The delayed choice quantum eraser experiment implies that the order of events is violated when a photon has chosen it's path, i.e. retrocausality (see http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser). I was wondering if an experiment has ever been performed to check if the path of photons are time independent.
I have an experiment where BBO crystal emits an entangled pair of photons. The idler photon passes through the optical switch and follows path 1. The signal photon is sent to a photo-multiplier which triggers a relay switch to its ON position. The relay switch will turn the optical switch on to potentially change the idler's path to path 2 at time t, after it has passed through the switch and before it is observed. After the photon is detected at either D1 or D2 the relay switch is set to its OFF position and the optical switch is set to route the next photon back to path 1.
If a photon's path was truly time independent (in support of the retrocausality theory), the photon should take the newly introduced path and be detected at D2 instead of the path it took when it entered the optical switch (path 1). If the photon is detected at D1, this would be evidence against retrocausality in the delayed choice quantum eraser experiment.
Here is a diagram of an experiment of what I am asking about: