Why is entanglement necessary for understanding quantum mechanics?

[Johan0001]

If I had a factory that produces pairs of gloves. And I packed one box with the left glove and another with the right.
Then I sent the first box to the north pole and the second to the south pole.
Now I have no idea which box contains which glove, When sending the identical boxes to their respective locations.

So now if I open the box in the north pole , and find a left hand glove.
Then OBVIOUSLY I know what glove is in the box on the South pole, at that instant.
And behold when I open the box at the south pole it is ALWAYS a right hand glove.

Why the need to send a signal faster than anything to the other box?
Why the need for such property , we call entanglement?

What evidence / experiment caused the scientific world to formulate this spooky action at
a distance, to explain this logical deduction when measuring/observing a closed system of events?

 

[Johan0001]

"And behold when I open the box at the south pole it is ALWAYS a right hand glove."
apologies should read:
"And behold when I open the corresponding box at the south pole , it is ALWAYS the othe half of the glove found at the north pole"

 

[jtbell]

Read up on Bell's Theorem and related experiments.

For example, on http://www.drchinese.com/Bells_Theorem.htm , an excellent "Overview with Lotsa Links" which is maintained by our frequent poster DrChinese.

 

[Zarqon]

To put it in a simplified way:

One cruicial thing you're missing is that in the quantum world there are different measurement bases, and only certain specific bases gives you the perfect anti-correlation that you describe. Other bases can give no correlation at all, which in your case would be equivalent to having a 50% chance of finding either two right-hand or two left-handed gloves. But classically, this can never happen, as you always find one of each, there is never any chance of anything else.

If they were entangled, then only when you look at your gloves from a certain point of view (a certain basis) would you find correlation, while for another view they can act as though they are completely independent, even though they are the same physically prepared system. This property simply has no cloassical interpretation.

 

[Johan0001]

Thanks ,very comprehensive and informative link.
The quote below sums it up nicely for me ..

"It is worth emphasizing that non-separability,
which is at the roots of quantum teleportation15,
does not imply the possibility of
practical faster-than-light communication.
An observer sitting behind a polarizer only
sees an apparently random series of 1 and
& results, and single measurements on his
side cannot make him aware that the distant
operator has suddenly changed the orientation
of his polarizer. Should we then conclude
that there is nothing remarkable in this
experiment? To convince the reader of the
contrary, I suggest we take the point of view
of an external observer, who collects the data
from the two distant stations at the end of the
experiment, and compares the two series of
results. This is what the Innsbruck team has
done. Looking at the data a posteriori, they
found that the correlation immediately
changed as soon as one of the polarizers was
switched, without any delay allowing for
signal propagation: this reflects quantum
non-separability"



However I am still not convinced that entanglement is a prerequisite of what we measure experimentally.
Looking at the combined results "Posteriori" gives us sense of Locality making the photons
"unneccessarily" to have communicated instantaneously

OR

"that they are considered a single non-separable object — it is impossible to assign
local physical reality to each photon.''

This is more in line with my view, they are 2 halves of a single entity, they can only behave in a certain way , no matter what you do.

The left glove will never fit the right hand

 

[jk22]

I think the problem is the quantum-mechanical description of the system : before the measurement in A the system is described by a non-separable function, the state of B is not determined in any direction. But directly after the measurement in A the system in B becomes well defined in that direction. In classical world there is no such description before you open the box the property is just hidden and revealed so there is no need for this spooky interaction.

 

[stevendaryl]

If I had a factory that produces pairs of gloves. And I packed one box with the left glove and another with the right.
Then I sent the first box to the north pole and the second to the south pole.
Now I have no idea which box contains which glove, When sending the identical boxes to their respective locations.

So now if I open the box in the north pole , and find a left hand glove.
Then OBVIOUSLY I know what glove is in the box on the South pole, at that instant.
And behold when I open the box at the south pole it is ALWAYS a right hand glove.

Why the need to send a signal faster than anything to the other box?
Why the need for such property , we call entanglement?

What evidence / experiment caused the scientific world to formulate this spooky action at
a distance, to explain this logical deduction when measuring/observing a closed system of events?

