The puzzle of entanglement in quantum theory

I. Action at a Distance. Imagine a table with a tablecloth draping to the floor. There is a vase on the table. Suddenly, for no apparent reason, the vase moves. What would be your reaction? My guess is that you would wonder what was the cause of the movement. Perhaps there is a motor under the table connected by a hidden wire to the next room where someone flipped a switch. Perhaps the motor is battery operated and was activated by a radio signal from across campus. Perhaps someone threw a ball hidden from your line of sight at the vase. There is a limit to how fast a causal agent, be it electricity flowing in a wire, a radio signal, or a hidden ball, can propagate. A fundamental principle of modern physics is the principle of relativistic causality: Causal influences cannot propagate faster than the speed of light. Less precisely: There is no action at a distance. For example, light takes eight minutes to travel from the Sun to the Earth. Thus, any causal influence from the Sun on the movement of the vase had to occur at least eight minutes before it moved. Atomic and subatomic particles can come within a hairsbreadth of violating the principle. This occurs when two or more particles are entangled. Entangled particles which are in different places are connected in a mysterious way that seems impossible. This so disturbed Einstein that he called entanglement “spooky action at a distance”. Entanglement is the topic of this lecture. Before looking at entanglement, let us take a quick tour of the fundamental theories of physics to see what they say about action at a distance.