Earlier quoted context omitted.
> Waste disposal is a solved problem: you put the spicy rocks back where they came from. In the Australian outback those are places people used to live. How are you going to stop people returning for 200,000 years? Greed. Hubris.
Do you think those aren't solved problems? First, fast reactors yield waste products that principally live only a couple of hundred years. [1] And even to answer your original question directly, there's a whole area of study that's fascinating on how to provide long-term warnings. [3] Not necessarily in the Australian outback, Yucca Mountain is a great choice. [2] [edit](That area is adjacent to the Nevada Test Site…
Many radioactive products are either very short lived, and will decay down to minimal levels within a few hundred years, or are very long lived, causing very low radioactivity.
The problem are the elements that are in between which is mostly the other actinides. Those are the ones that would require tens of thousands of years or more to reach safe activity levels. Fast reactor designs don't have significant amounts of such elements in the waste. The waste will decay to uranium ore-ore like levels within only hundreds of years.
The biggest issue is that they need relatively enriched uranium to operate at first. After they are started, they can be used as a breeder reactor that can take in natural uranium and convert it to the enriched uranium it needs to continue running.