I note that virtually all in-ear headphones and at least all the over-ear headphones I have are marked with left and right… what possible difference can it make? Apart from the shape of some in-ear headphones (not Apple, though…nor any others in my possession) I can’t think of any.
When you plug the headphones into a stereo, mp3 player etc one side will play the left channel of the music and one will play the right channel. Some people are fussy and want the music on the left channel to go to the left ear and the right channel to go to the right ear.
For music, it generally won’t make a difference because you don’t care which instruments are on your left and which are on your right. If you’re watching a film with headphones, though, then it would be a bit weird to see (for example) a car driving past the camera from left to right, but sounding as though it was going right to left, wouldn’t it?
In classical music, it is traditional that the violins will be to the audience’s left, progressing to the lower pitched instruments on the right. Not only symphony orchestras, but chamber ensembles follow this convention with few exceptions. If you frequently attend live concerts, hearing the reverse sounds quite “wrong”.
There’s a lot more to stereo music than where the “instruments” are, especially in this age of studio production. Even as far back as The Dark Side of the Moon there was a lot of editing to create spatial illusions. It sounds just as wrong to listen to the “mirror image” of the album as it would to watch a movie with reversed audio.
Some spatial illusions could include moving forwards or backwards, as well. If you wear the headphones backwards, then the front side of the headphones is now on the back of your head, and vice versa. It might feel like you are falling backwards through a bunch of sounds rather than flying forwards through it as the artist intended, which is significantly different.
Except there’s no difference in sound between the front side of the headphones and the back side, and even if there were, our ears are poorly adapted to picking it up. I, too, fail to see how the mirror image of a spatial illusion could be anything other than an equivalent illusion.
In “On the Run”, the whole track is spatial. A man runs with heavy steps from left to right, then back. Something sounding like a helicopter buzzes overhead from left to right a few times. The interview quotes that are interspersed into the entire album move from right to left. Even the synth loop underlying the whole thing moves distinctly. Then the plane crashes from upper-front-right to lower-back-left.
If you reverse the headphone it just sounds wrong. The important thing isn’t as much the absolute left-right split as it is consistency between listenings.
Also bear in mind that there’s feedback between your sensory modalities. I remember one demo of spatialized sound that had a recording of a helicopter flying in a circle around one’s head. If I kept my eyes closed, I could clearly hear the helicopter flying in a circle around me; if I kept my eyes open, I could clearly hear the helicopter flying in a semicircle back and forth behind me.
And no, I didn’t think to reverse the headphones to determine what the effect would be.
So in terms of music–unless you’re listening on good headphones in a quiet environment with your eyes closed–it shouldn’t make a real difference.