How was it proven that a quantum entanglement measurement of particle A, affects properties of particle B [duplicate]

Question

If I understood the wikipedia article correctly, quantum entanglement claims that information travels instantly between entangled particles. An act of measurement on one of the entangled particles changes (I think just determines) properties of other particle.

1. How was it proven that the properties are not just predetermined?

   For example, if I have 2 particles and know its charge is zero, then if I measure one particle and its charge is positive, I know that the other particle is negative cause of law (equation), their charge was always such, even before my measurement, it was predetermined. Or math equation $x+2=4$, I know the outcome, I know operation, I know one operand, I can solve it and find $x$. I can determine $x$ but I don't change it.

2. Can multiple particles be entangled? What happens then?

   Does the measurement of one particle effect other particles all together? If we make a math analogy with $x+y-2=0$, we measure $x$ and it is $1$, we know $y$ is $1$, but what if the equation is complex and there are multiple possible answers?

3. Can we say that in an atom, the nucleus and electrons is quantum entanglement?

   Suppose electrons around atom nucleus not particles but just a function, and they are not determined until we measure the nucleus. For example we found +6 protons in the nucleus, now using math equation $x+6=0$, we know that there must be 6 electrons. Then we measure one electron position, and again we can determine other electron positions using some math equations. How it is different from quantum entanglement? Why we say that in this scenario everything is predetermine and we only discover it, and in another scenario some "spooky action" takes place?

4. How is it different from "wavefunction collapse" (measurement problem) and the "which way" double split experiment?

   To me it looks like very close things.

Answer 1

I will address :

Can we say that in an atom, the nucleus and electrons is quantum entanglement?

In simple systems , like the hydrogen atom, yes. If we know the spin of the atom, and eject an electron and measure its spin, we instantly know the spin of the nucleus by algebra.

If we do not interact with it, the question does not apply.

We use this logic continually in particle physics to determine the properties of new particles and resonances observed. Algebra and group operations are very very useful :)

We use the logic of entanglement in situations described with classical mechanics with no bemusement. Take a vertical pulley with two equal weights , if one measures the position of one weight, instantly the position of the other is known, "faster than light" :).

Take a birth of twins, where it is known from prenatal checks that they are boy and girl. If the first one out is a girl, it is instantly, "faster than light", known that the other is a boy. "faster than light" in quotation marks because all knowledge is transmitted after all electromagnetically, and therefore limited by the velocity of light transferring the knowledge to our brain.

What confuses people is that in quantum mechanics, the measurement is not with a ruler, but with a probability distribution, a probable spot. The mathematics of the probabilities though are completely deterministic, therefore the quantum number conservation laws are obeyed "faster than light", as transmitted information goes. That is what conservation laws mean. It is application of elementary algebra and logic.

Answer 2

1. It is not proven that the properties are aren't predetermined, yet Bell's theorem shows us that who believes in determinism must abandon locality, and that who believes in locality must abandon determinism. Most physicists choose to abandon determinism, since locality, as tested time and time again by relativity, seems to describe the world well.

2. Entanglement is the following observation: For two quantum systems with Hilbert spaces $\mathcal{H}_1$ and $\mathcal{H}_2$ (and therefore associated projective spaces of states), the projective space of states is $P(\mathcal{H}_1 \otimes \mathcal{H}_2)$ and the "naive" product $P(\mathcal{H}_1) \times_\text{cart} P(\mathcal{H}_2)$ embeds into this by the Segre embedding, but not surjectively. For a discussion of why this is the correct product for spaces of states, see my answer here. The states which do not lie in the image of the Segre embedding are called entangled, because they do not conform to our classical preconception that every state of a combined system should be uniquely associated to states of the individual systems. Again, I repeat: An entangled state does not consist of uniquely specified substates, in particular, it is not the case that "particles are entangled", but rather "the system of particles form a state in which it doesn't really make sense to talk about their individual states". Now, a measurement on one particle will force a uniquely specified state of the subsystem measured, thus also changing the state of the combined system, as only those summands in the entangled state $\sum_{ij}c_{ij}\psi_i \otimes \phi_j$ will survive which contain the $\psi_k$ that was measured. If the $\phi_i$ are unentangled states (in particular if they are one-particle states), then this means that the result is an unentangled state, forcing all particles into uniquely specified states. If they aren't, entanglement has only been partially broken, and not all particles have definite states.