What this analogy misses is that in an actual experiment involving an entangled pair of particles, the experimenters can choose different types of measurements. Your analogy only has one type of measurement: Determine whether the glove is left-handed or right-handed.

Let's make your analogy more complicated by adding the element of choice. Suppose that there are a pair of couriers: One delivers three boxes to the north pole, labelled red, green and blue. The other delivers three boxes to the south pole, similarly labelled. The experimenter at the north pole, call her "Alice", picks a box and opens it. The experimenter at the south pole, call him "Bob", picks a box and opens it. The couriers only allow them to open one box a piece.

The rules are:

1. If Alice and Bob pick the same color glove, they always get the opposite handedness: one gets a left-handed glove, the other gets a right-handed glove.
2. If Alice and Bob pick different colors, they always get the same handedness: either both left-handed, or both right-handed.

If you think about this scenario, I think you will agree that there is no way to accomplish it without either guessing ahead of time which color Alice and Bob will pick, or by somehow teleporting gloves. You can't just start with three pairs of gloves, and for each color, either send the left one to Alice and the right one to Bob, or vice-verse.

Using quantum mechanics, you can't precisely mimic this new scenario, but you can come close:

1. If Alice and Bob pick the same color glove, they always get the opposite handedness: one gets a left-handed glove, the other gets a right-handed glove.
2. If Alice and Bob pick different colors, they usually (75% of the time) get the same handedness: either both left-handed, or both right-handed.

 

[StevieTNZ]

Your analogy does not include the fact that the gloves need to be a in superposition of fitting the left and right hand. That might be worth noting.

 

[Johan0001]

Hi Stevendaryl

The rules are:
1.
If Alice and Bob pick the same color glove, they always get the opposite handedness: one gets a left-handed glove, the other gets a right-handed glove.
2.
If Alice and Bob pick different colors, they always get the same handedness: either both left-handed, or both right-handed.


I agree with rule 1 but not with rule 2

A possible scenario is :
2 left handed gloves ( say Red and Blue) in the North pole, which corresponds to 2 right handed gloves ( Red , Blue) in the South pole.
So Alice picks the Red glove in the North pole ( left handed) and Bob picks the Blue glove
in the South pole (Right Handed).

Even with this element of choice , why should entanglement be a pre-requisite?






which is

 

[Johan0001]

"Your analogy does not include the fact that the gloves need to be a in superposition of fitting the left and right hand. That might be worth noting"

No sure what is meant by "Superposition" in the context of this sentence, could you elaborate?

 

[stevendaryl]

Hi Stevendaryl

The rules are:
1.
If Alice and Bob pick the same color glove, they always get the opposite handedness: one gets a left-handed glove, the other gets a right-handed glove.
2.
If Alice and Bob pick different colors, they always get the same handedness: either both left-handed, or both right-handed.


I agree with rule 1 but not with rule 2

What do you mean, you don't agree? I'm just giving you an example of a distant correlation that cannot be explained by simple classical means. QM has similar distant correlations (not exactly as extreme as that one).

 

[stevendaryl]

Your analogy does not include the fact that the gloves need to be a in superposition of fitting the left and right hand. That might be worth noting.

I don't think that it's fair to require that. Superpositions are part of the QM model, but they aren't directly observed. The question is: what observations force us to consider superpositions?

 

[stevendaryl]

A possible scenario is :
2 left handed gloves ( say Red and Blue) in the North pole, which corresponds to 2 right handed gloves ( Red , Blue) in the South pole.
So Alice picks the Red glove in the North pole ( left handed) and Bob picks the Blue glove
in the South pole (Right Handed).

Even with this element of choice , why should entanglement be a pre-requisite?

I don't see the point of your scenario, since it doesn't relate to the QM situation. As I said, here is a glove scenario that is almost exactly analogous to the QM case:

1. Alice and Bob are each presented with three possible boxes marked Red, Green, or Blue.
2. If they choose the same color, then they always find gloves with opposite handedness.
3. If they choose different colors, they find gloves with the same handedness 75% of the time, and different handedness 25% of the time.

