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As in the game Portal, if we create two portals on two different surfaces and then join the two surfaces with the portals facing each other, as soon as an object passes through one of them, what would happen to that object? Where would it go, and what would be its state?

And what would happen after we separate the two surfaces again?

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If the transfer is instantaneous you cannot move the portals during it. (Duh!)

If time is taken within the portal, the object gets trapped inside it. If the portals are close enough the loop closes and the object is permanently cut off from our universe. But this is unlikely as the wormhole should be too short for significant delay to happen without shredding whatever is thrown in.

If the transfer takes time on the outside, ie. it takes normal time for objects to enter or come out of portal, but insignificant time to pass between portals, which is most consistent with descriptions, you cannot push the portals close enough to each other since the head of the object collides with its tail.

This happens regardless of how you position of the portals. As distance between the portals approaches zero the area object uses on the portal surface approaches infinity. Which exceeds the actual finite surface area of the portal.

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Portals within the game Portal have limitations to avoid this phenomenon

In the game portal the portals are immovable. They collapse when they are moved.

The reason for that is exactly to avoid unsolvable situations like this. If the portals were allowed to move relative to one another you could easily create even bigger issues regarding energy and spacetime than you already have creating a portal like.

So with the basic premise of your question "portals like in Portal moving towards another" you already created something else than portals like those in Portal as they do not allow this phenomenon to occur.

That's why you can't really get any better answer than this. Your premise is not met in your question.

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