More Than You Wanted to Know About Photons

Gell-Mann Amnesia in action, but in a good way?

I generally enjoy Noah Smith’s stuff both here and on ex-Twitter, but he tossed off a tweet today that shaded toward Gell-Mann Amnesia territory (screenshot because petulant billionaires):

This is… not right. In a bunch of ways, some subtle, others less so. None of the wrongness is actually all that important, but having just spent a bunch of time teaching about photons, it might be fun¹ to spend a little while unpacking this. Which I’ll do in a Q&A format because it’s been a while and I need a little variety in my self-imposed writing projects.

OK, then, what’s wrong with Noah’s claim? It seems fine to me…

You don’t really think it’s going to be simple, do you? To explain the issues here, we need to back up a little and talk about what a photon is.

Fine, then, what’s a photon?

I think the most complete and least controversial definition I could give would be something like “A photon is a single excitation of light at a particular frequency, carrying an energy corresponding to Planck’s constant multiplied by the frequency and a momentum equal to Planck’s constant divided by the wavelength, directed in whatever direction the light is traveling, and one unit of angular momentum with a direction depending on the polarization.” I don’t think there’s anything in there that would be contested all that strongly, though there are some technicalities being swept up in the word “direction.”

The problems come when you try to put that in less technical language. As soon as you start down that road, you start generating disagreements.

You’re going to need to start down that road, though, because I’m not really following all that.

Totally normal, but also why physicists and philosophers have been yelling at each other about quantum physics² for more than a hundred years. There’s a very clear mathematical specification of what a photon is that doesn’t map neatly onto anything we have physical intuition about. When you try to start using analogies to make sense of it, every choice you make to highlight one aspect will fail to capture some other aspect, and somebody will get upset that you’re getting that bit wrong.

The clearest example of this in action is the very common description of a photon as “a particle of light,” which is good at capturing a couple of important features— a photon carries a definite and discrete amount of energy and momentum, and will only be detected at a single position at a particular instant— while creating the false impression that it’s like a little ball traveling along a particular path.

Wait, how is it not following a particular path? Doesn’t it just move along the beam of light?

Not exactly. The most obvious issue is that you can split the path of a beam of light, and see interference, if you make something like a Mach-Zehnder Interferometer:

This shows a beam of light coming into a beamsplitter that passes half the light through, and reflects half upward. The two beams are brought back together at a second beamsplitter, which splits the light from each path between two detectors, so that each detector sees one quarter of the original beam from each of the two paths³.

If the photon behaved like a classical particle, you would expect each detector to record half of the original amount of light— if you send in a million photons per second, you’d get 500,000 per second at each detector, no matter what else you did.

Yeah, I mean, that’s just common sense.

Except this is quantum physics, so common sense can’t be trusted. See, light also has wave-like character, so the actual result depends on the relative lengths of the two paths. If the waves at the detector in a way that makes the peaks of the wave from one path arrive fall atop the peaks of the wave from other, that gives you a larger fraction of the original light; when the peaks of one wave fill in the valleys of the other, you get less light. If you make one of the paths longer and shorter (say, by moving the bottom mirror back and forth, as indicated by the green arrows), you can shift where the light ends up. Each individual detector can get anywhere from 0% to 100% of the incoming photons.

That’s what’s represented in the graph labeled “A” on the right of that figure: the two colors correspond to the two detectors, and you can see that when one gets lots of photons, the other gets none, and vice versa.

So, the photon splits in two, and then comes back together?

Not really, in that the photon can only ever be detected at one place— you’ll never find half-a-photon on each of the two paths. But a lot of physicists (myself included) will say things like “The photon follows both paths at the same time,” which is weird and non-classical but still retains some particle essence. Other physicists, though, will vehemently object to that.

Object why?

Well, because it carries an implication that the photon has a definite position at a time between its creation in whatever the light source is and its detection at one of the detectors. A really strict interpretation of what quantum mechanics says would hold that the photon is simply an excitation of a mode of a field, which is inherently not localized to any particular position. The field is everywhere at once, and it’s only the detectors that are localized. Any statement about what the photon “is doing” in the time between creation and detection is nonsense.

That seems… weird.

It’s a very particular worldview, to be sure. Personally, I take the point that we need to be a little careful about these things, but don’t really have the visceral objection to the idea of a photon traveling along through space, because it’s a useful heuristic in a lot of situations.

We’re getting kind of off-topic at this point, aren’t we? Isn’t this supposed to be about the detection of photons?

Well, it’s both off-topic and on-, in a sense—

Schrodinger’s cat!

…sure. Anyway, the main point of that was just to illustrate that there are a lot of arguments about what you can and can’t say about photons and what they’re doing. Which carry over into arguments about what you can and can’t say about how they’re detected.

How are they detected, then?

Well, again, if you want a statement that I think would get the fewest possible objections from physicists, it would be something like “We record the detection of a photon when all or part of its energy gets transferred to some other system.” The most obvious way this happens is in something like a photomultiplier tube where a photon strikes a metal surface and gives up its energy to an electron. That electron is then accelerated away from the metal to another plate where it knocks loose several more electrons, and that process is repeated until there are enough of them to register as a current pulse that’s recorded electronically.

Okay, that makes sense, but you said “all or part of its energy.” How does it give up part of its energy if it’s a particle?

There’s a famous experiment called “Compton scattering” where a high-energy photon strikes an electron and transfers some energy to it, but not all. You start off with a photon and an electron at rest, and end up with an electron that’s moving and a photon with slightly lower energy, heading in a different direction.

