Entanglement is a phenomenon in quantum mechanics where two or more particles become correlated in such a way that the state of one particle is dependent on the state of the other(s), regardless of the distance between them. This correlation holds regardless of the speed of the particles or any time dilation effects that may occur.
When two entangled particles are measured, their wave function collapses, and their properties become determined. However, the measurement outcomes for both particles are instantaneously correlated, even if they are far apart. This instantaneous correlation, often referred to as "spooky action at a distance," is a puzzling feature of quantum mechanics.
According to the theory of relativity, information cannot travel faster than the speed of light. Therefore, the collapse of the wave function and the determination of the particle's properties should not violate this principle. Even if one of the entangled particles is moving at speeds close to the speed of light and experiencing time dilation, the correlation between the particles remains intact.
It is important to note that the concept of wave function collapse and the interpretation of quantum mechanics, especially in scenarios involving entanglement, are still subjects of debate and ongoing research. Various interpretations, such as the many-worlds interpretation or the pilot-wave theory, offer different perspectives on the nature of entanglement and its implications for the flow of information and causality.