Why massless clock cannot exist?

There is an article saying:

With such conformal invariance holding in the very early universe, the universe has no way of 'building a clock'.

First question is that does it mean a clock must have mass?

Second question, why massless clock cannot exist?

Reference

Penrose, Roger. “Before the Big Bang: An Outrageous New Perspective and Its Implications for Particle Physics.” Proceedings of EPAC 2006, Edinburgh, Scotland, 2006, pp. 2759–62.