Photon Continuity in Double-Slit Experiment

[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.

 

[DarMM]

Well according to QFT in general states don't have a particle decomposition. Of course there are regimes where it is an excellent approximation, that's why we can use QM where particle number is well-defined.

However according to work on field theory by Haag, Ruelle and others in general this picture is not possible and in general we can only work with the notion of number expectation values for asymptotically placed probes. Steinmann in his monograph "Perturbative Quantum Electrodynamics and Axiomatic Field Theory" discusses this, as does Haag in his "Local Quantum Physics", as well as Araki in Chapter 5 of his "Mathematical Theory of Quantum Fields". Particles are only really well defined as clicks in appropriate detectors. Araki uses the phrase "Particle Counter Observable", Steinmann "Particle Probe".

Even then the asymptotic particle states won't definitively lead to $N$ clicks. So in the most general case it is hard to decompose quantum field theoretic states into being combinations of particle states.

Ultimately this just means QFT doesn't have particles as a fundamental notion. I don't see anything that would make you say a bacteria is just a click in a detector, although that combined with "empiricism" sounds like it's heading into a philosophical discussion which isn't my aim. It's just a statement about how particles are defined in QFT in the most general case. Going from "In QFT particles seem to be associated with asymptotically placed detectors, resulting in a count distribution centered around $N$, an integer we call the particle number" to "bacteria aren't real" seems like a long mostly philosophical discussion.

 

[charters]

I'm not really talking about an exactly valid number operator though. I'm thinking about what I quoted in #58.

I agree Fock states are only truly asymptotically valid in QFT (though I am unsure if this still holds in string theory, so perhaps this is a symptom of underlying pathologies in QFT and should not be trusted). But I don't take this to be so relevant to the question of photons having trajectories through spacetime, versus only believing in detector click correlations.

I'm saying: whenever something like an individual photon (or EM coherent state) can be identified fairly well - which in reality is a huge percentage of the time, but definitely not all the time in QFT - then it does appear to follow a superposition of paths through spacetime. There does seem to be a wavepacket that traverses the intervening spacetime between detectors. It doesn't only exist *as* detector clicks per se, ie as merely an effect that jumps discontinuously from source to detector with no presence along a path in the meantime.

I only mentioned bacteria to anticipate the response of: "well we only access information about photons through detector clicks, so who is really to say where the photon is between clicks". I see this as a more general view about observing anything microscopic, which is different from the question of photons in particular not having paths. The latter is specifically related to the absence of a formal position operator for (spin 1) massless fields. The question is what ontological moral should be drawn from this mathematical result in light of experimental measurements in which photon paths can be reconstructed just as well as electron or molecule paths.

Even then the asymptotic particle states won't definitively lead to N clicks

Is this a Reeh Schlieder argument, ie the asymptotic detector is compactly supported but the asymptotic N particle states are global, and these don't commute? Or are you saying something else here?

 

[DarMM]

Is this a Reeh Schlieder argument, ie the asymptotic detector is compactly supported but the asymptotic N particle states are global, and these don't commute? Or are you saying something else here?

Basically that. It's a corollary of the Reeh-Schlieder theorem.

though I am unsure if this still holds in string theory, so perhaps this is a symptom of underlying pathologies in QFT and should not be trusted

I don't think we should not trust a feature of a stringently tested physical theory (QFT) because it's not present in a incompletely developed theory with no experimental support (String Theory).

then it does appear to follow a superposition of paths through spacetime. There does seem to be a wavepacket that traverses the intervening spacetime between detectors

This is going into interpretation stuff, about the quantum state being a "real" wave.

Ignoring this, even for two photons we don't have this notion of a wavepacket traversing intervening spacetime since it isn't a function on spacetime.

The point is in QED particulate behavior only manifests in specific detector types at asymptotic times. If you'd used the wrong types of detectors you don't get particle behavior even at asymptotic times. Really this is because QFT promotes "particle" to having the same counterfactual difficulties that spin and other observables have in non-relativistic QM.

source to detector with no presence along a path in the meantime

Even in fixed particle QM though talking about "paths in the meantime" is fraught with difficulty.

The thread is originally about photons, but my comments are more about particles in general in QFT. In QFT both electrons and photons are associated with asymptotic detectors, which due to Reeh-Schlieder are necessarily always noisy, i.e. no state definitely causes $N$ clicks.