There is no way to create such a situation using three pairs of gloves, unless you know ahead of time what colors Alice and Bob will choose (or if you can magically teleport gloves around). But you can create an analogous situation using entangled pairs:

• Instead of choosing a color, Alice and Bob choose one of three directions for measuring spin: 0 degrees, 120 degrees or 240 degrees (in the x-y plane, with 0 degrees being the y-axis).
• Instead of left-handed and right-handed gloves, they get spin-up or spin-down particles.

 

[bhobba]

What evidence / experiment caused the scientific world to formulate this spooky action at a distance, to explain this logical deduction when measuring/observing a closed system of events?

This is a variant of the famous Bertlmann's Socks the great physicist John Bell talked about and it indeed sheds considerable light on quantum entanglement:
http://cds.cern.ch/record/142461/files/198009299.pdf

It's such a pity that a man of such rare insight, and a virtual shoo-in for a Nobel prize, died young.

Whether such violates locality, and is spooky action at a distance, depends a lot on your definition of locality.

I hold to the cluster decomposition property:
https://www.physicsforums.com/showthread.php?t=547574

According to that locality basically only applies to uncorrelated systems - correlated systems may still be non-local. Entangled systems are correlated - so its OK to view them as non-local if you wish - I personally do.

But it purely depends on how you view it. The Consistent History guys view it differently:
http://quantum.phys.cmu.edu/CQT/index.html

See Chapter 24 on the EPR:
http://quantum.phys.cmu.edu/CQT/chaps/cqt24.pdf

Thanks
Bill

 

[Johan0001]

What do you mean, you don't agree? I'm just giving you an example of a distant correlation that cannot be explained by simple classical means. QM has similar distant correlations (not exactly as extreme as that one).

previously you stated :

If Alice and Bob pick different colors, they always get the same handedness: either both left-handed, or both right-handed.

later you stated that:

If Alice and Bob pick different colors, they usually (75% of the time) get the same handedness: either both left-handed, or both right-handed

I agree with the latter but disagreed with the former, to answer your question on what I disagreed on.

However the % ratio from my calculation is 66% of the time get the same handedness not 75 %.
How do you get to 75% ?

Is this not a classical correlation to entanglement?

 

[stevendaryl]

previously you stated :

If Alice and Bob pick different colors, they always get the same handedness: either both left-handed, or both right-handed.

later you stated that:

If Alice and Bob pick different colors, they usually (75% of the time) get the same handedness: either both left-handed, or both right-handed

I agree with the latter but disagreed with the former, to answer your question on what I disagreed on.

What does it mean to disagree? I was giving you a scenario that I made up. How can you disagree with something I made up? If I say: "Suppose I have two apples..." how can you disagree and say that no, it's three apples?

However the % ratio from my calculation is 66% of the time get the same handedness not 75 %.
How do you get to 75% ?
Is this not a classical correlation to entanglement?

The 75% comes from quantum mechanics. That's the issue about quantum entanglement: it can produce correlations that simply cannot be reproduced using classical means.

Specifically, if in the spin-1/2 EPR experiment, Alice measures the spin of one particle along one axis, and Bob measures the spin of the other particle along another axis, then the probability that they will get the same result (spin-up or spin-down) is $sin^2(\frac{\theta}{2})$ where $\theta$ is the angle between their two axes. If $\theta=120^o$, then you get a probability of 0.75.

 

[stevendaryl]

This is a variant of the famous Bertlmann's Socks the great physicist John Bell talked about and it indeed sheds considerable light on quantum entanglement:
http://cds.cern.ch/record/142461/files/198009299.pdf

It's such a pity that a man of such rare insight, and a virtual shoo-in for a Nobel prize, died young.

Whether such violates locality. and is spooky action at a distance, depends a lot on your definition of locality.

I hold to the cluster decomposition property:
https://www.physicsforums.com/showthread.php?t=547574

According to that locality basically only applies to uncorrelated systems - correlated systems may still be non-local. Entangled systems are correlated - so its OK to view them as non-local if you wish - I personally do.

The notion of "nonlocality" that is relevant for entanglement is that it's possible to have information about a composite system that cannot be factored into information about the two component systems.

 

[Jabbu]

I'm just giving you an example of a distant correlation that cannot be explained by simple classical means. QM has similar distant correlations (not exactly as extreme as that one).