3. No, in general, the nuclei and electrons of an atom do not form entangled states, since the usual configuration of an atom has each electron in its own orbital, so the state of the atom can be given by the unique orbital states of the individual electron, hence the state is not entangled.

4. Entanglement is very different from "collapse", it is just a statement about how a state may be written (see 2.). The idea of "spooky action" in entanglement is very much the same, since it is not a feature of entanglement: The same "spooky action at a distance" occurs when we consider a photon incident on a mirror: Since no mirror is perfectly reflective, there will be a photon state that looks like $\lvert \text{transmitted} \rangle + \lvert \text{reflected} \rangle$, and these states are spatially separated - they are localized on opposite sides of the mirror, getting farther away from each other each second, yet, somehow, detecting the photon on one side will "instantly" and "spookily" let the part of the state on the other side vanish. This naively non-local behaviour (one can show that no true transmission of information is possible, hence locality is preserved) has nothing to do with entanglement, but stem from the fact that quantum states aren't supposed to be local anyway. Entanglement is just a case of this where it runs so obviously counter to our classical intuition that many people think this is "spooky". But it just shows they hadn't (or still haven't) fully realized how wonderfully strange quantum mechanics truly is.

Answer 3

"How was it proven that the properties are not just pre-detemined"? This question really sums up the entire mystey of quantum mechanics. Feynmann famously said that the whole mystery of quantum mechanics is found in the double slit experiment, but Feynmann was wrong. THIS is the real question.

From a theoretical point of view, it was clear from the very beginning that the properties could not be pre-determined. That was the point of the EPR paradox. The problem was to propose an actual experiment that clearly demonstrated this. That wasn't so easy. You couldn't actually carry out the EPR "thought experiment" in practise. It seemed you could almost dismiss the whole thing as more of a philosophical question: hence the "shut-up-and-calculate" school of thought.

In another post, I wrote how the first serious proposal of a "practical" experiment in this regard came in 1950 from David Bohm, with his disintegration of a spin-singlet state into two particles with opposite spins. For practical reasons, this experiment was never carried out. (Actually, there may be theoretical difficulties with Bohm's experiment...there is a lot of glib talk about "measuring the spin of a particle" but the Stern Gerlach apparatus measure the spin of a stream of particles...narrowing it down to single particles isn't nearly as easy as people think.) In 1962, Feynmann proposed the disintegraion of positronium into entangled photons...but this has never been done either.

Finally, following Bell's famous 1964 theorem, people got motivated and came up with a system of entangling photons using something called "parallel down-conversion." THESE are the experiments which come closest to demonstrating that the properties were not fixed at the time of creation.

There is a certain difficulty with explaining these experiments because the mechanism of parallel down-conversion is not so transparent as the earlier proposed experiments. So it's hard to figure out what you're actually dealing with. A more serious difficulty arises from the statistical nature of the experiments. The "entangled" photons are immersed in a stream of "ordinary" photons, and sophisticated statistical methods must be used to extract the entanglement information.

These details are usually glossed over in the traditional "Alice-and-Bob" explanations.

Answer 4

This video well explains Bell's Stern–Gerlach experiment that is cited as proving that quantum entanglement is not explained by predetermined "hidden variables".

https://www.youtube.com/watch?v=ZuvK-od647c

Basically, the experiment involves detecting the spin of two entangled particles via the use of 3 randomly determined spin-direction detectors. Each detector detects spin in a direction 120 degrees from each other detector. The theory is that if the spins were predetermined, the detected spin direction would be opposite 2/3 of the time, while in reality, the experiment sees spin direction as opposite 1/2 of the time. The video makes a clearer explanation.