Yet Another Portal Paradox.

Moving portals are weird. So in this video I show some options how objects might collide with them.

[claytongrey]

I think both should move with ½ the momentum you apply to the cube

[nightblind]

Going under the assumption that you could actually move these portals somehow it would move both simultaneously as you’re essentially moving one door way with one object.

[minesboom]

I think, there could be another possibility: The Cube is split in half

[Kram]

This scenario is a bit like pushing one billiard ball against two others:
You push the cube into these frames with a certain force.
The frames are able to resist this force, as all objects do, through their mass.
If a frame has infinite mass, it's not gonna be affected by the cube at all, just staying still no matter what: It's the fabled "immovable object".
However, with finite masses, the momentum transfer works as always: the box is eventually going to push the portal, faster and faster the longer the pushing force is kept up (though potentially limited by some sort of global-ish drag force such as air resistance)

From the box' perspective, it's only seeing one object that's the combined mass of both portals. From the portals' perspectives, each feels the impact of a box diminished in proportion to how heavy that portal is. I *think* that math ought to check out.

In particular, if both portals have the same mass, we land at scenario 1, but if either portal is *way* heavier than both the box and the other portal, we get ever closer to scenario 2.
For specific setups, in the limit, both 1 and 2 are therefore physical (or physical in the limit)
Scenario 3 is the case where *both* portals have infinite mass.

So I think the reason there could be a case for all three is because you could smoothly interpolate between all three in a way that remains physical. Just consider frames with mass and it all should work out just fine.

Now what I'm wondering about is what sort of shenanigans happen in terms of momentum transfer as frames *with mass* pass through each other. Presumably, they'd give each other some sort of kick? It's gonna be particularly curious if we allow scale changes. Mass ought to be conserved, so I *think* the correct thing then is that the object's *density* changes to keep constant mass? It's certainly quite strange.

[unrellated]

It would move the wall on the side of the "equal and opposite reaction" of the moving cube's "action". Basically, when you're holding the cube, the portal that your hand is going into.

[cinfdef]

Since portals are just connections between space, and it is assumed that these portals can be moved via other means, then it can basically be assumed that both would be moved whilst dividing the forces between the two (almost as if you were pushing two items that were in the same location)

If you were to, hypothetically, make one of them completely static but the other not, then it would simply let one move and the other not move (as we have to ensure where the line is met between portal A and portal B, this means force is applied on one but not the other. if you think of two literal frames that aren't portals and are divided long-wise, and you mimic this exact scenario with one of them being static, the other would move and the cube would pivot off of the static one. The difference here is simply the point of reference and how, because the portal (the bridge between the spaces) moves along with the pushed object, it results in the first one appearing to not move and the second being able to.

It not easy describing this in words, best way I can say it is that depending on what portals are static and what aren't, all situations provided are technically viable if there are differences between static and non-static.

1. If both are non-static, both should move with equally half the force on both.
2. If one is static, only one portal will move and will probably rotate itself due to the unequal pressure point on the frame compared to its centre of mass.
3. If both are static, then obviously neither move.

EDIT: I do think that both would pivot alongside the movement, as we have to take into account the pressure points relative to their centres of mass. This also depends on the "seam-lines" of the portals themselves.

[HeadpriestPEPSI]

Doesn't the cube exist in both spaces at the same time tho?
It wouldn't make sense for it to not effect either frame

[jfb-]

2/2b makes no sense because the situation is symmetric. both cubes (really, the same cube) hit the portal frame at the same time so it doesn't make sense for them to behave differently. 3 makes more sense but it raises the question of where does the momentum go? The cube isn't bumping into itself. So 1 is the best answer.
How much momentum should each frame get? assuming the box is perfectly centred, each frame should get half the momentum that the box loses.

If the box was inside a regular door frame (which is what it looks like from the perspective of the box), it would give some momentum to the frame; which is split evenly among the top and bottom half.
In the portal situation then there is a region of space that is identified (consisting of a 2d plane), but each half of the frame still gets the same momentum.
if the box's centre of mass wasn't perfectly on that plane, then the momentum split would be different.

[ZIMOU]

I think the answer is 2b because if you put a cube inside a portal it won't go inside the portal it will go outside the other end so if you put the cube in the portal then you have it move to the right the wall piece at the other portal would move

[ImDed]

Personally I interpret the portals to be "immovable", but exist relatively to the physical frames or surfaces that hold them, therefore it depends on whether you consider the cube to be interacting with the inner edge portal, or the physical object it's anchored to/powered by.
If the cube is hitting the frame, then the energy is transferred to each side of the frame depending on how much of the mass of the cube is on it, as @claytongrey988 said.
If the cube is being pushed into the edge of the portal itself, then the portal should not move, and the cube could either be cut in half like @minesboom5945 said, or be repelled and bounce off.