Energy and momentum of a photon in a medium

In summary, the energy and momentum of a photon in a medium are influenced by the properties of the medium, such as its refractive index. The energy of a photon is given by the equation E = hf, where h is Planck's constant and f is the frequency of the photon. In a medium, the speed of light decreases, which affects the wavelength and momentum of the photon, with momentum expressed as p = E/c, where c is the speed of light in the medium. This results in a modified relationship between energy, momentum, and the medium's characteristics, impacting phenomena like refraction and absorption.
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  • #2
However I have not read the articles, I would say the third statement : neither energy nor momentum depend on medium. Medium is made of atoms or ions in vacuum. There photons mostly travel in vacuum and rarely interact with distributed atoms or ions. We may think of moving in vacuum and interaction with atoms separetely.
 
  • #3
I don’t know for single photons, but this particular dilemma is part of classical EM.

For classical EM it is called the Abraham Minkowski controversy. The controversy is basically just that both Abraham and Minkowski have plausible arguments but Minkowski argued that the momentum of an EM wave increases as it enters a transparent medium while Abraham argued that it decreases.

The classical controversy is resolved by considering the momentum of the medium also. The energy and momentum tensor of the EM wave and the material are each individually incomplete. Only the total tensor is well defined.

For details on the resolution of the classical controversy see Peiffer et al https://arxiv.org/abs/0710.0461

I imagine that the essence of the quantum version of this will be resolved similarly, albeit with a bunch more complicated math.
 
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  • #4
weafq said:
According to this paper: ht
Which is nonsense in a predatory journal.
 

FAQ: Energy and momentum of a photon in a medium

What is the relationship between the energy and momentum of a photon in a medium?

The energy of a photon is given by the equation E = hf, where h is Planck's constant and f is the frequency of the photon. The momentum of a photon is given by p = E/c, where c is the speed of light in a vacuum. In a medium, the speed of light is reduced, leading to a modified relationship where the momentum is p = E/v, with v being the speed of light in the medium. Thus, the energy and momentum are still related, but the effective speed of the photon in the medium must be considered.

How does the speed of light in a medium affect the energy and momentum of a photon?

The speed of light in a medium is slower than in a vacuum, which affects the momentum of the photon. While the energy remains constant (E = hf), the momentum is reduced because it depends on the speed of light in that medium. Specifically, the momentum in a medium is given by p = E/v, where v is the reduced speed of light in the medium. This means that for a given energy, the momentum of the photon will be less in a medium compared to a vacuum.

Can a photon lose energy when it enters a medium?

A photon does not lose energy when it enters a medium; its energy remains constant. However, its speed decreases, and it may undergo scattering or absorption, which can affect its propagation. If the photon is absorbed by the medium, it is converted into other forms of energy (like thermal energy), but this is a different process than simply losing energy while traveling through the medium.

What happens to the momentum of a photon when it is refracted at the boundary of a medium?

When a photon is refracted at the boundary between two media, its speed and direction change, which affects its momentum. The momentum vector changes direction according to Snell's law, which relates the angles of incidence and refraction to the indices of refraction of the two media. Although the magnitude of the momentum changes due to the change in speed, the total momentum must be conserved at the boundary, meaning that the momentum of the photon will be transferred to the medium and any other photons or particles involved.

How does the index of refraction of a medium relate to the energy and momentum of a photon?

The index of refraction (n) of a medium is defined as the ratio of the speed of light in a vacuum to the speed of light in that medium (n = c/v). The index of refraction affects the momentum of the photon, as the momentum is inversely proportional to the speed of light in the medium (p = E/v). As the index of refraction increases, the speed of

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