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?

 

[Jabbu]

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.

According to Malus it's 45 degrees relative angle that gives 50% chance: cos^2(45) = 50%, so if both photons have the same 45 degrees polarization relative to their polarizer, or at least same on average, then overall they will both have the same 50% chance to pass through. Where is this different than what actually happens?

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.

I think those experiments measure large numbers of both matching and mismatching pairs, and that it is only after some average is taken over many measurements that we can see some kind of overall correlation or discordance.

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?

Can you give more specific description of what are you talking about it the last two sentences?

 

[Nugatory]

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

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

When two photons are entangled in this way, their polarizations will always be perpendicular to one another. Suppose that while the two photons are in flight, I choose a particular orientation $\Theta$ for the left-hand polarizer, and the left-hand photon passes through. No matter what orientation I choose for the right-hand polarizer, the right-hand photon will pass or not according to Malus's law for a photon polarized at right angles to $\Theta$.

That's both the quantum mechanical prediction and the experimental result... But if you look at the way that the right-hand photon obeys Malus's law and conclude that the right-hand photon is in fact polarized at right-angles to $\Theta$ you've just concluded the part in bold.

 

[stevendaryl]

According to Malus it's 45 degrees relative angle that gives 50% chance: cos^2(45) = 50%, so if both photons have the same 45 degrees polarization relative to their polarizer, or at least same on average, then overall they will both have the same 50% chance to pass through. Where is this different than what actually happens?

If you created two photons polarized at angle 0 degrees, and Bob and Alice both had their filters set at 45 degrees, then:

1. 25% of the time, Alice and Bob would both see photons pass through their filters.
2. 25% of the time, Alice would see a photon pass through, but not Bob.
3. 25% of the time, Bob would see a photon pass through, but not Alice.
4. 25% of the time, neither would see a photon pass through.

But in actual experiments, possibilities 2 and 3 never happen.

 

[Jabbu]

When two photons are entangled in this way, their polarizations will always be perpendicular to one another. Suppose that while the two photons are in flight, I choose a particular orientation $\Theta$ for the left-hand polarizer, and the left-hand photon passes through. No matter what orientation I choose for the right-hand polarizer, the right-hand photon will pass or not according to Malus's law for a photon polarized at right angles to $\Theta$.

That's both the quantum mechanical prediction and the experimental result... But if you look at the way that the right-hand photon obeys Malus's law and conclude that the right-hand photon is in fact polarized at right-angles to $\Theta$ you've just concluded the part in bold.

I don't see what difference does it make whether polarizer angle is set yesterday or just before some photon is supposed to arrive. Is probability for the photon to pass through not always equal to cos^2(theta), where theta is relative angle between photon polarization and polarizer rotation angle that happens to be in the moment in time when, and where, they interact?

 

[stevendaryl]

If you created two photons polarized at angle 0 degrees, and Bob and Alice both had their filters set at 45 degrees, then:

1. 25% of the time, Alice and Bob would both see photons pass through their filters.
2. 25% of the time, Alice would see a photon pass through, but not Bob.
3. 25% of the time, Bob would see a photon pass through, but not Alice.
4. 25% of the time, neither would see a photon pass through.

But in actual experiments, possibilities 2 and 3 never happen.

I should say: in actual experiments involving entangled pairs of photons, possibilities 2 and 3 never happen. If you create unentangled photons, then it works the same way as classically.

 

[stevendaryl]

I don't see what difference does it make whether polarizer angle is set yesterday or just before some photon is supposed to arrive. Is probability for the photon to pass through not always equal to cos^2(theta), where theta is relative angle between photon polarization and polarizer rotation angle that happens to be in the moment in time when, and where, they interact?

Yes, there are two photons, one interacting with Alice's filter, and the other interacting with Bob's filter. The important angle is the angle between Alice's and Bob's filters at the time the two photons interact with the filters. So \theta is not known at the beginning of the experiment (if Alice and Bob change their filters in-flight).

 

[DrChinese]

Aren't photons emitted with some specific polarization, both same or opposite?

Not, not if they are polarization entangled. Entangled photons are in a superposition of states.

As mentioned by stevendaryl and Nugatory, if you measure Alice and Bob at the same angle setting - regardless of what it is - they will match (or mismatch depending on the type of entanglement as Type I or Type II) 100% of the time. Photons that are not entangled will not display this characteristic.

Have you read the EPR and Bell arguments? If you haven't seen those, I would strongly recommend that you do.

 

[DrChinese]

I don't see what difference does it make whether polarizer angle is set yesterday or just before some photon is supposed to arrive. Is probability for the photon to pass through not always equal to cos^2(theta), where theta is relative angle between photon polarization and polarizer rotation angle that happens to be in the moment in time when, and where, they interact?

There are 2 basic ideas usually advanced to provide a classical explanation to entangled particles.

1. The photons are polarized as per usual, but the angle is unknown. As explained by stevendaryl and Nugatory, this argument fails immediately because you do not get the "perfect correlations" which are common to entangled particles (when each is measured at the same angle). Instead of 100% mismatches, you would get more like 50%.

2. The photons are polarized via so-called "hidden variables" that give the answer to the polarization "question" at all angles. This was the EPR hypothesis (1935). It seems reasonable. For example, it might yield + at 0 degrees, + at 120 degrees, and - at 240 degrees. And so on for any angle. On the average, it would reproduce Malus.

But Bell discovered a fatal flaw in this scheme in 1964. Read about Bell's Theorem to see why.

