Cross-posting an excellent description of Positive Separation as written by Christopher Coon on the VATSIM Forums:
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We have a requirement called "positive separation" that in the radar/IFR/class B world anyway means you never have two aircraft in your airspace that require separation that are in possible future conflict. They could be 100 miles apart but if you allow that aircraft into your airspace in future conflict with another, in real world anyway you could be written up for a "box 1" and decertified, washed out or even fired despite not actually losing separation.
I see positive separation violated a lot here so I don't think it's being taught to controllers. I had an instructor level controller working me level at 290 with a crossing restriction at 15,000. Then a couple minutes later somebody went underneath me at 27,000. I asked him why he cleared me down to 15 when there was traffic at 270 and he said "you were two thousand feet above him, we only need 1,000." That's not how separation works. Or another C-level controller who had me on a converging course, same altitude with another aircraft he was working. He descended me before losing actual separation, but we should have never been in that conflict in the first place. When I asked him, he didn't understand his failure to provide positive separation. That's why I don't think it's being taught here.
Positive separation is not about keeping aircraft X miles apart or Y feet vertically, it's about not allowing them into possible conflict in the first place. You should never clear an aircraft into possible conflict with another in your airspace, or allow an aircraft into your airspace if it's in possible conflict with one of yours (you have to resolve the conflict before taking the handoff). In my crossing restriction example, I should have been given no lower than 280 until there was lateral separation ensured with the other traffic. In the converging same-altitude example the controller should have told the previous controller to turn or climb/descend the traffic prior to taking the handoff.
That's positive separation. Converging course with 12 descending to 4 is not separated from someone at 12 descending to 5 whether or not you lose actual separation. If controllers aren't taught positive separation, I don't see how they'll know the proper way to apply visual separation. They need to be positively separated both before and after, before you can use visual separation (7-2-1 of the 7110.65).
Positive separation also means aircraft converging at the same altitude that look like they might lose lateral separation later are not separated from each other even though they're 50 or 100 miles apart. There's no such thing as "I'll turn them away or change altitudes before they get too close" -- if you've allowed that situation to occur in your airspace or between two aircraft in your control, you've failed to provide positive separation and could be disciplined (in real-world, anyway). It's a fundamental part of the job I'd like to see VATSIM teach its controllers before worrying so much about procedures and the other mundane parts of ATC.
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And adding some additional words of wisdom from Wes Miles:
...but for clarification I would add Positive control/separation isn't necessarily ensuring you never have two aircraft in possible future conflict, but recognizing those possible conflicts during your scan, taking corrective action where needed, and being ready to pull the trigger on plans B-D in advance time to where separation is never questioned. I've seen an FAA supervisor apply SUPER-positive separation during a relatively busy day and it ended up causing them WAY too much work (and nearly 3 airspace violations). Try telling controllers at N90 or C90 they should never allow aircraft in their airspace that could be a potential future conflict. In the words of a wise instructor I once had who retired out of D10: "You have RADAR. Use what the taxpayers paid for."