Can ChatGPT Track Time Between Messages?

Quick question: Does ChatGPT have the ability to know the current time and add timestamps to its responses? For instance, if there's a 5-hour gap between my last message and the next one, does ChatGPT think it was just seconds ago, or can it actually recognize the time that has passed? I've noticed that when I asked it for the date, it gave me an incorrect answer, which has me wondering about its time perception capabilities.