## Bell's test: Introducing a control experiment

If we were to introduced a set of un-entangled, but same polarized, photons as control experiment what would the results be of the control experiment?

So we have the following three cases:

Bell test Experiment: Send entangled photons

Result is that P(-30,30) is not equal to P(0,30) + P (0,-30)...hence QE proved...

(side note - with not all loopholes closed simultaneously)

Control Experiment 1: Send "un-entangled" photons, but same polarization

What would the relation be between P (-30, 30), P(0,30) and P(0,-30)?

Control Experiment 2: Send "un-entangled" photons, but random polarization

What would the relation be between P (-30, 30), P(0,30) and P(0,-30)?

I guess in the last case it would be 0.5, 0.5, 0.5
 PhysOrg.com physics news on PhysOrg.com >> Kenneth Wilson, Nobel winner for physics, dies>> Two collider research teams find evidence of new particle Zc(3900)>> Scientists make first direct images of topological insulator's edge currents

Blog Entries: 1
 Quote by San K Bell test Experiment: Send entangled photons Result is that P(-30,30) is not equal to P(0,30) + P (0,-30)...hence QE proved...
I assume by P(x,y) you mean the probability of mismatch between the results of a polarizer oriented at an angle x and a polarizer oriented at an angle y. And one correction, it's called Bell's INequality, not Bell's equation for a reason. Bell's inequality in this case, is P(-30,30)≤P(-30,0)+P(0,30), so the significant fact is that QM predicts P(-30,30) is greater than P(-30,0)+P(0,30). The significant fact is not merely that P(-30,30) is not equal to P(0,30)+P (0,-30).
 Control Experiment 1: Send "un-entangled" photons, but same polarization What would the relation be between P (-30, 30), P(0,30) and P(0,-30)?
Well, the photons aren't entangled, then you no longer get perfect correlation at identical angles, i.e. it is no longer true that P(x,x)=0 for all angles x. But this is a crucial assumption for deriving the Bell inequality, so the Bell inequality need not apply in this case.

Still, if you want to calculate the probabilities anyway it's pretty straightforward (though tedious) to compute. All you have to know is that given an unentangled photon polarized in a direction θ1, the probability that it will go through a polarizer oriented at an angle θ2 is cos2(θ1-θ2).
 Control Experiment 2: Send "un-entangled" photons, but random polarization What would the relation be between P (-30, 30), P(0,30) and P(0,-30)? I guess in the last case it would be 0.5, 0.5, 0.5

Thanks Lugita.

 Quote by lugita15 I assume by P(x,y) you mean the probability of mismatch between the results of a polarizer oriented at an angle x and a polarizer oriented at an angle y. And one correction, it's called Bell's INequality, not Bell's equation for a reason. Bell's inequality in this case, is P(-30,30)≤P(-30,0)+P(0,30), so the significant fact is that QM predicts P(-30,30) is greater than P(-30,0)+P(0,30). The significant fact is not merely that P(-30,30) is not equal to P(0,30)+P (0,-30)
agreed.

a better answer is that - the correlation is stronger than that predicted by the laws of probability...

 Quote by lugita15 Well, the photons aren't entangled, then you no longer get perfect correlation at identical angles, i.e. it is no longer true that P(x,x)=0 for all angles x. But this is a crucial assumption for deriving the Bell inequality, so the Bell inequality need not apply in this case.
Same polarized photons won't give same answer for polarizers that are aligned? (i.e. polarizers are same angles to each other)

However entangled photons will give the same answer for polarizers that are aligned?

Bell's inequality does not apply. We are simply comparing polarized non-entangled photons with entangled photons (which necessarily are non-polarized). there is a reason for this.

 Quote by lugita15 Still, if you want to calculate the probabilities anyway it's pretty straightforward (though tedious) to compute. All you have to know is that given an unentangled photon polarized in a direction θ1, the probability that it will go through a polarizer oriented at an angle θ2 is cos2(θ1-θ2). Yes, you're right about that.
ok, just wanted to get the probabilities for P(-30,30), P(-30,0) and P(0,30), assuming Theta 1 is Zero degrees.

Blog Entries: 1

## Bell's test: Introducing a control experiment

 Quote by San K a better answer is that - the correlation is stronger than that predicted by the laws of probability...:)
It's the laws of probability plus local hidden variables.
 Quote by San K ok, just wanted to get the probabilities for P(-30,30), P(-30,0) and P(0,30), assuming Theta 1 is Zero degrees.
OK, based on a quick calculation in my head, P(-30,30)=37.5%, and P(-30,0)=P(0,30)=25%. EDIT:Sorry, I made a mistake the first time. Now the numbers should be right.

 Similar discussions for: Bell's test: Introducing a control experiment Thread Forum Replies Quantum Physics 17 Quantum Physics 2 General Physics 0 Quantum Physics 13 Quantum Physics 11