Am trying to understand a bit about wave-particle duality and I suppose a good place to start is the double slit experiment. An answer to this question will help me.
Take the typical set-up of this experiment, with photons being sent from a source through 2 parallel slits to create the well-known striped interference pattern on a screen and modify thus:
Replace the screen with a detector. Let this detector be a photomultiplier with an optical fibre that dips into the photons path like a hockey stick.
Move the fibre along a line in the plane where the screen was to record the photon strength along the line. It will show a reading with the same striped pattern.
Next, add a second detector-fibre in exactly the same plane. Move both detector-fibres along the plane and again measure the photon strength across the plane. They should give exactly the same result.
Now, move the second detector-fibre towards the slits slightly and remeasure. One detector-fibre in original position and another a bit closer. Does this affect the reading of either?
Move the second detector-fibre closer and closer to the slits. Does this affect either reading?
I am wondering if the second detector acts to collapse the wave function for the original detector.
You don’t need either detector to collapse the wave function. It’s not as if there are latent waves just waiting for a person or a detector to act as an observer so that the light can decide what pattern to fall into. With the double slit, the interference pattern will be there whether anything observes it or not. There’s no circumstance in which the pattern would appear as a single broad line with no interference fringes.
The question I think you’re searching for is the one usually asked – Which slit does the photon go through?
But as I’ve pointed out in the past, that’s still the wrong question. What if you have a three-slit mask? Even more to the point, what if it’s only a single slit? Now there’s no question about which slit it went through. But there’s an additional detail - that single slit creates an interference pattern all by itself, with a broad central region and alternating light and dark patches beyond. The width of that pattern is inversely proportional to the width of the slit.
So how does the photon “know” how wide the slit is?
OK, I thought the act of measuring the photons prevented the interference. I suppose that would only happen if every quanta is measured?
It seems reasonable that a photon - as a wave - would create an interference pattern from a single slit. #Huygensprincliple . Also seems the more one thinks of photons, electrons, protons, molecules etc as particles, the less consistent QM becomes. Even when thinking of the photelectric effect, the ejected electron is still just a wave.
How do I shift wave-particle duality in my head back towards particles?
Personally I just think of Fourier whenever I worry about any of this. I may not be strictly correct, but the duality of particle and wave can be thought of as nothing but the duality seen with a Fourier transform (and it is the underlying derivation for the uncertainty principle.) Whether you have an impulse (particle) or think of it as an infinite wave series (Fourier series) is simply a matter of point of view. If you were doing signal analysis you would simply pick whichever space made the mathematics easier.
Now you just let the particle move or let the wave expansion evolve as time progresses. Which you choose to do is a matter of what makes for the easiest explanation or understanding of what you are seeing or thinking about. And you are allowed to swap at any instant you might need to.
If “wave” and “particle” are two competing models that can be chosen between, then “wave” is more intuitive and consistent … everthing being a host of superimposed waves.
I thought that the duality though, was more fundamentally a result of the experiment?
But note that they’re always both a wave and a particle.[sup]1[/sup] That never changes no matter what experiment you run. It’s just that some experiments bring out the wave aspects and some bring out the particle aspects.
The single-slit experiment doesn’t prove that much, because you can imagine a light particle having some internal mechanism that allows it to bounce off the slit walls in a way that gives a diffraction pattern. Weird, but not that weird.
The double-slit experiment indeed proves that light is a wave, which of course isn’t that surprising on its own.
The photoelectric effect (sorta) proves that light is a particle, but maybe there’s some principle that allows light to be one or the other. Maybe there’s two kinds of light; particle-like and wave-like, and the photoelectric effect only produces particle-like light.
Where it gets indisputably weird is the single-photon double-slit experiment. One photon at a time, but clearly still interfering with itself (thus going through both slits) and producing a double-slit interference pattern. This is the simplest experiment that proves light is behaving as a particle and wave simultaneously.
The photoelectric effect is about light hitting the material, not light produced by a material. And if you like, you can put the piece of silicon or whatever on the screen of a slit experiment, to rule out the possibility of “two kinds of light”.
