Central to the official green growth discourse is the conjecture that absolute decoupling can be achieved with certain market instruments. This paper evaluates this claim focusing on the role of technology, while changes in GDP composition are treated elsewhere. Some fundamental difficulties for absolute decoupling, referring specifically to thermodynamic costs, are identified through a stylized model based on empirical knowledge on innovation and learning. Normally, monetary costs decrease more slowly than production grows, and this is unlikely to change should monetary costs align with thermodynamic costs, except, potentially, in the transition after the price reform. Furthermore, thermodynamic efficiency must eventually saturate for physical reasons. While this model, as usual, introduces technological innovation just as a source of efficiency, innovation also creates challenges: therefore, attempts to sustain growth by ever-accelerating innovation collide also with the limited reaction capacity of people and institutions. Information technology could disrupt innovation dynamics in the future, permitting quicker gains in eco-efficiency, but only up to saturation and exacerbating the downsides of innovation. These observations suggest that long-term sustainability requires much deeper transformations than the green growth discourse presumes, exposing the need to rethink scales, tempos and institutions, in line with ecological economics and the degrowth literature.