The moving electron can then collide with other things and create a flash of light that is detected, allowing you to say “A photon was here at this particular moment.” You can then separately detect the lower-energy photon that left, and measure its energy, which depends on the direction it went in a simple way. Arthur Holly Compton discovered this with x-rays in the early 20th century, and eventually figured out the right interpretation of the data. This is one of the pivotal moments in getting the majority of physicists to accept that light must have particle character.

I don’t want to spoil your fun, dude, but both of those sound like what Noah said: the photon is detected when it runs into something.

This is actually the more obvious of the wrongnesses of his answer: in both of these cases, the photon ceases to exist. The original framing is about how it “knows” something, but it’s not there to know anything any more.

I get that for the phototube, but how can you say that the photon is destroyed in the Compton thingy?

Well, the definition of a photon is an excitation of the electromagnetic field with a particular energy moving in a particular direction. In Compton scattering, the photon that leaves has a lower energy than the one that came in, and is heading in a different direction. The initial photon has ceased to exist.

The proper mathematical treatment of this process describes it as the annihilation of a photon at one particular energy and momentum followed by the creation of a different one with a lower energy and a momentum that is smaller in magnitude by an amount that depends on the change in direction.

That seems kind of pedantic, honestly.

I would like you to consider for a moment what it is that I do for a day job.

Point taken. You said this “not the same photon” thing was the more obvious wrongness. What’s the less obvious one?

Well, the original question was “How does a photon know it’s being observed?” which doesn’t have to mean direct detection of the photon. In fact, there are some very profound effects that can come from less dramatic forms of observation.

Such as…?

Well, if you look back at the Mach-Zehnder interferometer, I said that if the photons behaved like classical particles, with a definite position, you would expect 50% of them at each detector all the time. You’ll notice a figure labeled “B” on the right side of that image that does just that: no matter where the mirror is moved, each detector sees the same number of photons (more or less).

Yeah, what’s up with that?

That’s a case where they’ve done something to make it clear which path the photon took: for example, using a beamsplitter that reflects photons with vertical polarization and transmits photons with horizontal polarization. This essentially amounts to observing which path the photon took, and wipes out the interference pattern.

So they detect only vertical photons at one detector and only horizontal at the other?

Actually, it doesn’t matter whether they measure the polarization at the detectors or not— just setting up the measurement in such a way that you could measure which path the photon was on is sufficient to destroy the pattern. This is commonly called a “which-way” experiment⁴.

Right, so polarizing the photons makes them pick one path or the other?

Actually, it’s even weirder than that. You can do something after the second beamsplitter that removes your ability to tell which polarization the photon had, and when you do, the interference comes back. This is called a “quantum eraser” experiment, because it’s a bit like you’ve made a mark on each photon to indicate which path it took, and then erased the mark to recover the interference.

The actual data in those graphs above is from a quantum eraser— they used a polarizing beamsplitter and a system where they either erase the polarization tag (graph A) or not (graph B) without changing much. In really sophisticated experiments, they switch between the polarization-sensitive and polarization-erased states randomly and rapidly— in less time than it would take light to travel from the first beamsplitter to the detector. What you’re looking for at the detector changes while the photon is in flight, so it’s not as simple as just setting an outcome at the first beamsplitter.

So there’s a sense in which the photon always takes both paths, but is “aware” of whether its path has the potential to be observed or not, and acts accordingly when it gets to the detector.

That’s… super weird. How does it know?

That’s one of those questions that people yell at each other about. A lot. People who favor a more particle-like view tend to talk in terms of the polarization elements changing the state of the particle as it travels through the apparatus.

People who are more committed to the only-fields⁵ picture would say that the photon is only an excitation of a particular mode of the field, and that the available modes are determined by the configuration of the apparatus. You can only ever detect what you’ve set the detectors up to be able to detect, so it’s no surprise that that’s what you see.

How do they handle the thing with the rapid switching, though?

Well, they don’t need to, because they don’t believe in the photon as a thing that’s “in flight”— it’s an excitation of a field and those don’t have a position at any intermediate time. The available modes change instantaneously, which seems weird from a classical standpoint, but quantum physics isn’t bound by local realism, and you can show that there’s no transfer of information in these changes, so it doesn’t raise problems with relativity. It’s just very… abstract, but not significantly more so than the general field picture.

And this has what to do with Noah’s tweet, again?

Not so much with his tweet, but with the one he’s quoting. The point is, there’s a sense in which photons “know” that they’re being observed in a way that’s well short of actually detecting the photon, but has dramatic consequences for the pattern of photons that are actually detected in a quantum eraser experiment. And how you say that that happens is much more subtle than the idea of photons bumping into things.

Hmm. Well, I still think it’s weird that you object to what seems like a pretty anodyne comment, but I guess I learned something…

Then my work here is done, and I’m going to go back to making slides about quantum algorithms for next week’s classes.

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If you want a bunch more of this kind of thing, the absolute best thing you can do would be to buy my book. You can also click this button:

And if you have questions or can find an objection to my attempts at un-objectionable definitions, the comments will be open:

1. It will be fun for me; I can’t promise for anyone else.

2. And, in some cases, themselves.

3. The top detector sees (1) light that was reflected at the first beamsplitter and then reflected again at the second plus (2) light that was transmitted through both, the right-hand detector sees (3) light that was reflected at the first and transmitted at the second plus (4)light that was transmitted through the first and reflected at the second. Each of those four paths contains an equal share of the original light, and each detector gets two of the four.

4. Or sometimes “welcher-weg” because physicists think everything sounds cooler in German

5. Worst. Crowdsourced porn site. Ever.