BruceW said:
Yeah, it is possible in principle. The wavefunction will collapse instantaneously. And this would appear to violate relativity, but it actually does not. Relativity is only violated if information is transmitted at faster-than-light speeds.
Okay. I think though, the statement "Relativity is only violated if information is transmitted at faster-than-light speeds." is a cop out. It's also used as the get out of jail card for quantum entanglement - spooky action at a distance. Einstein never said, that if there is inconvenient events happening, as long as they can't transfer usable information (information that could be used in data communications) then they don't violate relativity.
Before I say anything else - take careful note, I'm using the term wave, instead of wavefunction.
The light's wave front traveling through space, does not violate relativity. And if instead of considering a wave, you considered the photon taking a straight beam like path through space - it doesn't violate relativity.
There's a painful trick with these waves. We cannot tell they're actually there, unless we collapse the wave. But by setting them up to create interference patterns, we can know that they were there, before we collapsed them.
Even though we can't interact with the information contained in the waves - we can see the wave distributes information to make the interference patterns possible. Where the interference occurs locally, it doesn't violate relativity. Where the problem really becomes painful apparent, is when the wave collapses - all the information (the interference pattern) is encapsulated in the point collapse of the wave. I don't think relativity has anything to say on this.
What's often said about quantum physics is it's the physics of the really small. This isn't true. A tiny excited atom may release a photon. But that photon can travel through space for billions of years. These waves are the hugest things in the universe. We don't even have to go into outer space to consider how big they are - just think of radio waves from television stations.
A photon travels from the sun. When you see anything illuminated by sunlight, what you're seeing is the collapse of the light wave - and the waves from the sun that collapse here have a circumference of 37.68 x 10^6 million miles. The wave could pick an infinite number of places to collapse - but it chooses your eye. And drops all it's energy into your eye. If the energy is evenly distributed through the wave, when it collapses, the transmission of that energy to the point of collapse, does violate relativity - or needs something else to explain it - probability is not an explanation.
The stars at night - the light from those stars is often thousands of years old. The circumference of those waves expands at faster than the speed of light by a factor of ∏, the entire surface area of the wave front even faster. They are colossal, yet, their waves collapse into your eye, as if they're the tiniest things.