White roots are fresh roots. As roots harden, or "lignify", they turn an opaque, but orangey- to creamy-brownish-red and remain nice and plump and round. When roots die, they turn a brownish-clear color and flatten out or deflate, then become mushy and smell like coconut milk (the latter is my observation and may not be 100% accurate). Dead roots often stick ("melt") to the side of a cup.
With small roots, this color/opacity observation is hard to see. With large roots, it is easy.
See Dom's cup in the last post. Note that one brownish-red (almost orange) root out of all of them (top left). That's a healthy root in the process of lignification. Note the white roots. Those are roots that are less than 2-3 months old which are still white and soft. I see no dying or dead roots in Dom's cup (good job, Dom!).
The hard part is learning when a root is lignifying and when it is dying. They look similar. The key things I look for are opacity and color. The more orange is there, the more healthy roots seem to be, the more brown, the more unhealthy they seem to be. The more clear, the more dead it is, the more opaque, the more life it probably has.
This is just my observation from the last couple years rooting. YMMV.