The noise in a detector is related to its size, i.e. the standard deviation of clicks is proportional to the detector volume. However for electrons since they are massive the standard deviation decays as $\mathcal{O}\left(e^{-mV}\right)$ and for photons it is only something like $\mathcal{O}\left(\frac{1}{V^{a}}\right)$ for some $a$.

Ultimately this is related to photons not really having a non-relativistic limit. Since position operators of particles aren't really a "native" notion to QFT, being able to construct one is in essence asking if you can form a well-defined single particle non-relativistic quantum theory. For electrons you can, since errors in detectors fall off exponentially and they have a non-relativistic limit. Photons don't satisfy either of these so you can't.

 

[charters]

Ignoring this, even for two photons we don't have this notion of a wavepacket traversing intervening spacetime since it isn't a function on spacetime.

Why not? If this concerns particle indistinguishability or higher dimensional configuration space, I think this position confuses Fock space indices with the localized wavepackets that actually matter/interact in the real world. See https://arxiv.org/abs/1002.2544

If you'd used the wrong types of detectors you don't get particle behavior even at asymptotic times.

What is a (non-theoretical, physically constructed) example of such a detector?

In QFT both electrons and photons are associated with asymptotic detectors, which due to Reeh-Schlieder are necessarily always noisy, i.e. no state definitely causes NNN clicks.

The noise in a detector is related to its size

No question this is correct under the assumption that a detector can be compactly supported, even though they are made of nucleons and electrons, which cannot be compactly supported. Obviously I'm skeptical about this assumption in general, but even granting it, I don't see how it is relevant here.

My issue is: even when allowing for some detector noise (both Reeh Schlieder and generic background), nondemolition experiments are able to quite reliably mark out the path a photon or multiple photons took, the same as can be done for massive particles. So, why isn't this good enough or trustworthy enough to evidence that a photon wavepacket travels along a continuous lightlike trajectory? Why doesn't this suggest the mathematical result is something of an artefact?

Why is the mathematical absence of a photon position operator more compelling than the experimental evidence, which seems to allow us to mark off time ordered photon positions? Or what experiment could be done with massive particles but not massless particles, such that the formal lack of a position operator would have real implications?

 

[DarMM]

Why not? If this concerns particle indistinguishability or higher dimensional configuration space, I think this position confuses Fock space indices with the localized wavepackets that actually matter/interact in the real world. See https://arxiv.org/abs/1002.2544

The general understanding in QM is that a wavefunction of let's say $N$ particles which individually move on a manifold $Q$ is a function in $\mathcal{L}^{2}\left(Q^{n}\right)$. This can't be regarded as a function on $Q$.
I noticed many of the papers citing that one are philosophical, arguing about metaphysics of identity. I don't want to go down this line.
Again the conventional understanding is that multiparticle wavefunctions cannot be seen as functions on the classical configuration space of a single particle and that this blocks regarding them as functions on spacetime.

No question this is correct under the assumption that a detector can be compactly supported, even though they are made of nucleons and electrons, which cannot be compactly supported

Well in QFT things aren't fundamentally made of particles. Electrons and nucleons are particles and thus a late time idealization. That they can't be localized is not really a problem for the detector. My attitude to this is similar to @vanhees71 here:
https://www.physicsforums.com/threa...ctron-violates-causality.975594/#post-6216222

nondemolition experiments are able to quite reliably mark out the path a photon or multiple photons took, the same as can be done for massive particles

Even in nonrelativistic QM we can make multiple position measurements in quick succession and they sort of trace a path. However from complementarity we know this doesn't mean we can ascribe a classical notion like a path to them. We can perform position measurements of electrons in hydrogen but we know it doesn't move along orbits.

In general most POVMs don't correspond to the quantization of any classical quantity. They're nameless as such aside from being the POVM representing that device.
https://arxiv.org/abs/quant-ph/0207020
The whole notion of thinking of $N$ photon states as multiple wave packets moving along paths is just not possible.

What is a (non-theoretical, physically constructed) example of such a detector?

Anything that measures coherent states, like teslameters or magnetometers.

 

[charters]

The whole notion of thinking of NNN photon states as multiple wave packets moving along paths is just not possible.

