In that situation both portals (the inside and the outside window frame) have equal, but opposite velocities and therefore cancel out any momentum from the person.
When dealing with OP’s scenario, only one portal is moving.
The problem with this analogy is that both sides of the window are at the same point in space so there is no pressure differential. What if the blue portal was at the bottom of the Mariana’s Trench? What force displaces the water to place the cube on the other side?
It wouldn’t. Same as if the other side of the portal was a brick wall. It wouldn’t go through or would be smooshed by whatever force is driving the portal.
This was answered decades ago
wikipedia.org/wiki/Steamboat_Bill,_Jr.
Nearly a century ago. Fun fact, this movie inspired Steamboat Willie, the very first appearance of Micky Mouse.
In that situation both portals (the inside and the outside window frame) have equal, but opposite velocities and therefore cancel out any momentum from the person.
When dealing with OP’s scenario, only one portal is moving.
The problem with this analogy is that both sides of the window are at the same point in space so there is no pressure differential. What if the blue portal was at the bottom of the Mariana’s Trench? What force displaces the water to place the cube on the other side?
It wouldn’t. Same as if the other side of the portal was a brick wall. It wouldn’t go through or would be smooshed by whatever force is driving the portal.