Sure, but maybe only light particles (of a certain energy) can dislodge electrons, and not light waves. Or maybe light waves are quantized (and it takes quanta of a certain energy to dislodge an electron), but the quanta don’t really behave like particles otherwise.
Right, and we’re back to needing the two slits again. The type of screen (chemical, electronic, or otherwise) doesn’t matter except that it can demonstrate spatial locality. But to get spatial locality and interference fringes and one-at-a-time behavior really gets you everything in one easy experiment.
Of course, you could rule out “two kinds of light” with sufficiently careful experiments, say by ensuring conservation of energy. But it’s not going to be easy to exclude all possible loopholes. It’s not a trivial undergrad-level demonstration.
They used a photomultiplier tube, and then tracked the statistics over time. The results are a bit noisy due to background photon sources, but nevertheless you can see the interference pattern in the capture buckets.
It’s possible to do the experiment with photo paper as well. But it’s possibly not as interesting because the end result looks the same as the multiple-photon version. The results still looks something like this.
If I understand you correctly, you want to gradually extract which-path information, and want to know what happens to the interference pattern in result.
Put simply, the more knowledge you have about the path taken by the photons, the less visible the interference pattern will be—i. e. it’s not an all-or-nothing situation, but rather, a kind of trade-off, which is encapsulated in the Englert-Greenberger-Yasin duality.
I don’t think your experiment would achieve the goal of measuring partial which-path information, since once the photon is measured by the first detector, it won’t be measured again by the second; thus, the presence of the first detector merely decreases the amount of photons that make it to the second one. For those, of course, you haven’t succeeded in measuring any which-path information at all, so the interference pattern it sees is going to stay the same, if reduced in intensity.
Are there any times where people tried the same one photon experiment and then moved the slits apart? If so, how far apart do the slits have to be before the one photon experiment stops producing an interference pattern?
It’s no different from the many-photons version. The further apart the slits are, relative to the photon wavelength, the less apparent the interference pattern will be. But the interference pattern never goes away entirely; it just gets swamped by the noise and the limitations of your detectors.
This was my undergrad project 25 years ago and I really wish I’d published it.
I used one of the new at the time CCD cameras borrowed from our observatory.
Light intensity was reduced with filters until only one photon at a time passed through the slit(s). This resulted in a single pixel image being captured. Repeat the experiment a few hundred times until you have lots of photos of single dots in apparently random locations. Then overlay each photo and watch the interference pattern build up one photon at a time like a flip book animation.
It was cool, but labour intensive.
There are some candidate theories that allow for both waves and particles. The most well known is the De Broglie-Bohm Pilot Wave interpretation of QM, in which particles are associated with a ‘guide wave’. As a very inexact analogy, imagine a surfer on a wave. The surfer is the particle. Look for a particle, and you’ll find it. Look instead for a wave, and you’ll find that too.
De Broglie-Bohm is fully compatible with QM equations, but it’s not widely accepted. But at least to me it makes more sense than the Copenhagen interpretation.
It’s not even clear what it means for an interpretation of quantum mechanics to be “accepted”. All that matters, as far as physicists are concerned, is that you get the same results (which you do). Some interpretations might make it easier to see how to set up some calculations, and thus be preferred in that sense, but the same physicist might switch between multiple interpretations for different problems.
I really don’t think this instrumentalist stance describes the prevailing attitude in (at least some parts of) physics regarding interpretational differences very well anymore. To take a recent example, the paper “Quantum theory cannot consistently describe the use of itself” by Frauchiger and Renner is explicitly interpretational in nature (its earlier incarnation was called “Single-world interpretations of quantum theory cannot be self-consistent”), it got published in Nature Communications in September of last year, and has already caused quite a discussion, amassing already 58 cites (with the earlier version sporting 38 cites despite never having been published) and a feature in Quanta magazine. Everybody in this discussion agrees on the calculations (which are ultimately rather trivial); what’s at issue here is how to interpret them.
