One option for using radiation but not radioactivity for timekeeping would be to use cosmic rays that the Universe throws at Earth. A pair of scintillator detectors can be arranged to detect cosmic muons, but there are two aspects of this approach that don't make it a great option:

• The scintillators Pomelo uses are small for this purpose, only catching about 20 muons per hour.
• The 11 year solar cycle influences the cosmic ray flux on Earth, which means the clock would run fast for about 5 years and then slow for another 5.

This idea was thus promptly abandoned.