re:John Stewart Bell paper 1964.
Today, a fully entangled state for two particles is referred to as a Bell state
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from Bing/Chat
**Bell tests** are experimental setups designed to test the predictions of quantum mechanics against those of local realism (as described by Bell's inequality). Here's how they are typically conducted:
1. **Entangled Particle Pair Creation**:
- First, a pair of entangled particles (such as photons or electrons) is created. These particles are generated in such a way that their quantum states are correlated.
- For example, a nonlinear crystal can produce entangled photon pairs via a process called **parametric down-conversion**.
2. **Measurement Settings**:
- Two distant detectors are placed far apart from each other.
- Each detector has multiple measurement settings (e.g., polarization angles for photons).
- The choice of measurement settings is random and independent for each detector.
3. **Particle Detection**:
- When one of the entangled particles reaches a detector, it is measured according to the chosen setting.
- The other particle simultaneously reaches the distant detector and is also measured according to its chosen setting.
4. **Correlations and Statistics**:
- The detectors record the outcomes of measurements (e.g., "spin up" or "spin down" for electrons, or polarization states for photons).
- Over many trials, statistical correlations between the measurement outcomes are analyzed.
- These correlations are compared to the predictions of local realism and quantum mechanics.
5. **Bell's Inequality Test**:
- Bell's inequality provides a mathematical criterion that local realistic theories must satisfy.
- If the observed correlations violate Bell's inequality, it suggests that local realism is not valid, and quantum mechanics prevails.
- Violation of Bell's inequality implies that the entangled particles' behavior cannot be explained by pre-existing hidden variables.
6. **Results and Interpretation**:
- If the experiment shows a violation of Bell's inequality, it supports the quantum mechanical view that entangled particles exhibit non-local correlations.
- Conversely, if the results agree with local realism, it would challenge quantum mechanics.
7. **Challenges and Loopholes**:
- Bell tests face challenges related to experimental imperfections (such as detector inefficiencies, locality loopholes, and freedom-of-choice loopholes).
- Researchers continue to improve experimental setups to close these loopholes and strengthen the case for quantum mechanics.
In summary, Bell tests provide empirical evidence that quantum entanglement violates classical notions of locality and realism. They play a crucial role in understanding the fundamental nature of our universe. If you have any more questions, feel free to ask! 😊
Below, another Alice and Bob episode, this time showing the strength of entanglement
in a Bell's inequality simulation:
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