Energy harvesting is the capture of ambient energy, its conversion into a usable form, and its storage for immediate or future use. Interest in energy harvesting has increased over the last decade because of its environmental friendliness and its ability to power devices without electric wires. This term has been frequently applied in recent years in the context of small autonomous embedded devices such as wireless sensor nodes. In this paper, we address the scheduling problem for a single processor device that executes preemptable time critical tasks. Each one has a certain energy requirement and arrives at an unpredictable time. We ask the question whether the traditional task scheduling algorithm earliest deadline first (EDF) is convenient for energy harvesting environments. The paper shows that EDF has a zero competitive factor but nevertheless is optimal for online non-idling settings.