The idea of a wave collapsing without an interaction that "measures" it is nonsense. Plus the idea that the second photon's wave function also collapses would directly contradict an entanglement experiment from 2012, where two entangled photons were explicitly measured at different times.
I ASSUME from the wording that what he actually refers to is precisely entanglement. A.k.a., spooky action at a distance. Although it's incorrect IMHO to describe it as communication between the two particles, and pure nonsense to claim that the particle knew what was in the mind of the researchers.
Let me try to explain entanglement in a kinda preschoolers' colouring book way. It will probably make the physicists cringe, but ah well, they can't have everything
Let's say the Roman Emperor in Constantinople has a big problem with the Germans in the West, and an arguably even bigger one with the Persians in the east. Now the thing is, he doesn't have the manpower or money to just declare war on BOTH at the same time, so he'll have to choose one.
He also has an army of the east and an army of the west, each with its own general. And he writes two letters, one to each general. One general will get the order to stay put and await the other army as reinforcements, the other will get the order to mobilize everything but the border garrisons and move to join with the other army.
But since the Emperor is concerned with spies and treason and all the byzantine intrigue, the two letters are encrypted and sealed, and nobody knows which general will get which order. Just that they are opposite of each other.
So two riders take a letter each and ride to the two generals. And nobody knows who'll get the order to move and which got the letter to stay... until ONE of the letters is opened. Then you instantly know what's in the other too, because it HAS to be the opposite.
You could think of it as, wow, in an age when the maximum communication speed was as fast as a horse could go, now the second letter learned the state of the first one in less than a second! From thousands of miles away! What amazing communication between two inanimate letters!
But it's not. The two letters have been the opposite of each other all along.
And you can't actually use it to communicate faster than the speed of horse. Changing the contents of a letter won't make the contents of the other change.
Well, entanglement is the same. E.g., two photons are emitted that have opposite spin. Except nobody "knows" -- fundamentally, as in, not even the photons themselves know it yet -- which has which spin. Just that the sum must be zero. So when you collapse THAT probability by measuring the spin of one, then you automatically know the spin of the other too. Because the whole time they HAD to be opposites.
As you can probably figure out by now, human consciousness doesn't factor in there at any point and in any way. And the particles' entanglement -- the total spin in my example, but it can be other stuff -- has nothing to do with "knowing" what the researchers want to do. The two simply must have a constant and known sum in some way. WHEN and IF one is "measured" by some interaction, the automatically the other one has the value that preserves that sum. If you delay measuring it, well, it just stays unknown longer. And if you avoid measuring either one for ever, well, then it just stays unknown.
It doesn't matter what you wanted. It doesn't matter whether you planned the experiment in a certain way, or even if it's a planned experiment at all. Just whenever one has to be a defined value instead of a probability, for whatever reason (the majority of possible reasons being completely unrelated to humans), the other has a defined value too.