After decades, we still lack a proper understanding of the quantum nature of gravity. Nonetheless, we have already seen many theoretical hints that gravity does not easily fit in the quantum mechanical framework. In this talk, I will discuss the issues associated with gravitating vacuum energy and take that as empirical evidence of the breakdown of QFT in the presence of gravity. Then, I will argue for a radical alternative where space(-time) is completely emergent from quantum mechanics alone, defined for finite-dimensional Hilbert spaces. After briefly reviewing how spacetime can be emergent, I will sketch a new research program that establishes experimental signatures to test the emergent nature of spacetime.