In conceptual debates involving the quantum gravity community, the literature discusses the so-called "emergence of space-time". However, which interpretation of quantum mechanics (QM) could be coherent with such claim? We show that a modification of the Copenhagen Interpretation of QM is compatible with the claim that space-time is emergent for the macroscopic world of measurements. In other words, pure quantum states do not admit space-time properties until we measure them. We call this approach "Achronotopic" (ACT) Interpretation of QM, which yields a simple and natural interpretation of the most puzzling aspects of QM, such as particle-wave duality, wave function collapse, entanglement, and quantum superposition. Our interpretation yields the same results in all measurements as the Copenhagen Interpretation, but provides clues toward the sub-Planckian physics. In particular, it suggests the non-existence of quantum gravity in the conventional sense understood as the quantization of a classical theory.