Re: "Everything between sample points is lost" (@the spectacularly refined chap)
"ultra"-sound meaning beyond sound, I presume?
You can't hear it; that's why we only pass up to about 20 kHz into the recording chain. If it's not present in the input, its not "lost" from the output. Nyquist's theorem is the law. The reproduction of a low-pass signal is essentially perfect - nothing is "lost".
Of course, no real-world implementation is perfect, but there's no big mathematical or philosophical discussion hiding here.