I think you'd be able to get it in a little ways before top of the box pushes against its own lid, preventing it from going in any further. If the lid pops back open, then the top of the box will begin sticking out of the box which will likely make it too wide to fit all the way through the wall portal.
But the rules of Portal is that the portals themselves break when moved by any substantial extent anyways so in the game it would just disable the portal altogether.
It's the scene with the lasers innit? So many "paradoxes" are solved with the answer of "portals cannot move relative to one another," and then they do the bit with the laser. -_-
The thing is, movement is relative. Everything on earth is constantly in motion if you're observing from any other celestial body, so motion itself can't be what breaks portals. What it might be, though, is acceleration. Those panels in the video seem to be moving at a constant speed, so aren't experiencing any substantial acceleration, making a portal on them possible
I guess the question becomes if one portal is in a box, what happens to the box? Does the whole process just get blocked after the first few inches as the outside of the box collides with the inside; does it push itself open; do the portals just slice though and turn the pieces of box in the way into confetti?
Just came here to check whether someone already posted the minutephysics video.
I think their explanation is rather good for passing portals through themselves. The box doesn't add much to the equation: it is just physical objects smashed into eachother...
That doesn't work because gravity makes the game's reference frame non-inertial. One of the big takeaways of general relativity is that idea a reference frame that's inertial except for gravity is meaningless. Even ignoring relativity, everything is subjected to centripetal acceleration due to the Earth's rotation (and the story canonically takes place on Earth).
I think the real answer is probably the least satisfying: the game's physics just don't correspond to real physics. Most portals appear to exist in a privileged reference frame that can be said to be motionless, but even that isn't the real rule; the real rule is that portals can exist where the level designers want to allow them to exist. They try to make it feel like there's a certain logic behind it, but they'll bend the rules as necessary to make a cool puzzle work, and they keep the everything consistent within a single puzzle, but some subtleties of how portals appear to work are subject to change between puzzles.
This always bothers me when people argue what would happen if you pushed Portal portals into each other. You can't. The moment the surface moves, it's unstable and the portal pops. They're quite specific about this in the games.
That's only in direction of motion. The height still won't fit. Of course, all hell breaks loose if they touch even if they don't pass all the way through.
The real question is what would happen if you tossed a normal size gate into an Ori supergate that were connected.
We know they CAN connect, since that's how they block the supergate from this side. And they never established whether a connected gate can move through space without losing a connection, just that you have to know where you are in space to dial out, and two gates can't activate when close together.
Didn't they establish that a ship has to stop to connect? Wasn't that a thing with Universe and the gate being ON the ship? So a gate can't be actively moving while connected, I think. My memory is a bit fuzzy. And I feel like there's still one time an exception is made, but it involves some one time use trickery.