Language changes enough in 2000 that you wouldn't consider it to be the same language. This is true of Italian (derived from Latin) and Mandarin (derived from Old Chinese) as well as English (derived from West Germanic).

If you're curious about how much language has changed in Rome, you should listen to Latin and Italian side by side. Here's a Latin teacher speaking Latin and using a pronunciation more akin to the original pronunciation than the Latin you might hear from the Pope. Here a basic Italian conversation. They're close enough to know they're related, but not enough that an Italian transported back in time would immediately be able to speak to the Romans of that time period with ease.

Here's English from about a thousand years ago which you can compare to spoken English today.

We also have the following section on the FAQ:

How far back could I go and still communicate?

• What is the furthest year I can go back in time to England and be able to communicate with people?

• Could a Middle English speaker and a Modern English speaker have been able to verbally communicate

• If we could go back in time, who would be the first English monarch with whom modern English speakers could easily carry on a conversation?

• When is the latest time I could've gone back knowing a modern language and still be able to communicate with people?

• How far back in time can I go and still be able to communicate with English speakers relatively easy?

• As a speaker of modern English, if I went back in time in England, how long until I wouldn't understand what the natives were saying?

• I'm fluent in Spanish today. If I traveled back to the height of the Wild West era, would I understand the Spanish, Mexican, Latin American, Caribbean, etc.?

• How far can I go back in time in China with modern Mandarin and still communicate with people in court?