The concept of digital twin (DT), which enables the creation of a programmable, digital representation of physical systems, is expected to revolutionize future industries and will lie at the heart of the vision of a future smart society, namely, Society 5.0, in which high integration between cyber (digital) and physical spaces is exploited to bring economic and societal advancements. However, the success of such a DT-driven Society 5.0 requires a synergistic convergence of artificial intelligence and networking technologies into an integrated, programmable system that can coordinate networks of DTs to effectively deliver diverse Society 5.0 services. Prior works remain restricted to either qualitative study, simple analysis or software implementations of a single DT, and thus, they cannot provide the highly synergistic integration of digital and physical spaces as required by Society 5.0. In contrast, this paper envisions a novel concept of an Internet of Federated Digital Twins (IoFDT) that holistically integrates heterogeneous and physically separated DTs representing different Society 5.0 services within a single framework and system. For this concept of IoFDT, we first introduce a hierarchical architecture that integrates federated DTs through horizontal and vertical interactions, bridging the cyber and physical spaces to unlock new possibilities. Then, we discuss the challenges of realizing IoFDT, highlighting the intricacies across communication, computing, and AI-native networks while also underscoring potential innovative solutions. Subsequently, we elaborate on the importance of the implementation of a unified IoFDT platform that integrates all technical components and orchestrates their interactions, emphasizing the necessity of practical experimental platforms with a focus on real-world applications in areas like smart mobility.