An essential part of being an individual is our personal history, in particular our episodic memories. Episodic memories revolve around events that took place in a person's past and are typically defined by a time, place, emotional associations, and other contextual information. They form an important driver for our emotional and cognitive interpretation of what is currently happening. This includes interactions with media technologies. However, current approaches for personalizing interactions with these technologies are neither aware of what episodic memories are triggered in users, nor of their emotional interpretations of those memories. We argue that this is a serious limitation, because it prevents applications from correctly estimating users' experiences. In short, such technologies lack empathy. In this position paper, we argue that media technologies need an Artificial Empathic Memory (AEM) of their users to address this issue. We propose a psychologically inspired architecture, examine the challenges to be solved, and highlight how existing research can become a starting point for overcoming them.