How do you reconcile this with the existence of the worldline formalism?

To be clear, I am not claiming a photon/any particle has *classical* path, I am just claiming it is reasonable to say the photon/any particle was present along the superposition of possible spacetime paths between emission and absorption, after accouting for interference among such paths.

Anything that measures coherent states, like teslameters or magnetometers.

But coherent states are in the global Fock space (can be seen as superpositions of the number operator) and are more easily localized than particle states/have even more classical seeming paths. The question was identifying some real world measurement which undermines the notion that massless particles/excitations sweep out a continuous, microcausal path through spacetime, such that we must restrict our speech to only detector click correlations.

 

[vanhees71]

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.

Hm, I meant the conjecture that textbook writers may be lazy not as an insult but as an excuse for not writing about the correct modern picture we have about photons. I'm sure almost all of these textbook writers know the correct theoretical description of photons. That's why I think it's rather laziness to rewrite the introductory chapters of their textbooks than ignorance of the theoretical and empirical facts.

Also at B-level you should not tell the people wrong things. You can, of course, not really explain what a photon is without the use of field operators, but you can at least write correct things in words rather the just copying long outdated wrong pictures from a time, where no consistent theory about the interaction of electromagnetic waves with matter on a fundamental level was available. Nevertheless this theory, QED, is available now since 1926 (Born, Jordan) or better knowns 1927/28 (Dirac)!

 

[vanhees71]

Well according to QFT in general states don't have a particle decomposition. Of course there are regimes where it is an excellent approximation, that's why we can use QM where particle number is well-defined.

However according to work on field theory by Haag, Ruelle and others in general this picture is not possible and in general we can only work with the notion of number expectation values for asymptotically placed probes. Steinmann in his monograph "Perturbative Quantum Electrodynamics and Axiomatic Field Theory" discusses this, as does Haag in his "Local Quantum Physics", as well as Araki in Chapter 5 of his "Mathematical Theory of Quantum Fields". Particles are only really well defined as clicks in appropriate detectors. Araki uses the phrase "Particle Counter Observable", Steinmann "Particle Probe".

Even then the asymptotic particle states won't definitively lead to $N$ clicks. So in the most general case it is hard to decompose quantum field theoretic states into being combinations of particle states.

Ultimately this just means QFT doesn't have particles as a fundamental notion. I don't see anything that would make you say a bacteria is just a click in a detector, although that combined with "empiricism" sounds like it's heading into a philosophical discussion which isn't my aim. It's just a statement about how particles are defined in QFT in the most general case. Going from "In QFT particles seem to be associated with asymptotically placed detectors, resulting in a count distribution centered around $N$, an integer we call the particle number" to "bacteria aren't real" seems like a long mostly philosophical discussion.

Just to put it in a more physical context concerning photons: I think what's measured today in quantum-optics labs is mostly well-described by the appropriate autocorrelation functions of electro-magnetic-field operators, as detailed in any textbook on quantum optics, e.g., in my favorite by Garrison and Chiao. This also automatically provides the necessary space-time information about the "clicks", i.e., that's how in a sense photons get "localized", but not in the sense of position observables but in the sense of space-time information of the "click events".

The expectation values have to be taken with the appropriate states describing the preparation of the electromagnetic field being detected. Some usual ones nowadays range from thermal radiation, described by the Statistical Operator $\propto \exp(-\beta \hat{H})$, coherent states (e.g., Gaussian beams from a laser), and finally also Fock states with a definite photon number (like single-photon states, entangled pairs from parametric downconversion).

Qualitatively photons are the prime example for the fact that "particle properties" occur in the detection process, i.e., without detection there's not even a well-defined notion of localizability of a photon as some "point-like object". Formally that's seen from the fact that one cannot construct a proper position operator for photons.

In the relativistic realm it's even difficult for massive particles since due to the constraint by the relativistic "speed limit" localizability of massive particles is although constrained though a position observable is always constructable, but make usually "particle sense" only for asymptotic free states. The reason is also heuristically simple: If you want to localize a massive particle like an electron you somehow have to force it into a small region in space, which rather leads to the creation of new particles like electron-positron pairs than a better localization as intended.

