Amorphous polymorphism is one of the key concepts in our understanding of water, its structure, physical properties and anomalies. The basic idea is that liquid water at ambient conditions is constantly fluctuating between high-density and low-density domains. The high- and low-density domains cannot be isolated at ambient conditions, but it is possible to obtain phase segregation in the deeply supercooled regime at temperatures below 233 K. Here we want to look at the proton's environment in Very High Density and Low Density Amorphous ices, in term of proton mean kinetic energy and momentum distribution. The relatively large density difference between these two polymorphs, should have clear and measurable signatures in a DINS experiment. In particular, the proton mean kinetic energy could shed light on the unsolved puzzle related to the kinetic energy excess in supercooled water.