocorrelation functions of the electric-field components.

Of course, photons "exist". They don't have a position in the strict sense, and one should avoid to use undefinable ideas. To define what a photon is and how to measure relevant observables of it, you need a theory, and the best theory we have about them is QED. Of course, theory is not reality, but you cannot describe and investigate reality without it.

 

[DarMM]

Of course, photons "exist". They don't have a position in the strict sense, and one should avoid to use undefinable ideas. To define what a photon is and how to measure relevant observables of it, you need a theory, and the best theory we have about them is QED

I'm not going to get into "exist", but certainly there are photons in QED. The only difficulty is that in QED they are a type of excitation distribution in idealized probes/detectors placed at spatial and temporal asymptotic infinity. Strictly speaking they aren't well defined at finite times or outside detectors nor are they associated with a fixed number of clicks (though this last point can usually be ignored).
That's quite far from what people might normally have in their heads.

 

[vanhees71]

Of course, we can philosophize endless about the "ontology of photons/elementary particles". There's enough paper wasted on this fruitless subject ;-)). For me the particles of the standard model simply "exist" in the very specific sense you describe it: There are predictions of the theory (QED) which are confirmed to amazing precision by all measurements.

It's also clear that QED tells us that a particle (photon) description is only possible in the sense of asymptotic free states and strictly speaking it also tells us that this is a far from trivial concept, because of the long-range nature of the em. interaction (aka the "masslessness" of the photon field), but that's another story.

 

[DarMM]

For me the particles of the standard model simply "exist" in the very specific sense you describe it: There are predictions of the theory (QED) which are confirmed to amazing precision by all measurements.
...
It's also clear that QED tells us that a particle (photon) description is only possible in the sense of asymptotic free states

Yeah no disagreement of course. Just the chasm between that what people normally think and QFT says is quite a hard one to cross and it's difficult to know what to say in a "B" thread.

I think the common notion is that a photon is a thing flying around out there with maybe some "quantum weirdness" associated with the uncertainty principle. This is the sort of picture you might get from non-relativistic QM where particles might have uncertainties and so on associated with their observables, but at least you clearly have the particle itself had all times.

In QFT though we lose even that, having a particle only as a late time excitation in a specific detector type as you said.

 

[vanhees71]

The problem is that even in otherwise good textbooks this wrong picture of a "photon" as some localized lump of matter (like a miniature "billard ball") persists. It's just laziness of textbook writers to introduce QM in an "as simple as possible but not simpler" way. In the case of popular-science writing it's not shear laziness of the authors but the impossibility to really describe photons without the adequate math.

But still there, I think you can do a better job:

I think it's sufficient to first tell the readers about the classical concept of light as an electromagnetic wave. It's not so hard to make the classical-field concept understandable without any math. Then you can refer to what we perceive as light (intensities, colors etc.) from a physical point of view. When this is made clear you can argue with Planck's finding that the energy exchange of electromagnetic fields with a typical frequency $\omega$ happens only in "discrete packets" of $E=\hbar \omega$. You can also tell that the electromagnetic field carries momentum, and that it also comes in "packets" of the size $p=2 \pi \hbar/\lambda$. I think to specify photons as these "energy-momentum packets" is a better picture than the "bullet picture". One can then also stress the "indivisibility" of these packets, i.e., that whenever they are detected on a photo plate or with a cell-phone camera (CCD) they leave a "single spot", and that is the only way you can associate a (transverse) position of these packets, and that's the only "particle-like feature" such a photon has and that in general you cannot say in advance, where a specific "packet" will be registered on the photo plate but that one can with the comoplicated math of QED only predict the probability distribution that it hits the plate at a given place.

 

[DarMM]

that whenever they are detected on a photo plate or with a cell-phone camera (CCD) they leave a "single spot"

Yes I think this gets to the heart of the matter. People are lead to think photons are something that hits the camera and causes the excitation of a pixel, where as under QED it is more the case that a photon is the excitation of a pixel in a camera and QED gives rules for the probability of a given pixel being excited a given amount.

