The statement that entangled particles must be on opposite sides of the universe is a misconception or oversimplification. The phenomenon of quantum entanglement does not imply any constraint on the spatial separation of the particles involved.
Entanglement is a peculiar property of quantum mechanics that occurs when two or more particles become correlated in such a way that their quantum states are linked, even when they are physically separated. When particles are entangled, measuring the state of one particle instantaneously affects the state of the other particle, regardless of the distance between them.
The concept of entangled particles having opposite spins refers to a specific example of entanglement called spin entanglement. In this case, two particles, such as electrons, can be prepared in a quantum state where their spins are entangled. If the spins of the particles are measured along the same direction, they will always be found to have opposite spin values (i.e., one up and one down), regardless of the distance between them.
However, it is important to note that the entangled particles can be in proximity to each other or widely separated. The correlation between their states is not dependent on their spatial separation. The nature of entanglement allows for instantaneous connections between the particles, regardless of the distance between them, which is often referred to as "spooky action at a distance."
The notion of entangled particles being on opposite sides of the universe is misleading because entanglement is not limited by distance. Experiments have demonstrated entanglement between particles separated by large distances, including those conducted on Earth that have successfully entangled particles over considerable separations.
In summary, entanglement does not require entangled particles to be on opposite sides of the universe, but rather it establishes a deep quantum connection between them that defies classical notions of locality and can operate over vast distances.