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

• anorlunda
In summary, the singlet state is a quantum mechanical state characterized by two particles being entangled with a total spin of zero. It is typically created through quantum entanglement and particles in this state have opposite spins and share other properties even when separated by large distances. The significance of the singlet state lies in its demonstration of quantum entanglement and its practical applications in technology. However, it cannot be used for faster-than-light communication as the actual transfer of information remains limited by the speed of light.
anorlunda
Staff Emeritus
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.

Thank you for your question. The singlet state, also known as the Bell state, is a quantum state that is used to describe the entanglement between two particles. This state is important in quantum mechanics because it illustrates the concept of non-locality, where the properties of one particle are dependent on the properties of another particle, even at large distances.

To answer your question, let's first understand how particles enter the singlet state. As you mentioned, particles can be separated by any distance and still remain in the singlet state. This is because the singlet state is a superposition of two states, in this case |u> and |d>, with equal probability amplitudes. This means that the particles have an equal chance of being in either state, regardless of their proximity.

Now, to calculate the probability of a pair of particles entering the singlet state, we need to consider the initial state of the particles. If the particles are initially in a state with lower energy than the singlet state, they would emit a photon and enter the singlet state. The probability of this event is determined by the energy difference between the initial state and the singlet state. This probability can be calculated using the principles of quantum mechanics, such as the Schrödinger equation.

However, if the particles are initially in a state with higher energy than the singlet state, the probability of them entering the singlet state is lower. This is because the particles would need to lose energy in order to enter the singlet state, and this process is less likely to occur.

To learn more about the probability of particles entering the singlet state, I would recommend studying the principles of quantum mechanics, particularly the concept of superposition and the Schrödinger equation. There are also many resources available online that explain the EPR paradox and Bell's Theorem in detail.

## 1. What is the "singlet state" in science?

The singlet state is a quantum mechanical state in which two particles are entangled, meaning their properties are linked and cannot be described independently. This state is characterized by a total spin of zero, meaning the two particles have opposite spins.

## 2. How is the singlet state entered?

The singlet state is typically created through a process called quantum entanglement, in which two particles are brought into a state of entanglement. This can be achieved through various methods such as using a beam splitter or through the use of entangling gates in quantum computing.

## 3. What are the properties of particles in the singlet state?

Particles in the singlet state have opposite spins, meaning if one particle is measured to have a spin of up, the other particle must have a spin of down. They also share other properties, such as energy and momentum, even when separated by large distances.

## 4. What is the significance of the singlet state in quantum mechanics?

The singlet state is significant because it demonstrates the phenomenon of quantum entanglement, which is a fundamental principle in quantum mechanics. It also has practical applications in quantum computing and communication, as information can be shared between particles in entangled states instantaneously.

## 5. Can particles in the singlet state be used for faster-than-light communication?

No, particles in the singlet state cannot be used for faster-than-light communication. Although information can be shared instantaneously between entangled particles, this does not violate the speed of light as the actual transfer of information is still limited by the speed of light.

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