I am a little bemused at some of the apparent nonsense I have read about entanglement, so in the hope of demystifying it I have devised a thought experiment not unlike the one Schroedinger proposed to demonstrate superposition.
In this experiment there are two cats, and the box is divided into two compartments linked by a single random device between them which can act only once and is equally likely to act towards one side or the other. The two compartments have two independent lids. They are white cats, and, since I am a cat lover I am not going to kill either of them. Instead, one of them will be dyed red by the random device between the boxes. This event will happen the instant the lids of both sides of the box are closed.
So I place my two beloved white cats into the box, one in each compartment, and close the lid. Now, I know for sure at that instant that I no longer have two white cats. But I don’t have a red cat or a white cat either. Instead, I have two cats that are both white and red, because according to the laws of probability there is an equal 50% chance that each will be either red or white.
(This is not really a quantum experiment because the dimension of time is missing but the reason for this will become clear.)
Now, apparently, I am about to perform something akin to magic, and transmit information faster than the speed of light breaking all the laws of causality. I am going to open the right hand lid.
I will know the colour of the cat I am looking at at the speed of light of course, as the colour information is transmitted to my eye. But simultaneously I will know the colour of the other one too. Because if one cat is white I know instantly that the other one is red, and vice versa. I will know this faster than the speed of light.
Unless I have missed something fundamental the ‘entangled’ fate of the two cats is what all the fuss is about. The fact that I have received a piece of information faster than the speed of light will not seem mysterious or magical to anyone other than, perhaps, a mathematician.
Now, you could take this thought experiment an unlikely stage further. You could have a much more sophisticated device between the two compartments that produced an interlinked result by an infinite number of degrees. So if the left hand cat were deep pink the right hand cat would be light pink. And vice versa. And equally for all shades of pink in between. There would be no shade of pink in cat that could not be instantly transmitted by cat A in this way.
Of course, a device that could produce such a result would take many years to develop, and it would cost a huge amount of money. But then, the machines that have been developed to test entanglement are far more complex than this and have cost millions of pounds too, so maybe someone somewhere would consider it an exercise worth doing. I hope not.