Experiments are far less spectacular than Alice and Bob adventures. I don't see why make up stories when we can describe actual experiments. In the experiment there is a photon A and polarizer A on one side, and on the other side there is a photon B and polarizer B. Photon A will try to pass through polarizer A, and photon B will try to pass through polarizer B. If both manage to pass or if both fail we record '1', it's a match, and if one goes through but not the other we record '0', it's a mismatch. This is repeated with 10,000 more photons, the number of matches and mismatches are compared and then somehow interpreted to imply all kinds of crazy stuff.

I'm not impressed. The result is so very indirect and only vaguely related to what is being inferred from it. There is Malus's law in classical physics which can calculate probability for a photon to pass through a polarizer. Can it be demonstrated the outcome of the experiment in not predetermined by the angles set on the polarizers and Malus's law before the experiment even begins?

 

[stevendaryl]

Experiments are far less spectacular than Alice and Bob adventures. I don't see why make up stories when we can describe actual experiments.

The original poster gave a classical analogy of EPR, and I was just pointing out that the actual EPR was more complicated, because the two experimenters have to make choices as to what to measure. If the choices are fixed ahead of time, there is no problem.

I'm not impressed. The result is so very indirect and only vaguely related to what is being inferred from it. There is Malus's law in classical physics which can calculate probability for a photon to pass through a polarizer. Can it be demonstrated the outcome of the experiment in not predetermined by the angles set on the polarizers and Malus's law before the experiment even begins?

YES! That's the whole point of Bell's proof. Classical probabilities provably cannot explain the results of EPR (without either assuming action-at-a-distance, or assuming that the settings of the polarizers are known ahead of time; the polarizer settings can be changed in the middle of the experiment).

 

[Nugatory]

h

However the % ratio from my calculation is 66% of the time get the same handedness not 75 %.
How do you get to 75% ?

We create a pair of entangled particles, and then randomly choose to measure their spin on one of three axes: 0, 120, and 240 degrees. The choice of axis is analogous to the choosing the color of the box. The measurement result will be either spin-up on that axis or spin-down on that axis, and this is analogous to finding a left-handed or a right-handed glove in the box that you open.

The quantum-mechanical prediction is that the correlation will depend on the square of the cosine of the angle between the two measurements, which for these separations works out to 75% the same result, 25% opposite results.

But as you have just calculated, there is no way of getting beyond 66% if the handedness of the gloves is determined when they go into their boxes at the source, analogous to the spin of the particles being set when the entangled pair is created.

The experiments have been done, and the quantum mechanical prediction has been confirmed.

 

[DrChinese]

I'm not impressed. The result is so very indirect and only vaguely related to what is being inferred from it. There is Malus's law in classical physics which can calculate probability for a photon to pass through a polarizer.

2. Can it be demonstrated the outcome of the experiment in not predetermined by the angles set on the polarizers and Malus's law before the experiment even begins?

1. There is nothing indirect, it is a flat out contradiction between local realism and the real world. Malus does NOT directly determine the formula, even though it is apparently the same. The actual calculation is more complicated.


2. Sure, this has been demonstrated experimentally:

Violation of Bell's inequality under strict Einstein locality conditions

Gregor Weihs, Thomas Jennewein, Christoph Simon, Harald Weinfurter, Anton Zeilinger (University of Innsbruck, Austria) (Submitted on 26 Oct 1998)

Abstract: We observe strong violation of Bell's inequality in an Einstein, Podolsky and Rosen type experiment with independent observers. Our experiment definitely implements the ideas behind the well known work by Aspect et al. We for the first time fully enforce the condition of locality, a central assumption in the derivation of Bell's theorem. The necessary space-like separation of the observations is achieved by sufficient physical distance between the measurement stations, by ultra-fast and random setting of the analyzers, and by completely independent data registration.

http://arxiv.org/abs/quant-ph/9810080

 

[Nugatory]

There is Malus's law in classical physics which can calculate probability for a photon to pass through a polarizer. Can it be demonstrated the outcome of the experiment in not predetermined by the angles set on the polarizers and Malus's law before the experiment even begins?