 

[Jabbu]

If you created two photons polarized at angle 0 degrees, and Bob and Alice both had their filters set at 45 degrees, then:

1. 25% of the time, Alice and Bob would both see photons pass through their filters.
2. 25% of the time, Alice would see a photon pass through, but not Bob.
3. 25% of the time, Bob would see a photon pass through, but not Alice.
4. 25% of the time, neither would see a photon pass through.

I should say: in actual experiments involving entangled pairs of photons, possibilities 2 and 3 never happen. If you create unentangled photons, then it works the same way as classically.

Are you saying there will be 100% matching pairs with 45 degrees? Don't both QM and Malus's law say it's cos^2(45) = 50% correlation?

 

[Jabbu]

Yes, there are two photons, one interacting with Alice's filter, and the other interacting with Bob's filter. The important angle is the angle between Alice's and Bob's filters at the time the two photons interact with the filters. So \theta is not known at the beginning of the experiment (if Alice and Bob change their filters in-flight).

The experiments I was reading about didn't need to randomly shuffle angles and they still confirmed QM prediction. I don't see what's the point of involving even more randomness. The only question I'm asking is how QM prediction differs from Malus's law prediction, especially since both equations seem to be the same.

 

[Jabbu]

Not, not if they are polarization entangled. Entangled photons are in a superposition of states.

When we measure correlation with angle theta of 60 degrees, does it mean:

1. polarizer A = +60, polarizer B = +60
2. polarizer A = -60, polarizer B = +60
3. polarizer A = -30, polarizer B = +30

Or something else?

Have you read the EPR and Bell arguments? If you haven't seen those, I would strongly recommend that you do.

Yes, I'm trying to clarify things that don't make sense to me.

 

[Nugatory]

I don't see what difference does it make whether polarizer angle is set yesterday or just before some photon is supposed to arrive. Is probability for the photon to pass through not always equal to cos^2(theta), where theta is relative angle between photon polarization and polarizer rotation angle that happens to be in the moment in time when, and where, they interact?

Yes, but what is the photon polarization? Somehow, it always to turns out to be exactly ninety degrees off of the angle that the other polarizer, the one we used to measure the other photon.

Let's assume that the photons were created with the left-hand photon polarized at zero degrees and the right-hand photon polarized at ninety degrees, and then while the photons are in flight we set the left-hand polarizer to 45 degrees. Fifty percent of the time the left-hand photon will clear its by polarizer (Malus's law).

Now, what is the probability that the right-hand photon will clear a polarizer set at 135 degrees? 90 degrees? 45 degrees? The observed results and the quantum mechanical prediction are 100%, 50%, and 0% for those three values - and that's what you get by applying Malus's law to a photon polarized at 135 degrees, not the 90 degrees that we assumed.

If we had set the left-hand polarizer to 30 degrees, then 75% of the time the left-hand photon would have cleared the polarizer (Malus's Law again) and in those cases the right-hand photon would obey Malus's law for a 120-degree photon.

It's as if measuring the left-hand photon at a given angle changes the polarization of its right-hand partner to that angle plus ninety degrees. That's the unique feature of entanglement.

 

[Nugatory]

When we measure correlation with angle theta of 60 degrees, does it mean:

1. polarizer A = +60, polarizer B = +60
2. polarizer A = -60, polarizer B = +60
3. polarizer A = -30, polarizer B = +30

Or something else?

#3 is an example of theta equal to 60. Other examples would be A=0 and B=60, A=11 and B=71, A=44 and B=-16... All that matters is that there is sixty degrees between them.

It occurs to me that you may be being confused by the way that the symbol $\theta$ is being used into two different ways. There are four angles in the experiment: The angle we set the left-hand polarizer to ($\theta_L$), the angle we set the right-hand polarizer to ($\theta_R$), the polarization angle of the left-hand photon ($\omega_L$), and the polarization angle of the right-hand photon ($\omega_L$).

The thetas that appear in Malus's law are the angles $\theta_R-\omega_R$ for the right-hand photon interacting with the right-hand polarizer and $\theta_L-\omega_L$ for the left-hand photon interacting with the left-hand polarizer.

The theta that appears in the QM calculation of the correlation probabilities is $\theta_L-\theta_R$, the difference in the detector angles.

 

[stevendaryl]

Are you saying there will be 100% matching pairs with 45 degrees? Don't both QM and Malus's law say it's cos^2(45) = 50% correlation?

If both filters are at the same angle, then there is perfect, 100% correlation--either both filters pass the photons, or both do not.

 

[stevendaryl]

The experiments I was reading about didn't need to randomly shuffle angles and they still confirmed QM prediction. I don't see what's the point of involving even more randomness. The only question I'm asking is how QM prediction differs from Malus's law prediction, especially since both equations seem to be the same.

No, they are not the same. If you have light that is polarized at 0 degrees, and you have two filters, Alice's and Bob's, that are oriented at 45 degrees, then 50% of the light will pass through Alice's filter, and 50% will pass through Bob's. That's true both classically (Malus' law) and quantum mechanically. But now lower the intensity so low that you see individual photons. You will find that randomly, half the photons reaching Alice's filter pass through, and half the photons reaching Bob's filter pass through. But there is no correlation between the two. Sometimes both Bob and Alice will see a photon pass. Sometimes neither. Sometimes one and not the other. That's the prediction for unentangled photons.

But now, if the photons are entangled (that is, Alice's photon and Bob's photons are both produced in an atomic decay so that they are correlated), then you see Alice's results correlated with Bob's results. If they both have their filters at the same setting, then they will get the same results: either both will see the photon pass, or neither will see it pass. This is not a consequence of Malus' law. Malus' law doesn't say anything about the correlation between Alice's and Bob's result. (Malus' law is about light intensity, not about numbers of individual photons).