Question

Consider a setup in which a single photon is split into an entangled pair and directed towards 2 independent experimental setups (A and B). Both A and B have lenses to detect the polarization of the photon emitted towards them.

The photon state is described as follows where |H> is a horizontally polarized photon and |V> is a vertically polarized photon.

|psi>=|H>A|V>B−|V>A|H>B

This state indicates that there is a possibility that both A and B can detect a photon if the experiment is repeated enough number of times. For example, when the state of the entangled pair is |H>A|V>B or |V>A|H>B, both setups observe a photon.

My question is, how are the energies conserved when such a state is observed ?

Since, the energy of the parent photon (prior to split) is given by: E=(h⋅c)/λ.

Are the 2 entangled photons in this state of a different color (so that the wavelength () is different and the energies sum up to be conserved) ?

Or, does the mechanism of the splitting the single photon necessarily add energy to the system in this case?

Answer 1

Energy conservation during the splitting of a single photon into entangled pairs is achieved through the redistribution of energy into the two photons, potentially resulting in different frequencies for each photon. No additional energy is required for the splitting process; it merely divides the original photon's energy between the two entangled photons.

Step-by-step explanation:

The question of energy conservation in entangled photon pairs involves understanding the phenomenon of photon splitting and conservation laws in quantum mechanics. When a single photon splits into two entangled photons, the total energy of the system remains conserved. The energy of the parent photon is redistributed into the two entangled photons. This may involve the two photons having different frequencies, that is, different colors, so their energies add up to the original photon's energy, following the equation E = (h·c)/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

It is important to note that the splitting of the photon does not necessarily add energy to the system; rather, it involves the redistribution of the photon's energy into two lower-energy photons. This concept is similar to the stimulated emission process described by Einstein, where a photon triggers the emission of another photon with the same energy, resulting in a conservation of energy within the system. The process of splitting the single photon must obey the laws of conservation of energy, and there is no need for additional energy to be added to the system.