So I figured I should say what my angle is, being the person who indirectly brought this topic back from the dead. Basically, I independently came up with essentially this exact idea, and found Vakus's post, and wanted to get the discussion going on it again because it felt like the question hadn't been explored that well before.

My idea had one significant difference from Vakus's version, though: in my version, you couldn't reopen portals that had closed. There was no "address" system - once a portal closed, no matter how you reopened it, it would just clone your current world, rather than bringing back the world that used to be on the other side. It's more limiting and depressing I guess, but it ties up a lot of loopholes which I think could be problems in Vakus's version.

How costly would keeping portals open be in your scenario? Because unless it would be vastly more expensive than in my scenario, you could just keep lots of portals permanently open and it wouldn't necessarily differ all that much from my scenario. I'm also somewhat curious what loopholes you were imagining.

The main differences would be 1) risk (if something happened to the portal while you were in another world there would be no way back) and 2) portal uniqueness (there can only be one portal connecting any two worlds). So the latter means that you couldn't, for instance, pass through a portal at the airport, fly to another city in a parallel earth where the rate is cheaper, and then pass through a portal back to your earth once you arrive.

But anyway, yeah, the loopholes. So, keep in mind that I still haven't found anything in your system that definitely breaks, but some of it seems like it could be problematic. The main one is this: while you didn't say it explicitly in your summary, I have to assume that when you open a portal, you copy every universe that your universe has ever interacted with, including those that have temporarily closed their portals to you.

The reason is that otherwise, you could make infinite energy or money. Just copy yourself, hand yourself a dollar, then close the portal and repeat (hand your copy 2, then 4, etc.). Since the closed portals don't duplicate, the money grows exponentially but the number of people you split with grows linearly.

Yeah you're right about it copying every universe you're connected to everytime you open a portal. That being said I'm not sure in what sense this is a loophole because I mention it in the question itself.

I'm saying it's not just the ones you're connected to, but also the ones that were connected at some point and have closed their portals to you.

(you know, in the version where you can reopen the portals)

So okay, assuming that every universe gets doubled, then what happens in the following case: you open a portal, then close it, then open a different portal. Then you and your copy on the other side of the second portal both dial into the first portal. Does the one who finished dialing first get it and the other one doesn't work? Or does each copy end up dialing their copy of that universe? Either could be self-consistent - I'm just wondering which you had in mind.

Well firstly you can't open a portal from only one side. You can communicate very expensively at low bandwidth through the microscopic portals present where a portal used to be, but to open a proper portal you need portal creating machines at both sides dialed in to each other. These microscopic portals also mean that a world is never really seperate to any it's ever been connected to.

In the scenario you described though they'd each dial in to a different version of that universe since the "signature" of each universe is only relative to your own universe. So since universes never truly separate when you opened the second portal you went from 2 universes to 4.

I see. Okay, that resolves most of my concerns. The last thing I was unsure about is how connected portals need to be in the same position in space. Does moving one cause the other to move even if the portal isn't open?

You need the machines running the portal pair to move in unison for you to move a portal. If you just moved one machine by say one portal radius then you'd end up with a portal with a shape like the middle of a venn diagram, as a portal can only exist where the energy fields made by the machines overlap in the same position in both universes.

Oh, interesting, that wasn't what I pictured at all. What about in the third dimension? Are these portals thin cylinders? I was imagining them as completely 2D circles, but obviously they'd never overlap unless they had at least some depth.

Yeah they'd have some depth but they'd be pretty thin because that minimizes cost. The thickness here also only really describes which angles they can be passed through from, since the portals just make it so there's no higher dimensional distance separating one universe from another.

Or rather the location corresponding to the portals energy field is a shared location in both universes

Sure, that makes sense. Okay, I was confused about how you could have leeway in how perfectly the portals were lined up while simultaneously making it so that the portals could never change your position. This resulting-portal-is-the-intersection idea solves that pretty neatly.

But yeah, all these details were why I figured being able to re-activate dormant portals could cause issues. If you say that you can't, then you don't have to think about any of it. A portal is always in the same location as its original mirror-universe twin by definition, so you never have to worry about getting the position right.