Figure 17

Space-time diagrams for two versions of a Bell test involving human choices made by astronauts on Earth and Moon. The source is shown at an arbitrary position between Earth and Moon. There is a limited time window for humans at each location to be presented with options and make a choice, indicated by the black arrows. These windows have maximum duration \(t_{E}\) and \(t_{M}\). Each time window starts after the last event that could influence the other side’s measurement and ends when the choice needs to be used or transmitted. These windows are shortened by hundreds of nanoseconds (too small to see at this scale) due to fiber delays, bounces within telescopes, and transmission through atmosphere. Dual Transmissions (Left): If the source is midway between Earth and Moon, in each round, humans on each side have ∼1.3 seconds to be presented with a choice, make a decision, register their decision with something like a button, and have that decision converted into a polarizer setting. When the entangled source is farther from Earth, people there have more time \(t_{E}\) to make their basis choice at the expense of time on the moon \(t_{M}\). The best situation is when the entangled source is halfway between Earth and Moon, when astronauts at each location have equal time to make a valid choice; that time equals the Earth-Moon light travel time, ∼1.3 seconds. Single Transmission and Storage (Right): In this asymmetric configuration, while the space-like separation of random choice is made by humans separated by the Earth-Moon distance, only one of the entangled photons is sent over a long distance link to Earth; the other entangled half is stored in a quantum memory at the source, awaiting the random choice classical signal transmitted from the Moon. By the geometry of the causal influences, the maximum time window \(t_{M}\) in which the astronauts on the moon need to make their basis choice is equal to the storage time \(t_{S}\). A longer storage time comes at the expense of Earth decision time \(t_{E}\). The best situation is to divide the decision time equally, (\(t_{E}=t_{M}=t_{S}\)). In this case, the source near the moon, transmits one entangled photon all the way to Earth, and stores the other entangled photon for the full 1.3 seconds