Does the breath literally stop in the fourth Jhāna? I've been trying to understand the descriptions of each of the Jhānas in various Suttas, and I don't get what's meant by an element in some descriptions of the fourth Jhāna. For example:

When one has attained the fourth jhāna, in-and-out breathing has been totally stilled.

– SN 36:11
It seems to me that that passage is saying that the breath literally stops, but this seems physiologically impossible. So perhaps the correct interpretation is that volitional in-and-out breathing ceases? Or is the passage, perhaps, referring to the perception of in-and-out breathing?
I've even gone so far as to look up the words in Pāli, but this has only added to my confusion, since they seem to translate as literally the cessation of breath. Is this, perhaps, a shortcoming of our understanding of Pāli?
If this is to be taken literally, what is the scientific basis for this phenomenon? Is it perhaps a perceptual phenomenon, where the meditator merely perceives the breath as having stopped? Or, if this is indeed an error in interpretation, then how is it to be interpreted?
I should clarify that I'm not seeking to troll, or challenge the tradition. I myself am a lay disciple of the Dhamma. I'm prepared to accept an answer one way or the other, but I really want to have a solid understanding.
Thanks.
The breathing is imperceptible, that is all, because there must be movement of the breathing for it to be perceived. However, obviously the body continues to have breath flowing through it.