Let’s say we have an unlimited budget and we don’t care much about practicality, and our goal is to be able to receive an egg, which has been boiled for an unknown duration, and determine its doneness, which I would define as how liquid vs solid the yolk is, without damaging the egg or rendering it inedible.
what are are options for building a device or otherwise making this determination?
Spin the egg then ever so briefly put your hand on it to stop it. If its boiled (solid) it will stay stopped. If its raw (liquid) it will resume spinning. But as you mentioned, it can’t tell the degree of solidness or liquidness.
As long as practicality is not an issue, just cut the egg in half and see how done it is. If it is not done to the desired level, discard it and do the same with the next egg until one is found that is cooked the right amount.
Optically transparent and X-ray transparent are not related. X-radiography is sensitive to density, which is probably not much different between raw and cooked. Small-angle X-ray scattering is sensitive to structural changes, but in order not to waste eggs, you’ll want to use the full USAXS/SAXS/WAXS suite at Argonne National Lab.