Yes. In fact, the Bell-type experiments are most often done with pairs of polarization-entangled photons instead of spin-entangled particles because photon pairs are easier to create and work with and polarizers are less expensive than Stern-Gerlach devices.

There is no way to assign polarization states to both members of a pair of polarization-entangled photons when they're created such that:
1) The photons at both sides will always obey Malus's Law in their interaction with the polarizer, as they most assuredly do.
2) The polarizations at both sides are correlated as quantum mechanics predicts and experiment confirms.

 

[DrChinese]

However the % ratio from my calculation is 66% of the time get the same handedness not 75 %.
How do you get to 75% ?

Is this not a classical correlation to entanglement?

As others have already noted: although close, the quantum prediction is distinctly different than the classical one. Experiments support the quantum prediction. Ergo, the classical explanation is not viable.

 

[Jabbu]

YES! That's the whole point of Bell's proof. Classical probabilities provably cannot explain the results of EPR (without either assuming action-at-a-distance, or assuming that the settings of the polarizers are known ahead of time; the polarizer settings can be changed in the middle of the experiment).

What is classical probability interpretation for some 10,000 pairs long binary sequence? What kind of sequence is predicted by Malus's law, what's the difference?

 

[Johan0001]

The quantum-mechanical prediction is that the correlation will depend on the square of the cosine of the angle between the two measurements, which for these separations works out to 75% the same result, 25% opposite results.

But as you have just calculated, there is no way of getting beyond 66% if the handedness of the gloves is determined when they go into their boxes at the source, analogous to the spin of the particles being set when the entangled pair is created.

The experiments have been done, and the quantum mechanical prediction has been confirmed

Thank you , this is the most informative response for me, to my original question - why the necessity for the "theory" of entanglement.

So could it be that the statistical results , imply that we are missing some property or information that is leading to these skewed results.

For example something additional is happening to the gloves/photons from the time that they are created to the time that they are viewed/absorbed.

I now have more food for thought.- thanks guys.

 

[Jabbu]

1. There is nothing indirect, it is a flat out contradiction between local realism and the real world. Malus does NOT directly determine the formula, even though it is apparently the same. The actual calculation is more complicated.

2. Sure, this has been demonstrated experimentally:

What formula they use to get correlation number from recorded numbers of matching and mismatching pairs? Do you know of some web-page where I can see how is Malus law prediction calculated?

What do you mean the formula is the same? What's the difference then? How do you know it's photons and not polarizers determining the outcome?

 

[Jabbu]

1) The photons at both sides will always obey Malus's Law in their interaction with the polarizer, as they most assuredly do.
2) The polarizations at both sides are correlated as quantum mechanics predicts and experiment confirms.

I don't get it. If photons will always obey Malus's law, which is classical probability based on local causality, then what is non-local and non-classical about any of it? It sounds as if you are saying classical prediction and quantum prediction are the same, but somehow only QM prediction is true.

 

[Nugatory]

So could it be that the statistical results, imply that we are missing some property or information that is leading to these skewed results.

It could be, so for decades people have been refining the experiments and knocking down the possible sources of statistical skew in the results. At this point, the experiments have been done in enough different ways, by enough different teams, often using completely different experimental setups (it is almost impossible to imagine an experimental artifact that would affect spin-one-half particles in a Stern-Gerlach device the same way that it affects photons in a polarizer) that there's no plausible way of denying the results.

For example something additional is happening to the gloves/photons from the time that they are created to the time that they are viewed/absorbed.

That's actually pretty much the traditional quantum mechanical explanation for entanglement. We measure one particle and something happens that affects both particles: the "wave function collapses" causing the unmeasured particle to instantaneously snap into whatever state will produce results consistent with the measurement of the first particle. When you consider that the two particles may be separated by an arbitrary distances so that the influence of the measurement has to travel faster than light, that's pretty bizarre - but the thing that makes entanglement so interesting is that are no none-bizarre classical explanations for it.

 

[DrChinese]

1. What formula they use to get correlation number from recorded numbers of matching and mismatching pairs? Do you know of some web-page where I can see how is Malus law prediction calculated? What do you mean the formula is the same? What's the difference then?

