Inside the tiny chip that powers Montreal subway tickets

To use the Montreal subway (the Métro), you tap a paper ticket against the turnstile and it opens. The ticket works through a system called NFC, but what's happening internally? How does the ticket work without a battery? How does it communicate with the turnstile? And how can it be so cheap that you can throw the ticket away after one use? To answer these questions, I opened up a ticket and examined the tiny chip inside.