Is there really something weird about quantum entanglement?

Question

When reading "vulgarized" explanations of entanglement and superpositions, it seems something really weird:

e.g.

two separated particles can interact instantaneously, a phenomenon called quantum entanglement

But when reading more about the topic, I get to the following conclusions:

1. A single particle can only be observed once
2. Entanglement or superpositions seems more a statisticall phenomenon than a real physical property.

Let put an example:

Suppose I put 2 empty water glasses one aside of the other. Then I fill randomly (without looking too much) 1000 rice grains between the two glasses. I send one glass to my colleague in Japan, and keep the other to me.

We know that (ok, my notation is not ideal): $$1000 = \psi(n_1) + \psi(n_2)$$

We could argue that both glasses are "entangled".

When I count the number of rices in my glass, I get $42=\psi(n_1)$. Now, we know that the glass of my colleague has collapsed to $958 = \psi(n_2)$.

So, my conclusion is that two entangled particle are just two particle with states which are known to be related. They interacted at their creation time, but after that, they are just normal particles known to have something complementary.

The same seems to apply to superposition:

example:

Let suppose again a glass, where I throw randomly a bunch of rice grains on it. I know that the number of grains that fall inside are about $500 \pm 500$ (you can imagine whatever probability function here).

So we have a superposition of all the possible grains number inside the glass. When I count them, it collapse to (e.g.) $321$ grains. This does not means that the glass had $1$ and $2$ and ... $321$ and ... grains at the same time, it just means that there were a probability for each quantity and reading them, makes it to collapse to a specific number.

My question is:

Is there really something "more" about entanglement and superposition than just statistical effects of replacing one variable by it observed value?

Answer 1

Superposition is weird : interference

Basically : classical probabilities are positive real numbers, so classically there can be no interference. If you do a classical probabilistic calculation for the double slit experiment, assuming the particle has a (classical) 50/50 chance of passing through either slit, the result on the screen would be sum of two Gaussian functions, without any interference.

Instead, in quantum mechanics, we sum probability amplitude, which are complex numbers and therefore can interfere destructively.

Entanglement is weird : Bell's theorem

The issue here is more subtle and harder to explain without getting into the math. As you point out, there can be correlation classically (the sum of the numbers of rice grains in both boxes is always equal to $n$). However, there is a situation, in which there is a classical bound on the correlations, which is violated by quantum mechanics.

Answer 2

There is more to it. In the quantum world, the superposition implies something like multiple realities. So, to use the example with the two glasses and the 1000 rice grains: quantum entanglement is where you have multiple realities where one glass has $n$ rice grains and the other glass as $1000-n$ rice grains, but $n$ is different in the different realities.

When you make a measurement, you always have to do some classical "handshaking" with the person with the other glass to make sure that you are both seeing the results in the same reality. Otherwise it would have been possible to use entanglement to do communication, which is not possible.

Hope this clarifies it a bit.