Does time pass on a Minecraft SMP server if nobody is logged on?

Question

I have a private Minecraft server where we are 2 people playing.

Earlier today I logged on, observed it was night, and logged back off.

Then I logged on just now, it was day again.

In the meantime, I know the other player has not been online.

So my questions (they are related) are these:

1. Does time pass in Minecraft if the server is running, but nobody is online?
2. Can I use this to my advantage to:
   1. Cook or smelt things in furnaces while I'm offline?
   2. Plant trees or other things before I log off and log back on to them being grown?
   3. Get grass to spread while I'm offline?

This might be a related question, but if not, please just leave a comment and I'll take it out to avoid having a too broad question:

1. Does time only pass in a region if players are in the region? Like, if both of us are online, then I log off, and the other player is far away, does "time pass", like trees grow, furnaces run, etc. in the region he's not in? I would imagine that would take a load on the server if there are large explored areas.

Answer

Time in the sense of day/night cycle and weather passes while no one is on, however in all other senses time doesn't pass in a given chunk unless a player is online and nearby enough for it to be loaded.

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