Mitochondrial connectivity is characterized by matrix lumen continuity and by dynamic rewiring through fusion and fission events. While these mechanisms homogenize the mitochondrial population, a number of studies looking at mitochondrial membrane potential have demonstrated that mitochondria exist as a heterogeneous population within individual cells. To address the relationship between mitochondrial dynamics and heterogeneity, we tagged and tracked individual mitochondria over time while monitoring their mitochondrial membrane potential (deltapsi(m)). By utilizing photoactivatible-GFP (PA-GFP), targeted to the mitochondrial matrix, we determined the boundaries of the individual mitochondrion. A single mitochondrion is defined by the continuity of its matrix lumen. The boundaries set by luminal continuity matched those set by electrical coupling, indicating that the individual mitochondrion is equipotential throughout the entire organelle. Similar results were obtained with PA-GFP targeted to the inner membrane indicating that matrix continuity parallels inner membrane continuity. Sequential photoconversion of matrix PA-GFP in multiple locations within the mitochondrial web reveals that each ramified mitochondrial structure is composed of juxtaposed but discontinuous units. Moreover, as many as half of the events in which mitochondria come into contact, do not result in fusion. While all fission events generated two electrically uncoupled discontinuous matrices, the two daughter mitochondria frequently remained juxtaposed, keeping the tubular appearance unchanged. These morphologically invisible fission events illustrate the difference between mitochondrial fission and fragmentation; the latter representing the movement and separation of disconnected units. Simultaneous monitoring of deltapsi(m) of up to four individual mitochondria within the same cell revealed that subcellular heterogeneity in deltapsi(m) does not represent multiple unstable mitochondria that appear 'heterogeneous' at any given point, but rather multiple stable, but heterogeneous units.