Entanglement is a phenomenon in quantum mechanics where two or more particles become correlated in such a way that the state of one particle cannot be described independently of the state of the other particles, even if they are physically separated. This correlation persists even when the particles are far apart, and measuring the state of one particle instantaneously affects the state of the other particle, regardless of the distance between them. This peculiar feature of entanglement is often referred to as "spooky action at a distance."
Non-locality in quantum mechanics arises from the concept of entanglement. When particles are entangled, their quantum states are described by a mathematical construct called a joint or composite state, which represents the correlation between the particles. This joint state cannot be factored into independent states for each particle, meaning that the properties of individual particles are not well-defined until they are measured.
When a measurement is made on one entangled particle, its state "collapses" into a definite value, known as an eigenstate, and as a consequence, the state of the other entangled particle instantaneously collapses as well, regardless of the spatial separation between them. This instantaneous correlation, or "spooky action at a distance," violates our classical intuition of cause and effect and suggests a form of non-locality in quantum mechanics.
The phenomenon of non-locality has been experimentally confirmed through various tests, such as the Bell tests. These experiments involve measuring correlations between entangled particles along different measurement axes and comparing the results with the predictions of local realism, a classical worldview that assumes the existence of pre-existing properties independent of measurement. The violation of certain inequalities, known as Bell inequalities, demonstrates that the correlations observed in entangled systems cannot be explained by local hidden variables theories, and thus, non-locality is a fundamental aspect of quantum mechanics.
It's important to note that while entanglement and non-locality are fascinating features of quantum mechanics, they do not allow for faster-than-light communication. Although the measurement of one entangled particle instantaneously affects the state of the other particle, this effect cannot be used to transmit information or signals faster than the speed of light. The observed correlations are probabilistic and cannot be exploited for superluminal communication.