Why isn't quantum entanglement just a lack of information?

Question

From this question and answer from joshphysics, I didn't understand one thing, even after reading the comments:

Why should assume that entangled electrons will only "decide" their state after observation?

Isn't it just a lack of information? For instance, knowing that we have a black and white marble and picking one afterwards with your eyes closed, doesn't mean that the marble "decides" to be white or black after the observation, i.e. there is no entanglement.

Therefore, I do not know what makes the states of the electrons so special.

Answer 1

Consider the situation where you have two electrons which are entangled with one another, you know one has spin up and the other has spin down, but not which is which. All you know is that for a given electron the chance of it having either spin is 50/50. Now suppose you go on to measure the spin of one of these. Consider the following two theories for what happens next:

1. According to the Copenhagen interpretation of quantum mechanics each is in a superposition of being spin up and spin down. The instant I measure one of them it will randomly decide to be either up or down, and send an instantaneous signal to the other to suddenly have the opposite spin.

2. What you are talking about is a local hidden variables theory. While we do not know the spin of each electron, you claim that it is there as a 'hidden variable' which definitely exists describing this, and there is no non-local instantaneous interaction between the electrons. When we measure the spin of one electron we just read this variable. It was always in that spin, there was no collapse of the wavefunction. Einstein was a notable proponent of this theory, see EPR Paradox.

For a long time, people thought that it would be impossible to tell the difference between these two theories. While they work in completely different ways, how can you possibly design an experiment to tell the difference? The answer was provided by John Stewart Bell in the form of what are known as Bell's Inequalities, which show that if you perform some cleverly designed experiments, you should actually expect a different result depending on which of the two theories above is correct!

To get an idea for how such an experiment could work, have a look at the Simple English Wikipedia page on Bell's Theorem which gives a very nice metaphor. The system described there can be created using entangled particle states.

Answer 2

Suppose you have four marbles, each either black or white. Because you haven't looked at them yet, you're only aware of certain probabilities. One way or another, suppose you know that Marbles 1 and 2 have only a 5% probability of being differently colored. Likewise, Marbles 2 and 3 have only a 5% probability of being differently colored, and likewise for Marbles 3 and 4. Then you can conclude that Marbles 1 and 4 have at most a 15% chance of being differently colored --- because in order for 1 and 4 to be differently colored, it must be the case that either 1 and 2 are differently colored or 2 and 3 are differently colored or 3 and 4 are differently colored.

Now suppose that your conclusion turns out to be wrong --- that actually marbles 1 and 4 in fact have a 95% chance of being differently colored. Then something must have been wrong with your reasoning, and if you work through the various things that could have gone wrong, you'll find the most plausible culprit is your assumption that the marbles started out with well defined colors.

Something very like that happens in quantum mechanics. (In the quantum mechanics version, it is not possible to examine marbles 1 and 3 at the same time, or to examine marbles 2 and 4 at the same time.) And as you can see above, if the only problem were "lack of information", you'd still be able to conclude that your quantum marbles 1 and 4 can be differently colored at most 15% of the time, and then experiments would prove you wrong.

Answer 3

Why should assume that entangled electrons will only "decide" their state after observation?

In my experimentalist's opinion this is called anthropomorphism, i.e. assigning consciousness to the elementary particle.

The electron decides nothing, it is in as an inevitable functional time path as a pendulum oscillating under gravity, except that the function that describes the behavior of elementary particles describes probabilities as functions of (x,y,z,t) and not paths/trajectories in in (x,y,z,t). Even the term "collapse" is confusing and misleading to this effect. It is the measurement that picks out a specific value from all those probable ones, nothing magical happens.

You should contemplate probabilities. We have actuarial tables which say that the probability of being alive by the 65th if you are male in Greece ( my country) is over 80%. Does that mean that a 60 year old male is in an indeterminate case? Yes, but this male is not spread out over 65 or 100 years neither dead or alive. The probability curve is composed of a large number of observations, and given a functional form as a function of time. He, at age 60 exists whole and only the measurement at death will evaluate at what part of the probability curve versus time this one measurement belonged.

Therefore, I do not know what makes the states of the electrons so special.

One should think of elementary particles as "quantum mechanical entities", they are not particles like billiard balls nor waves in (x,y,z,t). The are described by probability in (x,y,z,t), waves, because the probability is a solution of wave equations and has a sinusoidal variability over space.

The electron is special because it is an elementary particle and displays properties not evident in billiard balls and the extension of the billiard ball properties to classical point particles . The classical model did not work when observations reached the microcosm and necessitated the theory of quantum mechanics. (infinities falling in the atom, no explanation of spectra, black body radiation etc).

And one should treat probabilities attached to the functional dependance of the behavior of elementary particles as such, i.e. as probabilities.

It is erroneous to think that the electron is spread out all over the place in (x,y,z,t) as it is erroneous to think that a 60 year old man is neither dead or alive over the 100 year spread. The attributes ( like spin up or down) defining the electron are not known unless a measurement/observation is made as the state of the man born in 1954 ( dead or alive ) is not known until a check is made. Once a check is made a new probability curve ( actuarial table) will apply to the man , and in a similar manner a new probability function will apply to an electron once a measurement is made. The boundary conditions have changed.

Answer 4

Apologies to SE for the fact that I am reusing parts of an answer I wrote earlier, but to answer the core question of why you can't assume the system has a particular state before measurement I think this is the easiest example to think of.

Consider two entangled quantum systems which are described by three properties, A, B and C each which can take a value of up or down.

The two systems can be entangled such that if you measure the same property on both systems then you will get the same result 100% of the time, and each case occurs 50% of the time. That is to say both systems give up 50% of the time or both systems give down 50% of the time, but you will never get a result where one systems gives up and the other down. Just to reiterate is is only when you measure the same property, ie: both A, both B or both C.

But here is the problem if you measure different properties then you will get the same direction 25% of the time and opposite directions 75% of the time. For example if I measure A on one system and it gives a result of up, then when I measure B on the other system I will get up 25% of the time and down 75% of the time.

There is no way of pre-assigning up or down so that they are different 75% or the time. If you think through it the best you can do is different 2/3 times by excluding cases where A, B and C are all the same. The only other way around this is to assume that measuring one system instantaneously affects the other but these systems are arbitrary far apart and space like separated so who measures first is relative to your reference frame.

The simplest solution is conceding your ability to assign a value before measurement.