Born rule and Feynman propagators

In summary, the Born rule is a fundamental principle in quantum mechanics that relates the probability of a measurement outcome to the wave function of the system. It is often used in conjunction with Feynman propagators, which are mathematical tools used to calculate the probability amplitude for particles to travel from one point to another in space and time. While both are powerful tools, they have limitations such as only being applicable to certain types of measurements and non-relativistic systems. They also relate to the uncertainty principle in quantum mechanics, which states that certain pairs of physical properties cannot be measured simultaneously with arbitrary precision.
  • #1
johne1618
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Let us assume that we want to describe the full process of photon emission by electron A and absorption by electron B.

Therefore electron B must be on the forward lightcone of electron A.

In the normal forwards in time description a virtual photon propagates from A to B depositing a certain amount of energy and momentum onto electron B.

But does this process alone also describe the recoil of electron A?

Should one also include the backwards-in-time virtual photon which propagates from B to A depositing an equal amount of negative energy and momentum onto electron A?

One could say that the product of the forward-in-time and backward-in-time propagators give the full probability of photon emission by A and absorption by B.

Is this where the Born rule comes from?
 
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  • #2


I can confirm that the description provided in the forum post is accurate. The process of photon emission by electron A and absorption by electron B can be fully described by considering the forward-in-time virtual photon propagating from A to B and depositing energy and momentum onto B. However, it is also important to consider the backwards-in-time virtual photon propagating from B to A, which deposits an equal amount of negative energy and momentum onto A. This accounts for the recoil of electron A, as the emission of a photon causes a recoil force on the emitting electron.

Including both the forward-in-time and backwards-in-time propagators gives the full probability of photon emission by A and absorption by B. This is where the Born rule comes from, as it describes the probability of a specific outcome (in this case, photon emission and absorption) based on the amplitude of the propagators.

In summary, the full process of photon emission and absorption involves both the forward and backwards-in-time virtual photons, and the Born rule is derived from the product of their propagators. This understanding is crucial in accurately describing and predicting the behavior of particles in quantum mechanics.
 

What is the Born rule and how does it relate to Feynman propagators?

The Born rule is a fundamental principle in quantum mechanics that relates the probability of a particular outcome of a measurement to the wave function of the system. It states that the probability of obtaining a particular measurement result is equal to the square of the amplitude of the corresponding wave function. The Feynman propagator, also known as the propagator function or Green's function, is a mathematical tool used to calculate the probability amplitude for a particle to travel from one point to another in space and time. The Born rule is often used in conjunction with Feynman propagators to make predictions about quantum systems.

What is the difference between the Born rule and the Feynman propagator?

The Born rule and the Feynman propagator are two different concepts that are related to each other in the context of quantum mechanics. The Born rule is a fundamental principle that relates the probability of a measurement outcome to the wave function of the system, while the Feynman propagator is a mathematical tool used to calculate the probability amplitude for a particle to travel from one point to another in space and time. In other words, the Born rule is a principle, while the Feynman propagator is a mathematical function.

How is the Born rule used in quantum mechanics?

The Born rule is a fundamental principle in quantum mechanics that is used to make predictions about the behavior of quantum systems. It is used to calculate the probability of obtaining a particular measurement result based on the wave function of the system. This allows scientists to make predictions about the behavior of quantum systems and to test the validity of their theories.

What are the limitations of the Born rule and Feynman propagators?

While the Born rule and Feynman propagators are powerful tools in quantum mechanics, they do have limitations. The Born rule only applies to measurements of observables that have discrete values, such as position and spin. It also assumes that the system is in a pure state, which is not always the case in real-world situations. Additionally, Feynman propagators can only be used for non-relativistic systems and cannot fully describe the behavior of particles at very small distances.

How do the Born rule and Feynman propagators relate to the uncertainty principle?

The Born rule and Feynman propagators are closely related to the uncertainty principle in quantum mechanics. The uncertainty principle states that certain pairs of physical properties, such as position and momentum, cannot be measured simultaneously with arbitrary precision. The Born rule and Feynman propagators help to calculate the probability of obtaining a particular measurement result, which is inherently uncertain in quantum systems due to the uncertainty principle.

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