[nilak (OP)]

These two are close properties they are both conserved, with energy only having more speed dependence. These concepts were first incorporated into classical newtonian mechanics. Momentum is simply defined as mass times velocity, but it works well when we use it for objects. As we went deeper towards a fundamental level, we found that light is made EM waves the we discovered it can also have momentum. The fact that it had energy was clear, but momentum was thought to be a characteristic of objects, or particles with mass not radio waves or light waves. Light has energy, has momentum, but no rest mass. Rest mass remains another puzzle to solve. Although relativistic mass is not commonly discussed anymore, if light has energy, the mass is almost like the same thing. My hypothesis shows in fact that for particles the same thing happens. They would internally be made of waves with no rest mass with local Poyinting vectors propagating at no less and no more than c.
The problem with classical EM waves is they don't incorporate the momentum. Maxwell’s equations don’t incorporate momemtum. Although energy and momentum are similar, momentum has a unique feature in classical mechanics, it means the object can push other objects. From my hypothesys this is only an effect generated by interferences between waves, and it is like an illusion.
For light we can only deduct momentum relativistically. If we accelerate towards a light beam our velocity will increase relative to the source. We can now consider light having more momentum and more energy. The way we calculate the potential energy stored in the E and B field it doesn’t show that(this sounds like going from QM backwards towards classical). We can either modify the classical wave energy to express the energy or momentum increase generated by relative velocity, which would result in a change of Maxwell’s equations, or we can keep the Maxwell’s equations and modify our energy concepts. However, the later implies that the energy of a photon (according to my concept it works for particles as well) doesn’t increase with velocity, but there is a simple increase in power and frequency.
https://dwgtheory.quora.com/Energy-and-momentum

[PmbPhy]

Although relativistic mass is not commonly discussed anymore, ...

That's a common misconception. Its not only found in many recently published physics texts but its also taught at MIT. For example, please watch this: http://www.newenglandphysics.org/common_misconceptions/Alan_Guth_01.mp4

[nilak (OP)]

Well, I had some discussions with some physicists and many of them recommended to avoid using it as it can be misleading. I know relativistic mass is not an intrinsic property of light just like its energy isn't either. It is frame dependent. My hypothesis is something similar happens to matter. If you confine the light beam into a small region of space (for example in a coated box so that it creates a perfect mirror-that is in principle since perfect mirrors cannot exist)that can be brought at rest in any reference frame, when the box is at rest the light inside still has energy. One could say that there is rest energy/mass for the light inside but we know it is relativistic as well.
In the end the video the professor talks about gravity produced by light. I the fundamental interaction through gravity happens between light waves. There is an experiment made by Tolman, which shows  how pencils of light interact through gravity.

[PmbPhy]

Well, I had some discussions with some physicists and many of them recommended to avoid using it as it can be misleading.

That's only because they haven't thought it through carefully.

[GoC]

Or there is not enough information as to the cause. This could be misleading if you just blindly follow the math results. Math can follow a theory but not prove a theory has the correct understanding. Thus you can be misled.