 

[vanhees71]

The irony is that this view was already provided by Planck, but Einstein's view of 1905 prevailed though Einstein himself said that he was still puzzled by what "radiation really is" till his death. It's also ironic that Einstein got his Nobel prize for the only theory of his that didn't stand the later development of physics and that his Nobel certificate is the only (?) one that cites for which achievement he definitely did not get the prize, i.e., relativity ;-))).

 

[PeterDonis]

A WRONG description is never useful. Physics is an exact science

I think you're going to have a very hard time justifying those statements in the face of the obvious facts that physicists use approximations all the time and that all measurements have some finite error.

 

[vanhees71]

Of course you have to use approximations and any measurement has a finite error, but you shouldn't refer to wrong qualitative descriptions to begin with, at least if you know better!

 

[Nugatory]

but you shouldn't refer to wrong qualitative descriptions to begin with, at least if you know better!

Hmmmm... I remember when my five-year-old child asked me where babies come from and how exactly the seed gets into the mommy...

Wrong qualitative descriptions have their place.

 

[DarMM]

Hmmmm... I remember when my five-year-old child asked me where babies come from and how exactly the seed gets into the mommy...

Wrong qualitative descriptions have their place.

You didn't reveal the truth about Santa I hope.

Spoiler: Reveal at your own risk

He violates locality

 

[vanhees71]

Hmmmm... I remember when my five-year-old child asked me where babies come from and how exactly the seed gets into the mommy...

Wrong qualitative descriptions have their place.

Mh. I'm not an expert in children psychology, but I guess if in doubt adequate honesty should be a good strategy in this case too!

 

[jeremyfiennes]

Ok. I never imagined the question was that complicated, but I get the general drift. Thanks all.

 

[DrChinese]

1. The problem is that even in otherwise good textbooks this wrong picture of a "photon" as some localized lump of matter (like a miniature "billiard ball") persists. It's just laziness of textbook writers...

2. A WRONG description is never useful. Physics is an exact science.

1. You've made this insulting and baseless accusation ("laziness") a number of times previously. And I am going to argue these same textbook writers - many with impeccable credentials - are making deliberate decisions for the much the same reasons - and it is not because of their laziness. They know their audience.

2. I don't know where to start with this historically* ridiculous statement. All science - including physics - is provisional to a better theory. I don't know what gives you the impression current theory is exempt, but according to your standard QED will soon be WRONG.

-DrC*I wonder how Marconi built a useful radio with his WRONG theory.

 

[vanhees71]

I don't know, why you feel insulted, or are you also one of those textbook writers?

Ad 1. I made this somewhat ironic remark about the many textbook writers who start the QM 1 textbooks with some introductory chapter copying the wrong statements about photons being some localized point-like particles and bring the usual arguments for this picture (usually the photoelectric and Compton effect). It's just laziness not to reformulate this introductory sections in a way appropriate to the fact that this picture is outdated for over 90 years by now. It is bad to start the heuristics of a topic, and the heuristics is utmost important for students starting to learn a subject to get a RIGHT physical feeling for it, which is qualitatively wrong. The worst cases are to use the Bohr-Sommerfeld model of atoms since it cements the wrong picture of trajectories of electrons running around a nucleus to make up an atom, and this has to be unlearnt subsequently. It hinders to gain a heuristical understanding of quantum theory. It is hard enough to get used to the specific thinking, and I mean qualitative thinking as prerequisite to make sense of the quantitative full theory, you need for QT. It should not be made even more difficult by starting with wrong qualitative conceptions. Since relativistic QFT is even more subtle on the qualitative level than non-relativistic QM, this is the more important for this case and thus particularly photons.

Ad 2. I've no clue what you mean here. Particularly what have the achievements of Marconi to do with QM or QFT? He built his useful radio based on a correct theory, namely classical electrodynamics a la Faraday and Maxwell. It's also hard to conceive that QED will be found "wrong" in the sense that the Bohr model or the naive particle-like photon model (in other words the entire "old quantum theory") are wrong.

There's a difference from models that are really wrong already on a qualitative level like "old quantum theory" and models, of which just limits of applicability have been found like for classical Newtonian mechanics or classical electrodynamics, both of which are perfectly valid in specific and well-understood situations. They are approximations of more comprehensive models in specific limits and thus not qualitatively wrong. That's why it's much better to think about a photon rather in terms of a classical electromagnetic wave than in terms of a localized bullet-like object.

