How is the QM prediction derived for Bell's tests?

In summary, the QM prediction for Bell's tests, represented by the cosine curve, is derived from equations (8) and (9) for theta=0 and equations (12) and (13) for a general theta. This shows that as the basis is rotated, the cosine factors are introduced. This is not directly related to Malus's law, but there may be an indirect connection between the two.
  • #1
San K
911
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Question 1: how is the QM prediction (i.e. cosine curve, shown below) derived for Bell's tests? in layman' termss

Question 2: while Malus's law, some physicists say, is not related to this cosine curve.
Is there an indirect/lengthy way to connect the two?
http://upload.wikimedia.org/wikipedia/commons/7/77/StraightLines.svg
 
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Related to How is the QM prediction derived for Bell's tests?

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

Bell's test is a thought experiment designed to test the principles of quantum mechanics against local hidden variable theories. It involves entangling two particles and measuring their properties to see if they violate the principle of locality, which states that distant objects cannot influence each other. It is important because it has been used to demonstrate the non-locality of quantum mechanics and has implications for our understanding of reality.

2. How is the quantum mechanical prediction derived for Bell's test?

The quantum mechanical prediction for Bell's test is derived using the principles of quantum mechanics, specifically the concept of entanglement. This prediction is based on the assumption that the entangled particles share a state, and any measurement made on one particle will instantaneously affect the state of the other particle, regardless of the distance between them.

3. What is the role of local hidden variable theories in Bell's test?

Local hidden variable theories are alternative explanations for quantum phenomena that propose the existence of hidden variables that determine the outcomes of measurements. In Bell's test, the role of these theories is to provide a framework for comparison with quantum mechanics, to see if the predictions of quantum mechanics are consistent with the principles of locality.

4. How do experiments confirm the predictions of quantum mechanics in Bell's test?

Experiments designed to test Bell's test have consistently shown that the predictions of quantum mechanics are accurate. These experiments involve entangling particles and measuring their properties, and the results have consistently violated the principle of locality, providing evidence for the non-locality of quantum mechanics.

5. What are the implications of the results of Bell's test for our understanding of reality?

The results of Bell's test have challenged our understanding of reality and have led to the acceptance of non-locality in quantum mechanics. This means that objects can be connected in ways that defy our classical understanding of space and time. It also has implications for concepts such as causality and determinism, as the results of measurements on one particle can instantly affect the state of another particle, regardless of the distance between them.

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