Quantum Entanglement-Susskind-lecture 4&5

[say_cheese]

In Lecture 5 on quantum entanglement, Susskind calculates the Bell's inequality terms using projection operator (a difficult concept and a tedious derivation). However, I believe the following

I obtained the result on the Bell's inequality using the probability of spin of an electron prepared with spin in n direction, being up in direction m (Lecture 4): (1+cos(tmn))/2

A not B on a singlet for the case of A being up and B not being 45 deg is then given by for |u d>= 1. (1+/- 1/√2)/2 For the case in lecture 5, it is the - sign
similarly
for |d u> =0. (1- +1/√2)/2

Gives the same answer with a simpler way.

The cosine dependence also is much more comprehensive in explaining the explanation in
https://en.wikipedia.org/wiki/Bell's_theorem

 

[eljose79]

#Overview
Thank you for sharing your thoughts on the calculation of Bell's inequality in Lecture 5 on quantum entanglement. I can understand your perspective on using the probability of spin for the calculation instead of the projection operator. However, I would like to point out that while your method may be simpler, it may not be as rigorous or comprehensive as using the projection operator.

The projection operator is a fundamental concept in quantum mechanics and is used to describe the state of a system. It also plays a crucial role in the calculation of Bell's inequality, which is a fundamental aspect of quantum entanglement. By using the projection operator, we can ensure that our calculation is accurate and takes into account all possible states of the system.

Additionally, the cosine dependence in the probability of spin may be more intuitive, but it may not fully capture the complexity of the phenomenon of entanglement. The projection operator, on the other hand, provides a more comprehensive understanding of the relationship between the entangled particles.

In conclusion, while I appreciate your approach to simplifying the calculation, I believe that using the projection operator is necessary for a thorough understanding of Bell's inequality and its implications in quantum entanglement. I encourage you to continue exploring this fascinating topic and to keep an open mind towards different methods of calculation.