Send light through a beam splitter one photon at a time. Send one of the resulting beams to one lab and the other to a second lab. In the first lab, use a device to change the phase of each photon that arrives. Then measure its phase. In the second lab, just measure each photons phase.
Conventional logic would tell you that the photons arriving at the second lab would not be effected by what was happening in the first lab, and so the phase of the photons measured there would be unchanged. But no, it’s phase was changed too.
Now remember that an individual photon acts like a wave, until you measure something about it, like exactly where it is, or its velocity, or its state (like measuring its phase). Then the wave “collapses” and it is no longer a wave, spread out over space, but a particle, occupying just one location in space.
So, until the phase is measured, the photon really is a wave. It really does “exist” “in” lab 1 and also lab 2 at the same time. That’s the only way changing its phase in lab 1, also changes it in lab 2. So superposition (the idea that a particle exists simultaneously at more than one location) is not just a way of explaining what happens – it really is what happens. Else how can the particle, which arrives in lab 2 and does not arrive in lab 1, nevertheless have its state altered in lab 1?
The photon is a wave which is extended through space to include both labs. It is altered in lab 1 and then, when measured, is found to be a particle (no longer a wave) in lab 1 and not present at all in lab 2.
The really, really weird thing about this is that (iirc) this means that when its phase is being changed by the device in lab 1, so long as the device does not alert us to whether it is, or is not detecting the presence of a photon right “now”, then the device also enters into a state of superposition – it exists at the very same instant as both a device which is altering the state of a photon and a device which is not altering the state of a photon. If we were to set the device to alert us when it is altering a photon, that would collapse the superposition and the photon would either be in one lab or the other but not both. Since this would happen before the photon’s state was altered, it would defeat the purpose of this new experiment as so that’s why the device had to be operating at all times the same whether or not it was then acting on a photon. (I didn’t get to the really, really weird part yet. That’s next.)
But the device is really no different than the scientist in the lab. Not as far as physics goes. So, just as the device is in a state of superposition to the scientist before it alerts him as to whether it is or is not acting on a photon, the scientist is in a state of superposition to people outside the labs, until he tells someone about whether he did or did not detect the photon in his lab. And this new experiment tells us that superposition is real. So the scientist really exists, at the same time, as a scientist who did detect a photon, and a scientist who did not detect a photon. (Ok, that’s the freaky part.)
This experiment was done and summarized here.