Consequently also a "particle-number observable" is available only for asymptotic free states. The interpretation of "transient states" in scattering processes in terms of "particle states" is at least problematic. If I understand @DarMM right, it's even mathematically impossible within mathematically more rigid formulations of the theory!

 

[DarMM]

How do you reconcile this with the existence of the worldline formalism?

To be clear, I am not claiming a photon/any particle has *classical* path, I am just claiming it is reasonable to say the photon/any particle was present along the superposition of possible spacetime paths between emission and absorption, after accouting for interference among such paths.

A path integral is a way of computing the analytic continuation of quantum theoretic correlation functions, that is computing Schwinger functions. Thinking of this in terms of "being in a superposition of paths" isn't valid to me because it's a decomposition only possible after Wick Rotation where the Schrodinger equation becomes a Heat equation and thus can be recast as a modified Brownian motion.

But coherent states are in the global Fock space (can be seen as superpositions of the number operator) and are more easily localized than particle states/have even more classical seeming paths. The question was identifying some real world measurement which undermines the notion that massless particles/excitations sweep out a continuous, microcausal path through spacetime, such that we must restrict our speech to only detector click correlations.

Coherent states are just a simple example. As you said they're not particle states and their operators don't commute with particle operators. So we have non-particle states that are complimentary to particle ones, thus you can't really think of particles as being fundamental since there are observables that are complimentary to them.

Of course they are very classical in a sense, one can have non-particle states that are highly quantum. They're just a simple example of a very "non-particle" state, the field like states with minimum uncertainty. The actual Hilbert space is not a Fock space, so that fact that "field like" coherent states can always be expressed as a superposition of particle states in a free theory doesn't matter in the more general interacting case.

@vanhees71 has interesting details above about photons and detectors.

 

[vanhees71]

Why not? If this concerns particle indistinguishability or higher dimensional configuration space, I think this position confuses Fock space indices with the localized wavepackets that actually matter/interact in the real world. See https://arxiv.org/abs/1002.2544

I've already have a hard time to understand the arguments of the introduction. How can the authors claim that "all electrons in the universe are in the same state"? As fermions they are obviously not. The Fock space basis wrt. the single-particle position-spin basis shows that of course no two electrons can be in the same single-particle state since $[\psi^{\dagger}(\vec{x},\sigma_z)]^2=0$ (I argue with non-relativistic electrons to avoid complications with relativistic particles, but in principle the arguments are all the same).

Correct is of course that in any $N$-indistinguishable-particle Fock state, which is what the authors seem to discuss in the introduction, the particles cannot be individualized. Writing the state down in position-space-spin representation you can only give the probability distribution for finding the $N$ particles around any given place in $3N$-dimensional with given spin components, but it's impossible to somehow specify anyone individual particle. This is of course even more the case for more general states, i.e., there's no way to prepare a collection of any number of particles (or some state where the particle number is not determined either) such that one can individualize one or more particles. That's why one should not talk about "identical particles" but about "indistinguishable particles". You cannot say if you measure an electron, whether it's the same, you measured some time before or if it's another one since there's no way to individualize any electron against any other. They are indistinguishable but not necessarily identical. The authors are of course right in saying that particles are distinguishable whenever they differ in at least one intrinsic property (within the standard model by mass, spin, and various charge-like quantities like electric charge, baryon number, lepton number, etc.). E.g., an electron and a muon is distinguishable by their masses (but nothing else, being both charged leptons!).

The good thing is that we don't have to care much about this indistinguishability descriptions by just using the QFT formulation (no matter whether you deal with a relativistic or non-relativistic model). Then you don't even fall into the trapp of trying to individualize particles by their position and spin (or momentum and spin or whatever single-particle basis you like to use in an application). E.g., instead of writing down antisymmetrized $N$-electron wave functions ("Slater determinants") you write down the corresponding particle-number eigenstates, saying I prepare a state $|\{N(\vec{x},\sigma_z) \}_{\vec{x} \in \mathbb{R}^3,\sigma_z \in \{\pm \hbar/2\}}$, which just tell me the number of particles at each position and spin with $N(\vec{x},\sigma_z) \in \{0,1 \}$ for all $\vec{x} \in \mathbb{R}^3$ and $\sigma_z \in \{\pm \hbar/2 \}$.