The way noise cancelling headphones work is by listening to sound, and created the inverted sound to 'cancel it out'. Doesn't this mean that the headphones create double the amount of noise, but our ears just can't pick it up due to the noise being 'equalized'?
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This question blends over into the realm of Physics:
Yes, noise-cancelling headphones create what is known as 'anti-sound', which is (virtually) the same sound (and equally loud) as can be heard in the environment, but with an inverted phase. This inverted sound wave indeed cancels out the original sound wave from the environment, resulting in (virtually) no air displacement at your ears: i.e. no sound, no noise.
The actual anti-sound created by real-world noise-cancelling headphones is not exactly the inverse sound as your surroundings, but a (close) approximation. The quality of this approximation limited by the quality and latency of the microphones, chip, software and speakers in the headphones. This means that they will only reduce and not perfectly cancel all noise.
It also means that if you have a noise that only lasts a very short time, the headphones might actually be too slow to cancel the noise. In this case, your ears will first hear the original sound (at full volume) and then the anti-sound (also at full volume). In this case you could say that the headphones have created a lot of additional noise (which in that case will be heard).
To summarize: Yes, noise-cancelling headphones are constantly making noise themselves. The net effect of this is however that the amount of noise that reaches your ears is greatly reduced.