How to make your own infinite guitar:

1. Rewire the neck pickup of your guitar for low impedance (reduce the number of turns, and increase the thickness).

2. Construct a small amplifier which takes the signal from your middle or bridge pick-up to drive the amplifier.

The string generates a current in the pick-up, which drives the transducer, which then drives the string forevermore.

Note: this is my basic understanding of how this can be done. Any suggestions for corrections or additional detail are welcomed.