How Does Particle Proximity Affect Transition Probability to the Singlet State?

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SUMMARY

The discussion centers on the relationship between particle proximity and the transition probability to the singlet state, specifically for spin 1/2 particles. Leonard Susskind's assertion that the singlet state has lower energy than other states implies that a pair of particles can transition to this state by emitting a photon. The inquiry focuses on formulating an expression for the probability of this transition as a function of the distance between the particles, highlighting the need for further study on this topic.

PREREQUISITES
  • Quantum Mechanics fundamentals
  • Understanding of spin 1/2 particles
  • Familiarity with the singlet state and its properties
  • Knowledge of photon emission processes
NEXT STEPS
  • Research the EPR paradox and its implications in quantum mechanics
  • Study Bell's Theorem and its relevance to particle states
  • Explore mathematical models for transition probabilities in quantum systems
  • Investigate the role of particle proximity in quantum state transitions
USEFUL FOR

Quantum mechanics students, physicists studying quantum entanglement, and researchers interested in the dynamics of particle states.

anorlunda
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QM students study the singlet state, (|u>-|d>)/SQRT(2). Particles in the singlet state can be separated by any distance, and remain in the singlet state. That leads to the EPR paradox, Bell's Theorem and the more. My question has more to do with entering the singlet state.

Leonard Susskind, in a video lecture, said that the singlet state has lower energy than other states for a pair of spin 1/2 particles. OK, that suggests that such a pair, initially in some other state, would emit a photon and enter the singlet state. But common sense says that the probability of such an event must be a function of the proximity of the two particles.

My question: how would I write an expression for the probability of this event as a function of proximity? I'm hoping that you can point me to a source where I can study it.
 

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