Dear Aleksei

Photons are traditionally said to be massless. This is a figure of speech that physicists use to describe something about how a photon's particle-like properties are described by the language of special relativity. But a photon has energy and energy is equivalent to mass. I think this is a complex concept.

As we know, some particles such as photons are never seen at rest in any reference frame. So, there are two kinds of particles in physics;

Some particles like the photon move only with the speed of light c, in all inertial reference frames. Let’s call these kinds of particles the NR particles or Never at Rest condition particles.

Other particles like the electron always move with the speed v

Radiant energy is massless till a quantum mechanical process of absorption hv is performed. Photons are radiant energy and when detected  they become tied energy and  contribute to local curvature and time. This is basically a connection between quantum mechanics and GRT.

Photon has not understood well. Is it a wave or a particle? Photoelectric effect and De Broglie relation are showing its particle's behavior. Generally, we have almost the same understanding and imagination of large objects (at the level of molecules and larger). But in the case of subatomic particles, there is no clearly defined and visualized concept, and there are many uncertainties, especially in the case of photon and graviton. Therefore, any theory offers certain understanding (such as loop and string) of these particles. However, I am using the particles for photon without any imagination of them.

The equivalence between Maxwell equations and Schrödinger equation shows that the Maxwell equations actually describe the quantum properties of electromagnetic radiation at first quantization level. The concept of photon wave function is also useful in studying the quantum properties of radiation in homogenous and inhomogeneous medium in relatively simpler form than the full quantum electrodynamical treatment. There are still open questions in covariant Lagrangian formalism and consequently in the Feynman path integral formalism for photon wave function. (1)

Also, In physics, mass–energy equivalence is the concept that the mass of an object or system is a measure of its energy content.

http://www.m-hikari.com/astp/astp2012/astp5-8-2012/chandrasekarASTP5-8-2012.pdf

Dear Hossein,

Only the quantum Vector Potential can explain some crucial properties of photons, like quanglement and collective phenomena, and the Aharanov Bohm effect ,  one of the "misterious properties" of photons strictly connected to data transfer. It is for sure that the concept of mass like lumped object has to be completely forgot for photons. That photons have not been understood well is a fact. Feynman in 1963 still defended the gravitational potential energy of photons which doesn't exist.

I will copy Hans van Leunen comment about photon.

"In contemporary physics photons have well defined energy and momentum. Both are related to the frequency of the electron. See:

http://en.wikipedia.org/wiki/Photon#Physical_properties.

Planck's formula is well accepted. but it might have only local validity in the current space-progression region. See the remarks above about red-shift."

Please consider that photons have well defined energy and momentum, only.

There is some ambiguities about photon. For example "The basic premise is that because photons have a finite spread they are subject to tidal stresses and that this provides a mechanism for the transfer of momentum from the photon to the mass producing curved space-time. Any transfer of momentum without an equivalent transfer of energy will destroy the concept of the photon as a single elementary particle. It is therefore postulated that the interaction of the photon with curved space-time causes it to lose energy in the form of very low energy secondary photons."

http://www.nature.com/nature/journal/v277/n5698/abs/277633a0.html

What is the lifetime of a photon?

"The photon – the quantum of light or other electromagnetic radiation – is normally considered to have zero mass. But some theories allow photons to have a small rest mass and one consequence of that would be that photons could then decay into lighter elementary particles. So if such a decay were possible, what are the limits on the lifetime of a photon? That is the question asked by a physicist in Germany, who has calculated the lower limit for the lifetime of the photon to be three years in the photon's frame of reference. This translates to about one billion billion (10^18) years in our frame of reference."

http://physicsworld.com/cws/article/news/2013/jul/24/what-is-the-lifetime-of-a-photon

Photons cannot be at rest for non-zero rest mass observers as they are guaranteed to be at the speed of light in all frames of reference. They are the geodesics of the space-time observed by non-zero rest mass observers. In the reference frame of photon space and time coincide and are one and the same thing, so there no concept of speed. A zero rest mass observer in the frame of photon will be observe singularity, which means infinite results for any event occurring in the non-zero mass frame. It also means no localization in space of time (neither concrete nor probabilistic) of anything and it implies no concept of particle behavior and mass.

Null geodesics. Time does not exist for photons.

There's no such concept as a ``relativistic Newton's second law'' and  Newtonian mechanics can't describe massless particles. These are described in relativistic mechanics, which generalizes Newtonian mechanics and where one finds that massless particles don't have a rest frame, i.e. a frame where their velocity is zero, since they always move at the speed of light. This is standard material of an introductory physics course.

Dear Aleksei

Sorry for late to answer. There is a lot unanswered question in physics science, for example see

Kane, G., 2003, the dawn of physics beyond the standard model, Scientific American, vol. 288(6), p.68-75.

Dear Stefano

"relativistic Newton's second law" The relativistic Newton's second law is propounded by Einstein in special relativity.

Photon has no rest-mass, but photon's rest-mass is not zero.