A photon is a particle that can not be explained by any known facts of whats called classical mechanics, in a conventional way.
A photon has no mass but energy and it has speed and it has momentum although it does not have mass. Thats impossible in Classical Mechanics. Because Classical Mechanics associates with every mass; momentum and kinetic and potential energy. All those would be zero if mass were to be zero.
Also the speed of the photon is constant while its energy and momentum are changing. This is unimaginable in classical mechanics. In CM first momentum can’t be defined from mass and speed if mass is zero, then while speed is not changing how is momentum changing? So both variables speed and mass fail to define a momentum for the photon, and not just the failure to have a mass. How then momentum is defined for this particle? Its not defined as long as photon is just a particle. Thats impossible.
Now if speed is not changing how is energy changing? In CM changing a speed would always be a change in energy because KE is proportional to square of speed and so on. By defining lets say KE as p.p/2m we would get an infinite since mass is zero.
So how is energy a function of the speed? one varies while the other is constant.
One of the things about the photon having a constant speed is it is because it does not have any mass. SO no energy is wasted in moving the particle. But how does the energy change then? How can it have a variety of values of energy?
We are stuck if we continue to think from C. Mechanics angles and from “didn’t you say Photon is a particle?”.
Yes I did.
What I did not, is its no more a pure particle in the sense of a Classical Mechanics object. [eg the baseball moving behaves like a pure particle, if baseball moves faster it will have more energy, it does not have a constant speed because energy is spent in continuing to move the mass and eventually all energy is zero so while mass is not zero, speed becomes zero, energy is related to both variables mass and speed, but for photon energy is not at all related to the mass which is always zero and speed which is always one unit of speed of light]
The fact that photon has zero mass always and it moves with a constant speed is called as a important facet of Relativity Theory. But what is not even explained by Relativity as a theory of photon is how its energy value changes ? Relativity can be called as a New Classical Mechanics, also in the sense that it still envisages pure particles as does Classical Mechanics.
All these Classical Problems of photon is understood if one understands that while its a particle in some sense of the Classical Mechanics (again the laws that describe the base ball or the motion of airplanes) it is also a contrastingly different object of a particle. Its a wave at the same time (not necessarily at the same instant of time)
Making a photon as a wave in some of its attributes takes care of all the problem which we discussed above, how can it have zero mass and yet momentum, unchanging speed and yet changing energy.
A wave (also described by laws of classical mechanics, but a different set of laws that describe the particles like base ball) has the attributes of momentum without having a mass, an energy that changes with wavelength and frequency, but whose speed is fixed. So now energy does not depend upon mass (which photon does not have) or speed. At the very same speed and lack of mass its energy keeps on changing if the wavelength and frequency are changed.
Some of the energy of the photon as a particle are constantly fed into changing its wavelength etc (without changing speed) if for example it undergoes collision.
Also one knows now that a wave (the ones in classical mechanics as was known even in Newton’s time) has a momentum because it has wavelength. A wave has energy from its frequency. Its speed is a product of its wavelength and frequency. SO changing wavelength changes energy and frequency and momentum in such a way that the product of frequency and wavelength is always constant. SO the speed is constant while wavelength increases (in case) frequency will decrease and energy will decrease. This all happens for photon while it does not have mass.
The only change that is needed from Newton’s understanding is that energy can’t change in continuous amount. SO only certain values of energy are allowed as are values of all other variables except mass and speed which remain constant at zero and one in suitable units. In other words photon behaves like little packets of energy whose size depends upon frequency or wavelength. Its a particle with wave attributes (or a wave with particle attributes).
All other particles (like electrons and protons) will also be waves as well as they would be particle but no more speed and mass are fixed to be one and zero. They will take arbitrary values. (mass is varying with speed so that mass when the speed is zero is known as rest mass)