Marconi didn't use photons but "coherent states" for his radio, which are very well described by classical Maxwell theory.

 

[DrChinese]

1. I don't know, why you feel insulted, or are you also one of those textbook writers?

2. Marconi didn't use photons but "coherent states" for his radio, which are very well described by classical Maxwell theory.

1. You didn't insult me, you insulted other professionals by calling them lazy. If you disagree with them, I get that, but there is no need to sling insults. That's inappropriate.

2. Exactly why I say that a) there is no "right" theory, there are only theories (descriptions) that are useful in various situations. In many situations, it is useful to think of photons as point particles moving at c in a straight line. In other situations, it is useful to think of light as expanding classical wave packets lacking specific position. And in yet other situations, photons are excitations of the EM field. All of these are right in the sense they are useful descriptions, and authors of scientific books and papers use all of these varying descriptions (and many more) regularly in the literature.

You appear inflexible by sticking to one and only one description of the photon (one which is shunned by most textbook authors, by your own admission). Your description often seems useless in the context of B level threads. Labeling one description as "right" and another "wrong" - when both are useful in proper context - makes no sense to me.

Just my opinion.

 

[charters]

I think the common notion is that a photon is a thing flying around out there with maybe some "quantum weirdness" associated with the uncertainty principle. This is the sort of picture you might get from non-relativistic QM where particles might have uncertainties and so on associated with their observables, but at least you clearly have the particle itself had all times.

In QFT though we lose even that, having a particle only as a late time excitation in a specific detector type as you said

What then do you make of Haroche's photon non-demolition measurements or Vaidman/Aharonov's weak measurements revealing photon trajectories?

 

[DarMM]

What then do you make of Haroche's photon non-demolition measurements or Vaidman/Aharonov's weak measurements revealing photon trajectories?

Do you have an analysis of these directly in QFT? Most of the time I see them they're essentially in a fixed particle QM framework where the notion of a particle at all times is pretty clearly defined.

Ultimately I wouldn't see these as any more special than the hydrogen atom. In fixed particle QM it's composed of one electron and one proton at all times and this is a good approximation that matches most experiments. Most experimental set ups show results consistent with one proton and one electron. So we have
$$\mathcal{H}_{H} \subset \mathcal{H}_{e^{-}}\otimes\mathcal{H}_{p}$$

However ultimately in QED that's not what hydrogen is like, it's a state that under certain interactions evolves to a superposition containing states $|\alpha\rangle$ that at asymptotic times behave as electron, proton product states. So we have:
$$\mathcal{H}_{H} \not\subset \mathcal{H}_{e^{-}}\otimes\mathcal{H}_{p}$$

Interacting QFTs just don't have a well-defined particle number operator at all times. The Fock structure of particles only emerges at late times far from interactions.

 

[charters]

Do you have an analysis of these directly in QFT? Most of the time I see them they're essentially in a fixed particle QM framework where the notion of a particle at all times is pretty clearly defined.

Aharanov/Vaidman do their work in optics. Haroche I believe uses cavity QED. But I am not sure this matters, as these are actual experiments, not theoretical models. However photons/light behave in reality, these experiments are certainly telling us something reliable about this.

However ultimately in QED that's not what hydrogen is like, it's a state that under certain interactions evolves to a superposition containing states |α⟩|α⟩|\alpha\rangle that at asymptotic times behave as electron, proton product states.

Interacting QFTs just don't have a well-defined particle number operator at all times. The Fock structure of particles only emerges at late times far from interactions.

Agreed, but in realistic experiments, "late times" is not actually so late after all (nowhere near asymptotic infinity). So what we have on reasonable time and length scales is a state that is already nearly Fock-like - Jonathan Bain suggests the relevant scale is $10^{-13}$ seconds (https://link.springer.com/article/10.1023/A:1026482100470).

Over these distances and longer, it does seem like these photons (as perhaps emergent entities) follow (superposition of) trajectories. We can experimentally reconstruct these trajectories by making non-demolition measurements along the path. Given this, I find it difficult to accept photons are *just* click patterns in macroscopic massive detectors. Or at a minimum, I would this as requiring a broader commitment to strict empiricism, where I would have to say the same about electrons, proteins, and bacteria.