the momenergy 4-vector tilts more and more from the "vertical," that is, from a purely timelike direction.

Spacetime Physics - Page 197 - Google Books Result

https://books.google.com/books?isbn=0716723271

Edwin F. Taylor, ‎John Archibald Wheeler - 1992 - ‎Science

... from a purely timelike direction. However, irs magnitude remains totally unchanged, at the fixed value m. In conse- Magnitude of momenergy 4-vector: mass!