The present interdisciplinary study discusses the physical foundations of the neurobiological processes occurring during social interaction. The review of the literature establishes the difference between Intentionality and Intention, thereby proposing the theoretical basis of Shared Intentionality in humans. According to the present study, Shared Intentionality in humans (Goal-directed coherence of biological systems), which is the ability among social organisms to instantly select just one stimulus for the entire group, is the outcome of evolutionary development. Therefore, this interaction modality should be the preferred, archetypal, and most propagated modality in organisms, attributed to the Model of Hierarchical Complexity Stage 3. This characteristic of biological systems facilitates the training of the new members of the group and also ensures efficient cooperation among the members of the group without requiring communication. In humans, Shared Intentionality contributes to the learning of newborns. The neurons of a mature organism may teach the neonate neurons regarding the fitting reactions to the excitatory inputs of the specific structural organization. This enables the neonate neurons to develop a Long-Term Potentiation that links particular stimuli with specific embodied sensorimotor neural networks. The present report discusses three possible neuronal coherence agents that could involve quantum mechanisms in cells, thereby enabling the distribution of the quality of goal-directed coherence in biological systems (Shared Intentionality in humans). Recently reported case studies conducted online with the task of conveying the meaning of numerosity to the children of age 18–33 months revealed the occurrence of Shared Intentionality in mother-child dyads in the absence of sensory cues between the two, which promoted cognitive development in the children. The findings of these case studies support the concept of physical foundations and the hypothesis of the neurophysiological process of social interaction proposed in the present study.