Do physicists really believe in true randomness?

Basically, you have two entangled photons that travel in opposite directions. Let's say one heads toward New York and the other heads toward California. The particles arrive at their destination at the same time.

Each experimenter has a little filter (called a polarizer) that he can rotate, and each experimenter rotates his filter to whatever angle he wants the instant before the photon strikes it. Each experimenter then measures whether the photon passed through his filter or got absorbed.

Because each experimenter rotates his filter at the last possible instant before the photon strikes it, there's no way that the guy in New York could know what angle the guy in California chose, because to know this would require that information to travel faster than the speed of light.

Now let's ask the question: what is the probability that both photons had the same measurement? (That is, what is the probability that either both photons passed through the filter or both photons were absorbed). From looking at data from multiple runs of this experiment, it turns out this probability is a function of both filter angles.

But since nothing can travel faster than light, how is it possible that the probability is a function of two independently chosen angles? Well the simplest way this can happen is something like P = f(θ1)g(θ2). You can see here that the total probability is a separable function. In other words, the total probability can be computed using functions of two separate angles. It would be like computing the probability that two separate baseball players both hit the ball; you don't need any faster than light information transfer to figure this out.

However, in actual experiments, it turns out that P = f(θ1, θ2), and this function is not separable. What this means is the total probability is a function of both angles together -- you can't compute independent probabilities and combine them.

What does this mean? It means that somehow each filter "knew" the angle the other filter was rotated to, instantly. So reality is "non-local". BUT there's another option if you don't like that: the universe "knew" in advance what angles the experimenters would choose, and let each photon know this before they separated. This would give the correct experimental results, and you wouldn't have to give up locality. This is called superdeterminism, and it hasn't been ruled out yet, but let's be honest: is the universe really working that hard to conspire against us? (At least one Nobel-prize holding physicist thinks so).

EDIT: Also, why did this article instantly drop like 40 spots on HN? Is it because I shouldn't post comments on articles I submit? (I didn't write the original article by the way.) It's kind of annoying to spend twenty minutes writing a comment that nobody's going to see.

Something random can be seen as an event that has no causual expanation (and thus cannot be predicted by studying the previous state of the system). But there still must be an agent, bringing the random outcome into the universe. In the same manner, free will too can be thought of as a event that has no causual explanation.

In this case, the difficult question is how a "free will" based decision relates to the person making it (if it's a product of his memories then it's deterministic, and thus not free).

One way to solve this might be to think of the persons' decision making process as a "random number generator". So, the output is deterministic (the same for the same state of memories, like with a programmatic RNG), but with a unique seed for this person (the state of memories itself), and a unique RNG algorithm (the wiring of his brain).

In this case, unlike calculating a dice result given dimensions, weight, power of throw, wind conditions, etc, nothing can produce the same output as the free will person without going through the whole process (a total simulation).

I feel like the expirement is saying "we generate random numbers then prove random exists". Ok and a horse is a horse.

I think people mean they make decisions. Doesn't that mean randomness robs you of free will? The you (whatever that is) isn't making decisions, chance is.

If it's you making decisions, wouldn't those decisions have to depend on you and the situation, which means it's entirely deterministic? If I know you and I know the situation, I could predict your decision?