Is this a "fair" description of entanglement for a student?

In summary, two critical aspects of quantum entanglement are that it involves particles with opposite spin due to conservation of angular momentum, and that the wave function predicts the probability of spin measurements for a single particle, but not for a pair of entangled particles. When measuring the spin of one particle, the other particle's spin will always be opposite, violating the probabilities given by the wave function. This demonstrates the inseparability and non-locality of entangled particles, as described by Bell's Theorem and EPR paradox.
  • #36
atyy said:
Also, the standard 1961 textbook of Messiah does say that hidden variables cannot be ruled out and associates the hidden variable programme with Einstein. Messiah goes on to use Copenhagen (for the practical purpose of doing quantum mechanics) without ruling out hidden variables.

I think after Gleason published his theorem (1956 I think) the assumption was so obvious it could not be ignored. To be specific the assumption made was if A and B are two operators the addition of the expected outcomes is related simply ie if E(O) is the expected outcome of observable O then from a simplistic understanding of expectations you naturally think E(A) + E(B) = E(A+B). This is the assumption Von-Neumann made and is so reasonably obvious when you read the book you don't even bother questioning it. Greta did and saw it didn't necessarily hold up. But such was Von_Neumann's reputation people didn't listen to her - but may have listened to Einstein - he is one of the few that can stand up to Von-Neumann reputation wise. In proving Gleason's theorem you prove that is true - but the assumption is the probability is not basis dependent - called non-contextuality. Once you have seen that Von-Neumann is then quite suspect.

Thanks
Bill
 
<h2>1. What is entanglement?</h2><p>Entanglement is a phenomenon in quantum mechanics where two or more particles become connected in such a way that the state of one particle is dependent on the state of the other, regardless of the distance between them.</p><h2>2. How does entanglement occur?</h2><p>Entanglement occurs when two or more particles interact with each other and become entangled. This can happen through various processes such as collision, decay, or interaction with a third particle.</p><h2>3. Is entanglement a real physical phenomenon?</h2><p>Yes, entanglement is a well-established phenomenon in quantum mechanics and has been experimentally demonstrated multiple times. It is a fundamental aspect of quantum mechanics and has been used in various practical applications such as quantum cryptography and quantum computing.</p><h2>4. Can entanglement be explained in simple terms?</h2><p>While the concept of entanglement may be difficult to grasp, it can be explained in simple terms as a connection between particles that allows them to share properties regardless of distance. Think of it as two coins that are always connected, no matter how far apart they are.</p><h2>5. What are the potential implications of entanglement?</h2><p>Entanglement has potential implications in various fields such as communication, computing, and even teleportation. It also challenges our understanding of the fundamental principles of physics and has led to new theories and research in the field of quantum mechanics.</p>

1. What is entanglement?

Entanglement is a phenomenon in quantum mechanics where two or more particles become connected in such a way that the state of one particle is dependent on the state of the other, regardless of the distance between them.

2. How does entanglement occur?

Entanglement occurs when two or more particles interact with each other and become entangled. This can happen through various processes such as collision, decay, or interaction with a third particle.

3. Is entanglement a real physical phenomenon?

Yes, entanglement is a well-established phenomenon in quantum mechanics and has been experimentally demonstrated multiple times. It is a fundamental aspect of quantum mechanics and has been used in various practical applications such as quantum cryptography and quantum computing.

4. Can entanglement be explained in simple terms?

While the concept of entanglement may be difficult to grasp, it can be explained in simple terms as a connection between particles that allows them to share properties regardless of distance. Think of it as two coins that are always connected, no matter how far apart they are.

5. What are the potential implications of entanglement?

Entanglement has potential implications in various fields such as communication, computing, and even teleportation. It also challenges our understanding of the fundamental principles of physics and has led to new theories and research in the field of quantum mechanics.

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