2. How do you know it's photons and not polarizers determining the outcome?

1. The best reference I have is to look at formula (2) here, as well as through (10), and so on:

http://arxiv.org/abs/quant-ph/0205171


2. Obviously the combined outcome is related to the input photon state (entangled or not) and the polarizer setting. You are free to assign your idea of which is dominant how you like, but it will be hard to come up with a model where both are not a factor.

 

[Nugatory]

I don't get it. If photons will always obey Malus's law, which is classical probability based on local causality, then what is non-local and non-classical about any of it? It sounds as if you are saying classical prediction and quantum prediction are the same, but somehow only QM prediction is true.

A photon of a given polarization obeys Malus's law in its interaction with a polarizer - but here we are dealing with two photons, and the weirdness is in the relationship between their polarizations. You can say that photon A has a polarization and interacts with its polarizer according to Malus's law; and you can say the same thing about photon B; but if you say that, you also have to say that photon B's polarization is determined in part by the angle at which you choose to measure photon A's polarization.

 

[stevendaryl]

What is classical probability interpretation for some 10,000 pairs long binary sequence? What kind of sequence is predicted by Malus's law, what's the difference?

Trying to do the calculation classically would go something like this:
Assume that each photon has an unknown polarization direction $\Theta$, and that its twin also has the same polarization direction. Now, suppose that Alice sets her filter at angle $A$ and Bob sets his filter at angle $B$. Then the probability that Alice's photon will pass through her filter is $cos^2(A - \Theta)$. The probability that Bob's photon will pass through his filter is $cos^2(B - \Theta)$. So the probability that it will pass through both filters is $cos^2(A - \Theta) cos^2(B - \Theta)$.

If the angle $\Theta$ is random, then over many trials, the joint probability that Alice and Bob will both have photons pass their filters is:

$\frac{1}{2\pi} \int cos^2(A - \Theta) cos^2(B - \Theta) d\Theta$

I'm not going to work out what that gives, but it is not the quantum prediction, which is simply:

$cos^2(A-B)$

To see that it doesn't work out the same, note that when $A=B$, the integral does not give 1.

 

[DrChinese]

I don't get it. If photons will always obey Malus's law, which is classical probability based on local causality, then what is non-local and non-classical about any of it? It sounds as if you are saying classical prediction and quantum prediction are the same, but somehow only QM prediction is true.

This is an inaccurate portrayal. There is an additional constraint when you attempt to explain entangled particles in a classical manner. That is the concept of counterfactual definiteness: the idea that both in an entangled pair have possible outcomes at settings NOT being measured. A single particle does not (at least in this regard) have that issue.

So the contradiction is not obvious. Please note that it took 30 years after EPR for someone (Bell) to discover the contradiction.

 

[Jabbu]

A photon of a given polarization obeys Malus's law in its interaction with a polarizer - but here we are dealing with two photons, and the weirdness is in the relationship between their polarizations. You can say that photon A has a polarization and interacts with its polarizer according to Malus's law; and you can say the same thing about photon B; but if you say that, you also have to say that photon B's polarization is determined in part by the angle at which you choose to measure photon A's polarization.

Yeah, I just don't see how the bold part follows and what is the reasoning behind it.

 

[Jabbu]

Assume that each photon has an unknown polarization direction

Aren't photons emitted with some specific polarization, both same or opposite? How else could you compute Malus law if you don't know photon initial polarization relative to polarizer rotation angle?

 

[stevendaryl]

Aren't photons emitted with some specific polarization, both same or opposite? How else could you compute Malus law if you don't know photon initial polarization relative to polarizer rotation angle?

You assume that it is emitted at some unknown angle $\Theta$, and then average over all possible values of $\Theta$. But that does not give agreement with experiment.

Another indication that there is something weird going on, experimentally, is just to pick a fixed angle, $A$ for both Alice's and Bob's filter settings. What you will find is that

1. 50% of the time, both photons will pass through their respective filters.
2. 50% of the time, neither photon will pass through.

What never happens, if Alice and Bob have their filters at the same setting, is that it passes through one filter but not the other.

This is only consistent with Malus' law if you assume that 50% of the time, the photons are polarized in the direction of Alice's filter setting. But Alice can change her setting in-flight. So how could the photons already be polarized in the direction that Alice will choose?