[dsizzle]

That's just stating that commercial ANC headphones aren't designed as hearing protectors, which is true enough, but that doesn't mean they don't protect your hearing compared to nothing. Here's a paper analyzing ANC designed specifically for that purpose (and indeed it starts with the premise that it's possible) https://journals.sagepub.com/doi/abs/10.1260/095745606776985...

[mumblemumble]

Sure, but, according to the abstract (it appears fulltext is not available?), that's a device developed specifically for the task. Which is not the case for AirPods.

The difference matters. AirPods and similar devices are engineered to reduce the loudness of the sound. But hearing damage is caused by intensity, which is not the same thing. One is about how the sound is perceived, and the other is about the amount of energy being carried by the sound waves. It is possible to reduce a noise's loudness without reducing its intensity.

[dsizzle]

What technique can lower the loudness of a sound at your ear without actually decreasing the intensity? Compression and appropriately applied delay can make a recorded sound seem louder -- are you suggesting AirPods do the inverse of that?

The principle of ANC is straightforward and the textbook definition doesn't involve any psychoacoustic tricks https://en.wikipedia.org/wiki/Active_noise_control. You haven't given any reason to think AirPods are doing something fundamentally different.

[mumblemumble]

Look, I'm no expert on these things. The only thing I'm going on is that, when I looked into the issue, the general consensus of the people who did seem to have expertise in the field was, "look, this is a bad idea, here's why." I asked my audiologist about it, and what I've shared here is about as deep as she explained it.

I didn't ask to dig any deeper. I don't need to understand every grotty little detail of the reasoning behind my doctor's advice. I trust her to know what she's talking about when the subject is her core area of expertise.

What I do know is that it seems plausible to me. The perception of loudness is a product of a fairly complex system that involves both neural filters and sensing organs that work a very specific way, and a lot of that happens on the opposite side of the spot where the actual damage occurs in noise-induced hearing loss. I would guess that the problem is that any failure in the ANC to get the phase just right results in a waveform that's been modified such that it reduces the noise's detectability by the cochlea much more than it reduces the actual energy being carried?

That said, I would suggest you're trying to put the burden of proof on the wrong proposition. Given that AirPods are not being sold as hearing protection, and have not been tested by the EPA, one would think that we the default hypothesis should be that they are not adequate hearing protection. Especially since we're talking about people's health here. So perhaps you can come up with a study demonstrating that consumer-grade ANC such as AirPods (we have to assume that the device in the paper you linked above may not function comparably to popular consumer devices, so the study's findings may not be relevant here) can be safely used as protection from occupational noise?