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I know there is evidence that it is not predetermined and I tried reading articles on it but most of them either don't explain the intuition behind the experiment or they speak in a foreign language (That language being science). If you could explain the intuition behind the experiment and also give an analogy that would be great.

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    $\begingroup$ Is the question about hidden variable theories, Bell's Theorem, Non-locality of Quantum Mechanics or something else? Bell's Theorem and results of Bell test experiments together rule out local hidden variable theories. $\endgroup$ – cutculus Aug 23 '14 at 11:42
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    $\begingroup$ It doesn't really make sense to talk about such advanced concepts in quantum mechanics without "science" as you say, does it? Most quantum mechanical concepts are very far from our intuition (formed mainly by our daily classical phenomena occurring around us). About the pre-determinism you ask, maybe you will find useful elements here: physics.stackexchange.com/questions/128886/… In the strict realm of quantum mechanics, you may develop an intuition, but first you need to form a good basis in this field. $\endgroup$ – Ellie Aug 23 '14 at 12:44
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    $\begingroup$ "Pre-determinism" isn't even a workable concept in classical physics. I can, for instance, replay a recorded random sequence trough a classical black box to an observer, and the observer has absolutely no way of knowing, whether the random sequence was created in real-time by some dynamics inside the black box or whether it is a "pre-determined" copy of an already existing sequence. If a concept isn't useful in classical mechanics, one shouldn't try to apply it to QM. $\endgroup$ – CuriousOne Aug 23 '14 at 14:10
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    $\begingroup$ Entanglement is not intuitive, so we usually resort to a mathematical description to describe the effects. We think this description is correct because of a class of experiments called Bell's Inequality measurements. If we try to predict the answer to these measurements using the intuitive, predetermined model of photon `entanglement', we get an answer that does not match the experiment results. We then have to introduce the non-intuitive physics of entanglement to get the measured answer. BTW: if you work with the math long enough, you can develop an intuition in regard to entanglement. $\endgroup$ – Jason A Aug 23 '14 at 20:31
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    $\begingroup$ @Ray Kay - If you're looking for a relatively simple analogy, take a look at the one involving scratch lotto cards that I gave in this answer. $\endgroup$ – Hypnosifl Dec 28 '14 at 16:57
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Quantum entanglement can not be described as a predetermined correlation between particle's states because of the observed violations of Bell's inequalities. All of this is best explained in the language of science and math. If you want to avoid such explanations, you might try an explanation like this: quantum casino - less than zero chance. In short: would you want to emulate Bell inequality violations via predetermined correlations, you would need negative probabilities in the preparation of the particle states.

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How do we know that photon entanglement isn't the result of the photons's states being predetermined?

Photons are elementary particles, and elementary particles cannot be explained without quantum mechanics.

Quantum mechanics describes the state of the photon and the system it resides in, all in one probability distribution.

It is analogous to throwing a coin heads/tail. There exists a probability distribution for the result of the throw/experiment, it is 50% for each. If you throw heads up, you know the other side is tails, as it is entangled, but the state itself is not known until you throw the coin. It is one point to accumulate in the 50 50 probability distribution.

With particles there exist conservation laws, analogous to the constraint if heads is seen the other side necessarily is tails, but that is all. The experiment itself, the throw, is random . Quntum mechanically the probability is predetermined but not the state the photon will be found, it is a draw in the probability distribution.

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