Exactly. What would that 'other frame of reference' be and how would the portal know about it?

Whats the difference between an object moving and everything else moving? For an observer on the sun every one of us has huge momentum which would be preserved when entering a portal. Momentum is always relative to some frame of reference. Momentum 'toward' the portal would be conserved and mirrored through the other portal.

I brought this up on another comment that's for some reason now deleted but, if the universe moves around you, would you not perceive it as movement?

well, in my opinion it is a bit of a paradox. i think you are partially correct.

your door analogy may be right from the perspective of the platform on which the cube is. however, one flaw is that the whole space is moving, not just the door. as soon as the cube enters that door, it will be inside that space, and if you consider the cube part of it, moving that space "downward", then due the cube being held by the platform, you could consider the cube moving "upward" in the space behind the orange portal. if you consider preserving momentum there, then as soon as the apparatus stops moving, the cube should not stop its momentum and move further up in the space.

or look at it like this: if you are behind the orange portal, meaning you are looking at the blue portal, you will see a cube moving towards you. then as soon as the platform hits the wall of the orange portal, the preserved momentum should make the cube "fly".

the change of perspective leads to two different conclusions, therefore i think it is a paradox.

the problem sort of is that there are two "spacetimes" that are kind of being changed. one could interpret it as both of these effects "pulling" against each other since when the cube has partially passed the portal, one part of the cube is "in one of the spacetimes", ant the other part in the other. ultimately though, the cube then would actually fly because in the limit (infinitesinally close to when the platform hits the portal wall) the cube is completely on the other side of the portal, so from the view of that spacetime, the cube does get pushed and should fly.

i don't even remember if it is possible in the video game for walls with portals that move. a video game would probablt have some kind of "center of mass", like a single vector of coordinates where describing the position of the object. there is no notion of "partially" being somewhere (except for collision boxes, but i don't mean that). so also from that view the box would fly. however, in most video games (with or without portals), if a platform moves up and suddenly stops, the object won't travel further in that direction anyway, especially not ulwards (even sideways usually not).

More like a hole in the wall with you standing perfectly still while the wall moves past you.

Except the wall has no mass or width.

Correct. If a stationary door/portal has no affect on the cube's velocity than that's also true for a moving door/portal.

Stop stealing all my upvotes

Perfectly understood the assignment, 10/10, no notes.

Okay, after thinking about this a while, I've decided that conservation of momentum just doesn't work, unless the portal actually absorbs the mass of every object passing through it, which would probably cause its own set of contradictions.

Instead, I think forces that act through the portal are applied to the portal. What do I mean by this? Well, take this classic case of a cube floating halfway through two floor portals:

      ____            ____
     |    |          |    |
___++++++++++______----------___

(sorry, can't do better than ASCII art right now)

The system has reached equilibrium, and nothing is moving. Both halves of the cube are being pulled down by gravity, but cancel each other out by applying a normal force on each other right at the portal interface. What I'm claiming is that this normal force is applied to the portals, which ultimately transfer it to the floor. If this entire floor was a scale, it would measure the calibrated weight of the Weighted Storage Cube.

But this is the static analysis. What happens when objects are in motion? To be continued...

I don't think this can work. Think through it in several steps rather than just one. Once the cube just started entering the portal, a part of it will already be on the other side, as close to the 2nd portal as possible. When the portal continues moving, more of the cube needs to be on the other side, so it "pushes" the first part of the cube further away. The cube imparts momentum onto itself.

Another way to look at it is using reference frames. It really doesn't make a difference whether the cube is moving towards the portal or the portal towards the cube. It only matters what the difference of velocity is. The difference of velocity must be maintained on the other side of the portal, and since the 2nd portal is stationary, the cube must move.

you can in one specific spot in portal 2!

So the cube is just smashed?

It's a practical answer which is slightly upsetting because I wanted more discourse.

What if the blue portal is at the bottom of the Marianas Trench?

Speedy thing go in, speedy thing come out. Clearly explained in game.

For anyone who doesn't know, Optozorax on YouTube has made a finite element analysis simulation of gravity ontop of his portal simulation so we can get an answer to the question. The answer is both. Both happen depending on how fast the portal is moving and the where the second portal is placed in the gravity well.

The cube has a speed of about 30km/s around the sun. You want to measure speed relative to the blue portal, but why that one and not the orange one?

But reference frame changes as the cube passes through the portal. The piston would feel resistance as its momentum is transferred to the cube to conserve it.