Photons in free space are massless. In the photoelectric effect (in a conductor) the photon behaves like a particle...but is the mass of that particle? If so how does it depend on the refractive index and the incident wave? Is there any order of magnitudes?
No, the interaction of light with matter is described usually with a linear term in the dispertion law. For vacuum it is \omega = c k, where c is the speed of light, k is the wave number. In medium it is \omega = c k / n, where n is the refractive index. So, the refractive index affects the speed of light propagation in the medium.
For a particle with mass the dispertion law is \omega = \hbar k^2 / 2 m. Square is smaller than linear for a small argument. Therefore, to have the mass term leading one has to put the coefficient at linear part to zero. It would mean stopping light altogether, to have the infinitely large refractive index. This does not happen usually.
For a medium with spatial dispertion the light is coupled with other excitations, such as excitons. The resulting excitations can have mass, but they are no longer called photons. They are called polaritons. And the mass comes from excitons.
This question can be answered better in the case of a superconductor where one observes the phenomenon of Meissner effect in which the magnetic field dies out over a length scale which is called the penetration depth. This short range nature of the magnetic field implies that the mediating gauge particle for the interaction which is a photon in this case is massive. This is also called HIgg's mechanism through which the photon acquires the mass . In this case, a photon acquires a longitudinal mode in addition to its usual transverse character.
To answer this question, one may asked another, dose photon really exist?
In publishing his photoelectric Effects in 1905, Einstein used quanta (photon) as justification to knock and expel electron from the atom; the re-introduction of a particle in electromagnetic radiation (EM-R) after Maxwell’ unified electric-magnetism and the generation of EM-R by Hertz, was greatly opposed by his contemporary scientists, but after Compton interpretation of the Compton Effect, most scientists accepted the wave particle duality, and photon was introduced as massless particle (photon was coined in 1926 by both Frithiof Wolfers and the chemist Gilbert N. Lewis https://en.wikipedia.org/wiki/Photon).
But before his death, Einstein mentioned in more than three occasions his failure to understand what photon is (Developing Ideas about Photons: (since the First Paper about Photoelectric Effect by Einstein in 1905).. AAAPPS Bulletin).
Historically, radiation energy was only realized to embedded EM-R when Planck presented his formula (E=hv) in 1900, if that formula was not discovered, we could have been in similar speculations mode.
Hence came the importance of our formula (24) in “The Photoelectric Effects-Radiation Based With Atomic Model,” at: http://fundamentaljournals.org/ijfps/downloads/82_IJFPS_March_2015_18_31.pdf
The formula showed, the Magnetic Radiation Force (F_mR) embedded in EM-R similar in nature to the Planck’ energy.
If the equation is true, this means photon is just an imaginary particle, if so, this automatically answered the above question, and that there is no photon in insulator or a semiconductor, which raise many questions; of course these could only be speculation if someone managed to dispute or discredit Eq. (24), in the above paper, or physics as been know for the past century could be revolutionized.
No, the interaction of light with matter is described usually with a linear term in the dispertion law. For vacuum it is \omega = c k, where c is the speed of light, k is the wave number. In medium it is \omega = c k / n, where n is the refractive index. So, the refractive index affects the speed of light propagation in the medium.
For a particle with mass the dispertion law is \omega = \hbar k^2 / 2 m. Square is smaller than linear for a small argument. Therefore, to have the mass term leading one has to put the coefficient at linear part to zero. It would mean stopping light altogether, to have the infinitely large refractive index. This does not happen usually.
For a medium with spatial dispertion the light is coupled with other excitations, such as excitons. The resulting excitations can have mass, but they are no longer called photons. They are called polaritons. And the mass comes from excitons.
To answer this question, one may asked another, dose photon really exist? it is really good quation. The answer we will get from people who are dealing with non- tech engineers or super or advanced resuluation microscopic view.
People say light is dual in nature " Iam sorry for this". But I agree with light is a discrete packets of energy.
"No, the interaction of light with matter is described usually with a linear term in the dispertion law": all the system is non-linear in nature.
Dr. Arbab I. Arbab
I published a paper in which I discovered Compton allegation of quantum (photon) momentum was untrue, this is in: “Compton was Greatly Mistaken Using the Quantum”
http://iosrjournals.org/iosr-jap/papers/Vol10-issue1/Version-1/E1001013040.pdf
If the paper is correct, this could represents the last blow to photon.
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