Wheeler's delayed choice experiment

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Wheeler's delayed choice experiment was originally a thought experiment proposed by John Archibald Wheeler in 1978 (Mathematical Foundations of Quantum Theory, edited by A.R. Marlow, Academic Press). Wheeler proposes a variation of the famous Double-slit experiment of quantum physics, where the target detector can be changed at the last moment, according to a "delayed choice" of the observer. There is a detector screen, which will detect the normal wave interference pattern produced by the double slit, which can also be removed. Behind the screen are two tightly focused telescopes, aimed to observe one slit or the other, which would detect which path the photon traveled. According to the results of the double slit experiment, if we know which slit the photon goes through, we change the outcome of the experiment and the behavior of the photon. If we know which slit it goes through, the photon will behave as a particle. If we do not know which slit it goes through, the photon will behave as if it were a wave. This wave-particle duality of photons (and in fact all quantum particles) is one of the fundamental mysteries of quantum mechanics.

On the surface, the outcome of the experiment seems simple. If we observe the photons with the screen, we get the wave like behavior. If we observe the photons with the telescopes, we get the particle like behavior. However, imagine a more bizarre scenario where the scale of the experiment is magnified to astronomical dimensions: the photon has originated from a star or galaxy on the other side of the universe, and bent by an intervening galaxy, black hole, or other massive object, so that it arrives at our detector by one of two different paths. If we observe the photon with a screen like detector, such as a photographic plate or other imaging device (as in the original experiment), we should see an interference pattern, but if instead we use a binocular telescope (two telescopes focused to either side of the black hole) we will observe two small points, because the photons must behave like particles. So, in fact which side of the black hole did the photon go to? The photon has been traveling through space for billions of years, is it a particle or a wave?

Consider another variation, the delayed choice quantum eraser, where we combine Wheeler's delayed choice experiment with a quantum eraser experiment, so we can choose to observe the photon or not observe the photon after it hits our detector. We can apparently change the outcome of an event which occurred in the past!