Superposition or just unobserved states?

[davezap]

Can the kind members of this forum please help me make the logical leap from an entangled pair of electrons or photons to that of the pair being in a superposition where the observation of one effects the state of the other?

For example, my understanding is that, through the conservation of angular momentum we can have a particle decay into two entangled electrons one spin-up and the other spin-down. Further when we measure the spin of one of these electrons and find that 50% of the time we get the up and the other 50% must be down, and then can deduce the state of the idler with 100% certainty.

So what I'm missing here is how observation of the signal in any way effects the idler? I mean if we detect a spin-down then we know it was ALWAYS spin-down when it was created - don't we?

An analogy might be their are two roads to your house, you hear a knock at your door and upon opening it you see your good friend. You know your friend must have taken one of the two roads or else he would not be standing in front of you. Opening the door did not change what road he took in the past though?

Isn't it just simple to say that we didn't know the state prior to observing it? and that the observation had no influence on the outcome of states?

I'm sure this has been done to death experimentally and so perhaps I could be pointed to the appropriate experiment that demonstrates the so called "spooky action at a distance".

I'm sure this an obvious question from someone who has a casual interest in physics and my question is probably born out of reading lay person explanations that seldom include the math (not that I'm asking for a lot of that here). I feel I'm missing something fundamental at this point.

I realize there is an open question on the forum "Meaning of Observation" however I think mine while related is asking something completely different. That question is basically asking what is considered a detector, I'm asking how does detection change anything at all.

Thanks.

 

[Nugatory]

So what I'm missing here is how observation of the signal in any way affects the idler? I mean if we detect a spin-down then we know it was ALWAYS spin-down when it was created - don't we?

That's what we'd expect based on lifetime of experience with macroscopic objects, but it is not that way. Google and search this forum for "Bell's theorem".

The summary: There are subtle differences between the predictions of quantum mechanics and the predictions of any theory in which the spin had a definite value from the time the pair was created. These differences can be tested experimentally and they support the quantum mechanical prediction and cannot be reconciled with any theory in which the spin has definite value and we just didn't know what it was until we measured it.

 

[Mentz114]

That's what we'd expect based on lifetime of experience with macroscopic objects, but it is not that way. Google and search this forum for "Bell's theorem".

The summary: There are subtle differences between the predictions of quantum mechanics and the predictions of any theory in which the spin had a definite value from the time the pair was created. These differences can be tested experimentally and they support the quantum mechanical prediction and cannot be reconciled with any theory in which the spin has definite value and we just didn't know what it was until we measured it.

A question :
Is it OK to say that if we measured the values, what we (would) get must be eigenvalues of some operator ? Or is that exactly what is forbidden ?

 

[stevendaryl]

So what I'm missing here is how observation of the signal in any way effects the idler? I mean if we detect a spin-down then we know it was ALWAYS spin-down when it was created - don't we?

As @Nugatory said, that interpretation is ruled out by detailed analysis of the predictions of quantum mechanics.

The problem is that spin is a vector, not just a number. So for any direction in space $\vec{D}$, we can measure the electron's spin along the $\vec{D}$ axis. In the case of entangled electron/positron pairs, if one experimenter measures the spin along axis $\vec{D}$, and gets spin-up for one particle, then the other experimenter will get spin-down for the other particle along that axis.

So what this means^* is that your explanation, that the correlations are due to pre-existing values, would imply that for every possible direction $\vec{D}$, it is determined ahead of time whether the particle has spin-up or spin-down in direction $\vec{D}$.

So let's pick three different directions: $\vec{a}$ is along the y-axis, $\vec{b}$ is in the x-y plane at an angle of 120^o clockwise away from $\vec{b}$, and $\vec{c}$ is in the x-y plane at an angle of 240^o away from $\vec{a}$. So if you're right, that the results are pre-determined, then that means that there are 8 different types of situations with regard to our three axes:

1. The electron is spin-down along all three axes. (And the positron is spin-up along all three). We'll label this case DDD.
   
2. The electron is spin-down along \vec{a}, \vec{b}, but spin-up along \vec{c}. The positron is the opposite. We'll label this case DDU.
   
3. Etc.

There are 8 possible spin-states: DDD, DDU, DUD, UDD, UDU, UUD, UUU

So let's assume that when we have an entangled electron/positron pair, that the electron is in one of those states, with a certain probability.
In order to reproduce the experimental results (and the predictions of quantum mechanics), these 8 states have to have the following probabilities:

P(UUU) = P(DDD) = -0.0625
P(UUD) = P(UDU) = P(DUU) = P(UDD) = P(DUD) = P(DDU) = 0.1875

Obviously, something can't have a negative probability, so this interpretation is impossible.

As to how those numbers are derived, I can give a little more details, if you like.

^*Superdeteriminism loophole

The argument assumes that the choice of which axis to measure the electron's spin relative to is independent of the spin-state of the electron. You could imagine that this is not the case. Maybe even though the experimenter thinks he is making a random choice as to which axis to measure, the choice is actually determined ahead of time. This is the superdeterminism loophole.

