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Comment by witherk | Hacker News Reader

Wave particle duality used to stress me out before I read Feynman talk about it.

"Things on a very small scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen.....

There is one lucky break, however—electrons behave just like light. The quantum behavior of atomic objects (electrons, protons, neutrons, photons, and so on) is the same for all, they are all “particle waves,” or whatever you want to call them. So what we learn about the properties of electrons (which we shall use for our examples) will apply also to all “particles,” including photons of light."

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Single beam of electrons diffracts like single beam of light, but otherwise electrons behave very differently than light: two electron beams interfere with each other, while two light beams do not.

Am I right that thinking of everything as waves isn't a bad mental model?

If everything is a field, then light is simply a three dimensional wave in that field. This makes the double slit experiment seem much easier to grasp:

A single photon (which is a wave with a discreet amount of energy) travels through both slits at the same time. This causes the wave to interfere with itself and when it hits the wall it registers as a single point, as the photon must always be a discreet quantum of energy.

To me, this makes intuitive sense and removes a lot of the mystery and confusion that gets invoked whenever pop-sci writers explain the experiment. They tend to say something along the lines of: photons are like billiard balls, so they can only go through one slit or the other, but if you don't detect which slit it goes through it seems to go through both.

Am I close to what's actually going on, or am I way off?

If you want to think about it, I suggest that you keep a “library” of classic experiments in your head.

There are experiments that show that light is not a particle (in the classical sense) and other experiments that show that light is not a wave (in the classical sense). Quantum mechanics is the result of trying to find a theory consistent with both sets of experiments.

Originally, the double slit experiment was seen as proof that the wave theory is correct. So if you want to challenge your wave theory, look to different experiments. Wave theory of light was predominant from the mid-19th century to the emergence of quantum mechanics in the early 20th century, so I would focus on science from the early 20th century, such as the ultraviolet catastrophe and the photoelectric effect.

Consider the photoelectric effect. If light were a wave that carried energy, this wouldn’t explain why an equal amount of energy has a different effect depending on its wavelength. The quantum explanation is that one packet of light contains a different amount of energy, which depends on wavelength. “Light is a wave” kind of falls apart as a theory, because it is unable to explain this.

> If light were a wave that carried energy, this wouldn’t explain why an equal amount of energy has a different effect depending on its wavelength.

Not by itself but the accompanying theory - classical EM theory - does explain why different frequencies interact differently. Absorption/dispersion spectra are well described by wave theory. What the classical wave theory can't explain easily are coincidence counts in extremely weak light (antibunching), or things such as the Compton scattering.

"When it hits the walls it registers as a single point" is pretty vague and seems to me to be where you're kinda glossing over a lot of the not-just-a-wave complexity.

Im fairly certain you could make an experiment where one photon went through some apparatus and two specks of light appeared at the photo detector (with new wavelengths of course). What mechanism in your wave-only theory describes this split? Why do these waves sometime split or fuse and other times stay as single particles? The 'it stays as one particle cause it started as one particle' explanation would lead to a very monochromatic universe!

No, you can't do that with one photon.

What you can do with one photon is to observe that it almost never appears in the screen in positions where geometry dictates there would be destructive interference of the photon was a wave.

If you literally try one photon only once, well, you can't really talk about probabilities; whatever happened happened (possibly you witnessed an unlikely event). But if you repeat the experiment N times, even if you do it spaced by many miles and many days, and collect the data you'll notice that the measurements cluster in ways that are compatible with interference bands.

If an actual physicist can tell me whether that I wrote above is fundamentally wrong, I'd be happy and have more questions

So, 'something' must be able to turn a photon of one wavelength into a photon of another wavelength, otherwise we'd only have 1 wavelength of light in our universe.

Moreover, if we assume conservation of energy, changing a photon w/ wavelength A into B leaves over some energy C, that again, assuming some mechanism of changing energy into light, a new photon could be emitted.

So which assumption is wrong? (1) Light comes in many different wavelengths (2) Conservation of energy (3) Non-light energy can be changed into light energy (4) Light color follows the photon model for the relation between energy and wavelength.

(or just do a simple google search: https://arxiv.org/abs/2009.03039 where it's sounds like it's been observed directly)

If his apparatus was a "beta barium borate" crystal, isn't this exactly how entangled pairs of photons are created?

