Interesting. However, I disagree that if such a machine existed, people would lose motivation. They'd realize that the rational part of the brain is used just for rationalization and is not always actively engaged in real-time decision-making... but that's about it. They'd then beat the machine with little practice, regardless of how it is implemented.
>The heart of each Predictor is a circuit with a negative time delay — it sends a signal back in time.
If a Predictor was hooked up to a geiger counter instead of a button, the light would flash exactly one second before the counter would click. It would flash even before the decay occurred.
It doesn't mean that you don't have free will, it just means that during a one-second loop, you are constrained to logically consistent choices. You can't choose to fool yourself about your future behavior during that one second.
If it's real time travel, then that wouldn't show that free will doesn't exist. It would just show that there are different timelines, and the universe is forked every time a decision is made.