Bell's test: Introducing a control experiment

In summary, the control experiments showed that the results of the Bell test experiment - in which two particles are entangled and their polarizations are randomized - were not as expected.
  • #1
San K
911
1
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
 
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  • #2
San K said:
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
Yes, you're right about that.
 
  • #3
Thanks Lugita.

lugita15 said:
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...

lugita15 said:
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.

lugita15 said:
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.
 
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  • #4
San K said:
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.
San K said:
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.
 

1. What is Bell's test and why is it important in science?

Bell's test is a scientific experiment that was proposed by physicist John Stewart Bell in 1964. It is used to test the validity of the quantum entanglement theory, which states that particles can be connected and influenced by each other at a distance. This test is important because it helps scientists understand the fundamental principles of quantum mechanics and can also have practical applications in technologies such as quantum computing.

2. How does Bell's test work?

In Bell's test, two entangled particles are created and separated. These particles are then measured at different angles to determine their correlation. If the particles are truly connected, their measurements will show a higher degree of correlation than what is predicted by classical physics. This result would support the idea of quantum entanglement.

3. What is a control experiment in Bell's test?

A control experiment in Bell's test is a critical component of the experiment design. It involves performing the same experiment with non-entangled particles to compare the results with those of the entangled particles. This helps to eliminate any external factors that could affect the outcome and ensures that the results are solely due to the entanglement of the particles.

4. What are the implications of Bell's test on our understanding of quantum mechanics?

Bell's test has significant implications for our understanding of quantum mechanics. Its results have been used to disprove local hidden variable theories, which suggested that the correlation between entangled particles was due to hidden variables rather than quantum entanglement. This test also supports the principle of non-locality in quantum mechanics, where particles can influence each other instantaneously regardless of distance.

5. How is Bell's test relevant in modern research?

Bell's test is still a relevant and active area of research in modern science. It continues to be used to test and improve our understanding of quantum mechanics and has also led to the development of new technologies such as quantum entanglement-based cryptography. It is also being used to explore the boundaries of quantum mechanics and to potentially uncover new scientific principles and phenomena.

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