Check out the lively discussion on reddit about this picture:
Of course, there are a few caveats to any discussion about the physics of portals. Portals don’t actually exist and even in the game world they can’t move (except for one special example). So, not only could this scenario not happen in real life, it couldn’t even happen inside the game. That being said, it’s still a fun thought experiment.
I would tend to argue that B is the correct answer and it completely comes down to relative velocities. The cube has a velocity relative to the orange portal, which means it also has a velocity relative to the blue portal. So when the cube pops out of the blue portal, it should have that same relative velocity.
Some of the comments arguing for A use people jumping through hula hoops or door frames in their response. The space on either side of a hula hoop or door frame maintains the same relative velocity; the space around each portal has a different relative velocity in the scenario depicted above.
I like this argument but I don’t agree with it. Reddit user Falconhaxx uses the means of transmission between the two portals to argue for A. Basically, the cube can either instantaneously appear at the blue portal or move through in infinitesimal slices. Either it pops from one portal to the other or it gradually moves through. In the case that it instantaneously appears at the other portal, option A is correct. Rather than doorways, think of the portals as transporters. Whatever state an object is in when it hits the first transporter will be carried over as it instantly teleports to the other. So, if the cube has no velocity when it reaches the first teleporter, it would have no velocity at the second transporter.
On the other hand, if portals gradually move objects through (which is the stance I tend to take), then the cube would be ripped apart by changing forces. As pieces of the cube go through the portal, each feels an infinite force differential which would rip it apart. Think of dividing by 0. The forces on the cube change over no distance at all (gravity is pointing one way when the cube goes into the blue portal but gravity is pointing a different direction when it comes out), which is more than any piece of matter can handle. As a result, the cube would be sliced into infinitesimally thin slices as slice after slice of it moves from one side of the portal to the other (I bet you didn’t know you could use a variant of the word ‘slice’ four times in one sentence).
Of course, the latter argument could be used for any object going through portals. If the game played by those rules, Portal would hold the record for being the world’s first deli meat slicer simulator. Sure, the game breaks a few laws of physics (that sounds like a good topic for a post…), but it wouldn’t be fun if it didn’t.
In the end, relative velocities make much more sense. If the cube has a velocity relative to the entry portal, it should have a velocity relative to the exit portal.
Think I’m wrong? Comment and let me know!
Edit: This guy has a good point too. Does the relative momentum of the blue portal to the cube matter?
Physics with Portals 