no-signaling theorem

The no-signaling theorem is the guarantee that entanglement, for all its strange correlations, cannot be used to send information faster than light. No matter what measurement one party makes on their half of an entangled pair, and no matter what result they get, the statistics seen by the distant party are completely unchanged. There is no operation on one side that the other side could ever notice on its own.

The reason is built into the mathematics. When you ignore the far particle and look only at what you can measure locally, your description is the same whether or not your partner has measured, and whatever they chose to measure. Your local outcomes look like ordinary random noise; the special correlations only emerge later, when the two separated records are brought together and compared, which itself requires a slower-than-light channel.

This is why entanglement and relativity coexist in peace. The correlations are non-local, yet useless for messaging, so causality is never violated. The no-signaling theorem is also taken seriously as a principle in its own right: some researchers ask how much of quantum mechanics can be derived simply from demanding strong correlations that still forbid faster-than-light communication, treating no-signaling as a deep constraint on any sensible theory of nature.