In answer to the first part of your question, yes. There are many things that are not yet clearly understood but are believed to exist, quantum physics is one. Science is always difficult when you get down to mathematical equation as evidence. What's to say math isn't a restriction in our interpretation? If that is true then we have a lot of things wrong. In math the universe appears to have order. Still even in science understandings do change, Tesla believed in Ether, Newton didn't, his theory trumped Tesla's, now some people think that what science is calling "dark matter" is Teslas Ether.
So quantum physics is either a real thing or, it's a made up story and scientology has spread over to science. Just read Jaden Smiths comments, "trees are blue," mirrors aren't real because our eyes aren't real." Still, quantum physics says that we are vibrations of energy coming together in one place, that may explain how music and words can manipulate us, and then Jaden doesn't seem so "far out" does he? The Torah also says "Bereshit bara elohim et ha'shamayim ve'et ha' aaretz.”. (Aleph and Tav).
Certainly an interesting thought which we could philosophize about for ages.
https://m.youtube.com/watch?v=TCZ155wj74UIf As for " If something can't exist can it be defined?" What is the point? Have you heard of the Meekymookeybumskeynicker? Me neither, but if you wish to elaborate on the last question I'd be glad to hear it, maybe I'm coming from a different perspective :)