Thinking of them as waves helps your intuition for entry-level QM phenomena like the dual-slit experiment and other lab-scale interferometry experiments.

Unfortunately, I would say it doesn't help (and could actually block you) when you want to build intuition around QFT and high-energy processes.

In your mind, you would still then think of a photon as a wave running around interacting with electronwaves that then oscillate and produce new photon waves.. and you'd think for example that "hey, I can just solve the wave equation and I solve the experiment".

While it's really so much more messy, as you'd note when you start considering the number of degrees of freedom involved required in your simulation to approximate reality. It's not classically interacting waves timestepped forward in time, it just looks like that in the most trivial situations.

Thinking of photons as waves in 3d space breaks down as soon as there's entanglement around (eg delayed choice eraser). You need to think of the system as a whole as a wave travelling through configuration space.

The problem with treating everything as a wave is that all these entities can only exist at certain energies. So the field is quantized.

IS quantisation a property that waves cannot have?

> while two light beams do not [interact]

Photons do interact! There is no two-photon vertex, that’s true, since there is no fundamental interaction between two photons. But put four photon/charged particle vertices together and you’ll get the 4-photon box diagram [1], whose contribution is nonzero.

[1]: Since I’m not good at painting diagrams in ASCII on HN, here’s a link to the Wikipedia article with the box rendered nicely: https://en.wikipedia.org/wiki/Two-photon_physics

The propagator is a two photon vertex... interpreted as one in, one out, moving through time :-)

Maybe you meant there’s no 2–>1 vertex.

That's a prediction. Evidence is so far inconclusive.

Two coherent beams of light will absolutely interfere.

I think that was meant to mean that the two beams interact. Two crossing light beams will pass right through each other without much happening while two electron beams will interact. But this is because electrons are charged and photons are not. On careful inspection and with high energy photons one would also notice an interaction between two light beams due to photon photon scattering [1]. But one could reasonably call this a kind of distraction due to different charges of different particles. Ignoring those makes photons and electrons behave identical in respect to the phenomena discussed in the article.

[1] https://en.wikipedia.org/wiki/Two-photon_physics

Electron beams interfere in ways that light beams don't, though. If they cross in vacuum, they deflect each other due to the electric charge carried by electrons. Light beams can only deflect each other in media with non-linear response to electromagnetic fields, i.e. the response to one beam modifies the response to the other beam.

Technically speaking even the vacuum is nonlinear, according to current theories (although it hasn’t been observed yet).

Well yes one has charge and the other doesn't, they aren't literally the same thing so are different QED. The point is the rules are the same.

Don't try to understand transistors in concepts you're familiar with, such as cars and bananas. A transistor is neither a car, nor a banana. You have to have a new kind of understanding, one that transcends such mundane, familiar concepts.

Get it?

Feynman explained nothing by saying that particles are "not like" two other familiar concepts. That's flipping two bits in an infinite set of to "false". You can't gain understanding by flipping all but one remaining bit in that infinite set to false! Particles aren't like tiny springs either, or tiny metronomes, or tiny bolts of lightning, or... an infinite list of things they aren't!

Similarly, Feynman's Path Integral method is trotted out as a mental model of how particles "work" at the Quantum Level, but this is literally just a mathematical trick for solving a class of problems efficiently. This is not my opinion, Feynman said so. It's not a "model of the world", it is literally just a specific case of Monte Carlo Integration!

Just to add a nitpick here, apart from them sharing some wave-like descriptions at some levels in the theory, there is not that much in common between photons and electrons. Fundamentally they play different parts in the theory (one being a matter particle the other a force carrier) and mathematically they are represented differently and behaves very differently (one being a fermion and the other a boson). In particular the boson/fermion distinction is usually glossed over in popular treatments of QED (because it's so unintuitive and messy).

Meanwhile, in a very real sense the following equation holds:

    electron + positron = 2x photon

So it's somewhat (very?) false to say that they're fundamentally distinct, when both leptons and photons are fundamental components of electromagnetic phenomena, and are even interconvertible!

If you squint hard enough, it looks like leptons behave like sufficiently energetic photons self-interacting to the point that they form a localised circulation. This requires a charge separation to be stable, hence the requirement for a pair of oppositely charged leptons to be formed from a photon.

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