|I have a question about quantum entanglement that has been bugging me for years.|
My understanding is that a photon in superposition will create an interference pattern on a screen with a double slit in front of it, and if you activate detectors at the slits to determine which slit the photon passes through, the wave function will collapse and the photon will not create an interference pattern on the screen.
It is also my understanding that when you have a pair of entangled photons, they are both initially in superposition, and if you use a detector on one, the wave function collapses for both photons. So if you send them each toward a screen with a double slit in front of it, both screens will either show an interference pattern if you haven’t used a detector, or they won’t if you did. The detector can determine the spin direction or polarity of one photon, and because they are entangled, you will know the spin direction or polarity of the other instantly (due to quantum non-locality).
Now let’s say Alice and Bob are at two different points in interstellar space, 2 light years apart, and they want to communicate. Directly between them (1 light year from each), we have a photon generator that creates pairs of entangled photons, and sends the photons from each pair toward Alice and Bob. Once the photons arrive, if Alice uses a detector, she can know the spin direction or polarity of Bob’s photon (the other photon of the entangled pair).
But Alice and Bob can’t control the spin direction or polarity of their photons. The no-communication theorem shows that if Alice detects the spin direction or polarity of her photon, and Bob detects the spin direction or polarity of his photon, they will each know the spin direction/polarity of the other, but they will have no way to change the spin of the other, so no information can be transferred directly. And if they don’t use a detector, they won’t know what the spin direction or polarity is, even for their own photon.
But what if Alice and Bob don’t bother trying to determine the spin direction or polarity. Let’s say Alice and Bob both have screens with double slits in front of them, with detectors at the slits. If Alice wants to send a bit of information to Bob, she either turns on the detector at her slits (a binary 1) or she doesn’t (a binary 0). If she leaves her detector off, her photon generates an interference pattern on her screen, and because her photon is entangled with Bob’s, his photon creates an interference pattern on his screen too, so he instantly knows that Alice sent him a 0. When the next pair of photons arrive at their interferometers, if she turns on her detector, her waveform collapses, and no interference pattern is created on her screen. Because her photon was entangled with Bob’s, the waveform of his photon also collapses, and no interference pattern is created on his screen either, so Bob instantly knows that Alice sent him a 1.
In this way, Alice and Bob simply need to agree which timeslots will be used for sending bits in each direction. The generator can be setup to send a stream of entangled photons in each direction, and Alice and Bob can each send bits to each other instantly during their assigned timeslots. They only need to wait 1 year for the photons in the stream to reach them, but thereafter, communication is instantaneous.
Is there a key that I’m missing, or is FTL communication possible?