Hi @Bubblesofearth.
I too have been curious about Quantum Entanglement. But as far as I can tell it’s a lot more subtle than the situation you describe, and I think its very difficult to have any real appreciation of it from popular accounts. If you have a maths background then I can recommend the excellent online lectures by the renowned theoretical Physicist Leonard Susskind: “The Theoretical Minimum” (
http://theoreticalminimum.com) . They are designed to give you a good level of appreciation with the minimum of maths.
I don’t think the example in your description captures the quantum behaviour, your description is analogous to the situation with two coloured balls. Imagine an experiment that randomly places one of two differently coloured balls into two opaque boxes. One is given to you and one to your partner. You each go to far apart places and open your box. You each immediately know by looking at the colour of your ball the colour of the other, which is now far away. No information needs to be sent between the locations. This is similar to the situation you describe and has no mystery.
Now imagine an experiment with two quantum photons. In a “complete” classical description of two photons you would have to know everything about the individual photons. This is also a possible situation In Quantum Mechanics, ie each photon may behave independently of the other. but there are more possibilities in the quantum description, ie states where you know all there is to know about the combined photons as a single system, without knowing anything about the individual photons. These states are the states when the photons are maximumly entangled. Now this seems a bit like the situation with the coloured balls but the behaviour of the quantum system is different. That’s where the surprise lies.
I am not a quantum physicist so I can only give you my best efforts description without reviewing all the lectures. But its something like this:
For a very simple quantum system which has two states, spin-up, spin-down, you can only get a yes/no answers to a question about the spin, eg is the spin in this direction up or down? That’s all you can ask, and all you can know. Once you know the answer for one direction, you could then ask the same yes/no question for a different direction and you get a new yes/no answer.
If you ask the same question for the same direction (and you are careful not to change things), you get the same answer. But if you chose a new direction, you get a new yes/no answer for the new direction, you can’t know what the answer will be, but quantum mechanics allows you to calculate the probability of Yes and the probability of no. Once you make the new measurement in the new direction all information about the original direction is lost. It’s as if the new measurement forces the system into a new state, which answers your question for the new direction, and removes any knowledge of previous measurements. All you know is the result of the last experiment.
The way quantum calculations are done, is to model a quantum system as vectors in a complex Hilbert space, which assigns complex amplitudes to vectors made up of base states representing the possible outcomes of experiments. Once you know the state of a system you can calculate how it will change over time, and what the probabilities for the answers to different questions will be. Thus far, all experiments have agreed with the statistical answers given by quantum mechanics. Some possible states of a system are a combination of different base states. This is where the super position of states enters, and the ‘alive and dead cat’s.
The more elements in the quantum system the more complicated it gets. Your calculations now need to take account of every possible combination of every possible base state of all the elements.
Now back to your question. The quantum description of the two photons has states which do not correspond to two separate photons. These are the maximumly entangle states. We now have a single system - of the combined photons.
What happens when we make a measurement on one of the separated photons? If we make a measurement on one photon we can infer things about the measurements on the other. This seams like the situation with the two balls, but there is a difference.
In the combined system, a measurement on one photon seams to change the possible outcomes of experiments on both photons instantaneously. If we set up experiments which decide in which directions to make measurements after the photons are well separated, the results agree with the statistical predictions of quantum mechanics. It seams that the particular measurement made on one photon, really does instantly change the possible outcomes of measurements on the other. This is the counter intuitive bit.
However, such are the statistics of quantum mechanics that this setup cannot be used to send information between the two measurement points faster than the speed of light.
As Leonard Susskind describes it, this is equivalent to us not being able to simulate the outcome of the above experiment using two independent computers. ie if we programme two computers with all the rules of quantum mechanics, and allow them to exchange some information to capture the initial entangled state of the photon they are assigned to model. We then separate the computers to a great distance so that they can’t communicate because of the speed of light. We then ask each computer to simulate the outcome of a series of random quantum measurements as in the real life experiment. Later we bring the computers back together so we can compare their results. The surprising thing, is that we can’t do it. We can’t reproduce the results we would actually get in nature, even allowing for quantum probabilities. Unless we allow the computers to communicate instantaneously. That is why the real world quantum results are so surprising.
That’s about it from me. It might all be wrong in detail, but I think it’s correct in spirit.
Hope this helped.
Everyman