The result of a thought experiment invented by Albert Einstein, Boris Podolsky and Nathan Rosen and publised under the title Can quantum-mechanical description of physical reality be considered complete? in issue 41 of Physical Review in 1935. It was intended to show contradictions, or at least a lack of completeness in quantum theory, which could only be resolved by adding additional hidden variables. The experiment works like this:
  1. Take two physical systems that initially interact with each other in such a way that both are described by a single Schrödinger wave equation. This allows you to infer information about one system from an observation made on the other.
  2. Separate the systems
  3. Make a precise measurement in one system that allows you to infer information about one in a set of noncommuting observables in the second system.
  4. Make a precise measurement of one of the other observables of the set in the second system.
  5. Et voila! You have just violated the uncertainty principle in that system.
  6. Watch the universe evaporate in a cloud of logic.
To be more specific: in step 1, take two photons that emerged from the decay of a neutral pion at rest. The law of conservation of momentum says that they must have exactly opposite momentum, since the original particle had none. In step 3, measure the momentum of the first photon. You now know the momentum of the second one without having actually touched (measured) it. In step 4, measure the position of the second photon, which the uncertainty principle says you cannot know at the same time as the momentum.

It counts as a thought experiment because current technology is unable to create completely isolated physical systems, let alone separate and move apart two that contain particles moving at the speed of light. Basically, any straightforward setup would fuck up the measurements many times over.

However, in 1964 John Bell formulated a derived formula (now called Bell's Inequality Principle) which would show the existence of the above-mentioned hidden variables and could be tested for in a variety of far more manageable circumstances. Results were negative, but many physicists argued that there are subtle flaws in Bell's reasoning or that the experimental setups were not adequate. The issue remains unresolved.