 

[Mentz114]

I realize there is an open question on the forum "Meaning of Observation" however I think mine while related is asking something completely different. That question is basically asking what is considered a detector, I'm asking how does detection change anything at all.

In a projective measure of spin for instance the spin direction is changed by a physical rotation .

See https://en.wikipedia.org/wiki/Stern–Gerlach_experiment

 

[Nugatory]

A question :
Is it OK to say that if we measured the values, what we (would) get must be eigenvalues of some operator ? Or is that exactly what is forbidden ?

No, that's OK. In fact, that's exactly pretty much what the Born rule says.

 

[davezap]

Google and search this forum for "Bell's theorem".

Thanks for pointing me in that direction, I've come across a few descriptions relating to linear polarization and the probabilities therein. That's strange enough for me at the moment :) and is the simple experimental demonstration I was looking for in my original question.

As to how those numbers are derived, I can give a little more details, if you like.

Thanks for your explanation it does help but going deeper into the math might loose me. What I'm getting from Bell is that only two explanations for the quantum observations exist, either hidden local variables are at work or faster than light communication, between the particles. If local hidden variables are ruled out then EPR is wrong, and this has been experimentally demonstrated to be so. Still increasingly elaborate experiments are performed to close the remaining loopholes. I think these loopholes related to non-local hidden variables? and having enough distance between detectors to rule out.. but anyway please don't explain all that as it's way off topic.

At this point I need to digest it a little more.If either of you or anyone else can recommend a good primer on the broad QM topic (as in a paper book / Amazon) my time would be better served getting to grips with the basics. It's been a few years since I did my engineering degree, but think I can get a handle on the maths again as I understand it's all vectors, matrices and complex numbers (more or less) things they make engineers learn believe it or not ;)

[edit] just for clarification I'm looking for a textbook that explains the math and gives explanations of experimental setups and observations if such a book exists. I'm not looking for pop-science '10 fun facts to wow your friends at the pub'

Also purchasing a few cheap polarizes is well within my capability to satisfy my apparent need to understand through experimentation.

Thanks again.

 

[mikeyork]

So what I'm missing here is how observation of the signal in any way effects the idler? I mean if we detect a spin-down then we know it was ALWAYS spin-down when it was created - don't we?

"ALWAYS" is an interesting word in this context. It presupposes the concept of time -- something we understand very little about.

This particular aspect of the quantum paradigm is rarely discussed. If there is anyone on this forum who knows of any published papers that address the issue of what "always" means between state preparation and state detection I would love to now about it.

An analogy might be their are two roads to your house, you hear a knock at your door and upon opening it you see your good friend. You know your friend must have taken one of the two roads or else he would not be standing in front of you. Opening the door did not change what road he took in the past though?

Your friend can tell you what road they took. A particle cannot tell you what they were doing before you detected it.

 

[davezap]

"ALWAYS" is an interesting word in this context. It presupposes the concept of time -- something we understand very little about.

This particular aspect of the quantum paradigm is rarely discussed. If there is anyone on this forum who knows of any published papers that address the issue of what "always" means between state preparation and state detection I would love to now about it.Your friend can tell you what road they took. A particle cannot tell you what they were doing before you detected it.

Well yes :) I just threw the word ALWAYS in without much thought but did intend to mean from the time the pair were created onward to the time of detection.

After a little more reading I'm happy with the idea that QM provides a mathematical framework to explain observations and that is where it meets it's limit. QM is not a branch of philosophy however interpretation of what QM might 'mean' is.

 

[entropy1]

I mean if we detect a spin-down then we know it was ALWAYS spin-down when it was created - don't we?

I am not sure if I understand the question entirely. This is my take on it:

Suppose we have to measurement apparatusses M1 and M2, and a pair of entangled particles E_a and E_b. Suppose M1 and M2 have their measurement axis aligned parallelly. Now we create E_a and E_b, and send E_a to M1 and E_b to M2.
(A) Now, if we measure the spin of E_a to be 'down' at M1, we measure E_b to be 'up' at M2.
(B) However, we could decide to turn the orientation of M1 and M2 clockwise or anticlockwise while the particles are already in transit, keeping them parallel. If we now measure E_a to be 'down' at M1, still we will measure E_b to be 'up' at M2.
Now, could we say that the spin of E_b was 'up all along'? The orientation that is measured differs between (A) and (B)! Which orientation would the spin have had?
The matter is that the outcomes on M1 and M2 depend on the relative orientation of M1 and M2, and not so much on the spin property of E_x (if it even has one).

 

[vanhees71]

A general pure spin state can be described with the vector
$$|\psi \rangle=a |1/2 \rangle+b |-1/2 \rangle,$$
where $\langle \psi|\psi \rangle=|a|^2+|b|^2=1$.

According to Born's rule, the probability to find spin up when measuring $\sigma_z$ is
$$|\langle 1/2|\psi \rangle|^2=|a|^2.$$