Portal Paradox

Wormholes seem straightforward when both ends are stationary—one enters at one end and exits from the other at the same speed. However, complications arise when we begin to move one end of the wormhole. For instance, picture a baseball resting on a table, with one end of a wormhole descending towards it at a speed of 1 m/s (the orange end), while the other end points upward (the blue end). The question then becomes: what occurs when the baseball enters the wormhole?

Two primary outcomes seem possible: either the ball exits the blue end without moving or it is ejected upwards at 1 m/s. However, both scenarios lead to contradictions.

Considering the first outcome—how can the baseball come out of the blue end without any motion? It requires movement to rise from the table, meaning it cannot simply materialize; it must pass through the wormhole. Thus, this scenario is impossible.

Now, if we explore the second outcome—where the ball shoots out at 1 m/s—we encounter another issue. Where does this extra momentum originate? The baseball must gain kinetic energy to exit the blue end, raising questions about conservation of energy. Furthermore, if we assess the baseball's motion from different reference points, it appears stationary in the room but possesses substantial momentum relative to the Solar System. This leads to a contradiction: does the baseball exit at 1 m/s or several kilometers per second? Thus, neither possibility holds true.

Infinite Gravity-Well Paradox

What if we could create a perpetual motion machine using a wormhole? Imagine positioning the ends of a wormhole directly above a massive object, like a planet or a star, so that dropping an object into this setup would result in it falling indefinitely. Now, consider throwing a magnet into this endless gravitational fall while encircling it with a coil of wire.

As the magnet moves through the coil, it generates an electric current, effectively creating a perpetual motion machine and an unlimited source of electrical energy. Each time the magnet traverses the wormhole, it seemingly gains gravitational potential energy for free, raising the question: where is this unlimited energy coming from? This scenario contradicts the law of energy conservation, which states that energy and mass cannot be created, only transformed.

Grandfather Paradox

The wormholes discussed so far have focused on spatial transport, but they can also theoretically facilitate time travel, leading to the Grandfather Paradox. Imagine positioning the ends of a wormhole at right angles so that one could exit into the past, potentially colliding with their former self. This scenario suggests that one could inadvertently prevent their own existence, as they would not have traveled back in time if they had not entered the wormhole.

This is akin to the classic thought experiment of traveling back in time to eliminate one's grandfather, raising the question of how one could exist to perform such an act. Thus, if wormholes indeed allow for temporal travel, they could fundamentally undermine the laws of causality.

While there are complex solutions involving quantum mechanics and numerous wormholes, these remain challenging to articulate. Nonetheless, it is clear that a single wormhole could disrupt causality.