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Boiled down to its basics, the experiment involves splitting laser light into two beams, so that characteristics of one beam are reflected in the other beam as well. That's an example of what physicists call quantum entanglement. Specifically, Cramer has been planning to fiddle with one of the entangled laser beams such that it takes on the property of waves or particles. If one beam behaves like particles, the entangled photons of light in the other beam should behave like particles, too.
So what happens when the beams go their separate ways, and you conduct a wave-vs.-particle measurement on one beam? When someone else checks the other beam, the same measurement should yield the same result. In fact, you could visualize using the wave-vs.-particle toggle as a means for communicating information, sort of like Morse code. Theoretically, you could check one beam to receive a message instantaneously from whoever is fiddling with the other beam - even if you're separated from the receiver by millions of light-years.
That's what Einstein considered "spooky action at a distance." Such an effect could send information faster than light beams could travel, running counter to special relativity - and thus Einstein thought the effect was impossible to achieve. However, the evidence is mounting that quantum entanglement actually happens.