Inspired by The Portal Paradox, by minutephysics
Portal is a hilariously mind-bending game which challenges you to use brains over weapons in a diabolical world of Aperture Science Facility. A young woman, Chell, is forced to solve tests designed by psychopath AI, GLaDOS, using a portal gun with a promise to receive a cake when she solves the puzzle. The player can create portals on ceiling, floor, or wall and move through them instantaneously.
Objects in the game, or player themself can pass instantaneously from one end of the portal to another. An object entering one end of the portal at a certain speed leaves the other end at the same speed. The direction of the object leaving the portal depends on the orientation of the other end of the portal. This leads to a paradox — if one end of the portal moves toward the object: does the stationary object simply come out of the portal with zero speed or the object shoots out of the portal with corresponding relative speed?
Obviously, these types of portal do not exist in real life but if they did and obeyed the laws of physics then the question reduces to: if an object has to enter and exit the portal at the same speed then what’s that speed relative to? Velocity is governed in relation to some other object, there is no absolute zero velocity point. This leads us to two options. First, when the object passes through the portal it maintains the same speed relative to the environment though direction may change. Second, the speed of an object, while exiting, is the same as the speed of the portal through which it enters. Another possibility is, the object’s velocity is measured relative to the exit end of the portal. Although the last possibility is quite vague.
First option which suggests the object remains stationary when entering and exiting the portal seems invalid, because how could a stationary object remain stationary while leaving the portal. The object would have to move. There is a way this option might work, as the cross-section of the object passes through the portal then while exiting, the particles will pile up at the portal as 2D cross-section of the object ensures zero velocity. Moreso, in order to retain the shape and topology of the object the exit portal will act as a wall and the entry portal will bounce off the object prohibiting the exit.
Second option seems more reasonable — velocity of the object is measured relative to the individual ends of the portal. This would be roughly what we expect if the portals are connected to each other through a wormhole then the object would obey the Law of Conservation of Momentum in curved spacetime.
Physics point of view suggests that the second option is logical while the designer of the game has opted to otherwise because they are easier to program. Since it is fictional, it’s up to you to decide which approach you would like to follow — the physicists or the programmers.
As we look more into it, we bump into more possibilities and numerous questions pop up.