This document discusses a proposal for a Future and Emerging Technologies (FET) Flagship project called the Time Machine, which would be a large-scale, long-term initiative to digitize cultural heritage collections across Europe and enable new forms of access and analysis of historical data. The Time Machine proposal is being led by a consortium of over 80 partners from 23 countries. If selected, it would receive up to €1 billion in funding over 10 years. The goals of the Time Machine include pooling digitized cultural heritage "big data" to allow deeper exploration of European history over time, connecting collections, and encouraging new uses of heritage in society through digital tools and simulations.