Fully harvesting the gain of multiple-input and multiple-output (MIMO) requires accurate channel information. However, conventional channel acquisition methods mainly rely on pilot training signals, resulting in significant training overheads (time, energy, spectrum). Digital twin-aided communications have been proposed in [1] to reduce or eliminate this overhead by approximating the real world with a digital replica. However, how to implement a digital twin-aided communication system brings new challenges. In particular, how to model the 3D environment and the associated EM properties, as well as how to update the environment dynamics in a coherent manner. To address these challenges, motivated by the latest advancements in computer vision, 3D reconstruction and neural radiance field, we propose an end-to-end deep learning framework for future generation wireless systems that can reconstruct the 3D EM field covered by a wireless access point, based on widely available crowd-sourced world-locked wireless samples between the access point and the devices. This visionary framework is grounded in classical EM theory and employs deep learning models to learn the EM properties and interaction behaviors of the objects in the environment. Simulation results demonstrate that the proposed learnable digital twin can implicitly learn the EM properties of the objects, accurately predict wireless channels, and generalize to changes in the environment, highlighting the prospect of this novel direction for future generation wireless platforms.