Let's say I have an undo button. It works as follows:
- I enter a number $N$
- The device splits the universe into $N+1$ possibilities
- In one universe, the device outputs "Fail"
- In all the others, it outputs a different number from $0$ to $N-1$
- If it outputted a number, after some time, I can press either "keep" or "undo".
- If the neither "keep" nor "undo" is pressed forever, then it defaults to "keep".
- If it outputted "Fail", it defaults to "keep".
- All the universes that resulted in "undo" are destroyed, and a random "keep" universe is kept.
- In particular, if in every number universe, "undo" was pressed, the "Fail" universe is kept.
The device is basically free to use.
Somethings to note:
- If I get "Fail" due to random chance, I can keep retrying until I get a number.
- Of course, I will never get a number if every number causes an "undo".
- There is only one of this device.
- You can not run another experiment while it's running.
- The different universes have literally no interaction.
What could this undo button be used for? The two ideas had so far is search and rescue (go to a location based on the number, "undo" if the person isn't there, keep if they do (if you get "Fail" repeatedly, they are completely missing)) and the stock market (choose a stock based on the number, if it goes up "keep", if it goes down "undo"). If think there are much broader applications though.
Essentially it outputs a number from $0$ to $N-1$, and if you don't like the number, you can undo it.
Another interpretation of the device is to say it picks a random number from $0$ to $N-1$ (or "fail"), and when you hit "undo", it reverses time and picks another number (or "fail").