As it has been already derived and presented (i.e. in the posts The gem (1), and The gem (5)),

for a single photon we have

This equation universally defines, determinates the state of each and every photon

( For some given energy, photon’s EM-oscilation-period has to be such that their product is .

Or, for some given EM-oscillation-period, photon’s energy has to be such that their product is  ).

The differential of this equation (the application of infinitesimal calculus on this equation) gives the law of change of that state (A photon can, and does change it’s state, i.e. Compton experiment, Pound-Rebka experiment):

, ,  can only have positive values – they are intrinsically positive. Follows that one, and only one of the infinitesimal differentials (infinitesimal changes) in each of the ratios is negative, that is,

, and 

To highlight that, we will write:

Of these three equations, the last two represent the force.
These two equations represent the primary (primordial, elementary) derivation of force
Physically most fundamental place of appearance of force.
Physically most fundamental way of occurrence of force.
The most fundamental theoretical way of introduction of the force.

The middle equation can be written as:

This equation represents the primary (primordial) definition and derivation of that what is generally known as momentum:
,  

The momentum is the fundamental (experimentally proven) property of photon.

So, this derivation (introduction) of force and of momentum,the fundamental derivation, 
          the derivation from the change of the state of the most fundamental physical entity,
          so, we can say, the derivation from the change of the fundamental state
is the deepest possible explanation, the deepest possible reason why the force can be presented either as the change of momentum  over time (in time), or as the change of energy  over length (along length)

The photon’s momentum is

A photon exchanges its momentum with inertial-mass-entities while interacting with them.

Before and after interaction, i.e.with an electron (i.e. in Compton’s experiment), the velocity of a photon is the same.

Since we have that

,

then that what is changing during the interaction has to be, and is the photon’s non-inertial mass . Actually, that what does (ex)change is the photon’s energy, and therefore, the  (the measure of coupling of that energy with spacetime) also changes.

Wave-particle duality of a photon

The inner EM-details of a photon are unknown – there are a few modeling attempts, model-propositions, but the only definite statements we can make about the wave property of a single photon are:
A photon is an elementary EM oscillation which propagates linearly through space in time.
The photon’s inherent wave-property arises from these oscillations.

While propagating through spacetime whose  and  are constant, the energy, the momentum, the velocity, the length, and the oscillation period of a photon do not change, and that should be considered as the photon’s form stability, that is, these are the primary attributes of the photon’s corpuscularity – a photon is elementary particle.

In other words, a photon is particle because it has all of the mechanical properties:

-       it occupies a (tiny) piece of space,

-       it has velocity,

-       it has energy (which is at the same time its total energy, its EM-energy, and its kinetic energy),

-       it has momentum,

-       it interacts with other entities (exchanges the momentum, i.e. with electron, or with some material surface),

-       a photon has the mass-property. The mass of a photon represents the amount of interaction, the amount of coupling, of the linearly propagating photon-energy with the lengthwise inductance and the lengthwise capacitance of the spacetime occupied with that energy.

The differences between photon’s mass and the mass of inertial-mass-particles are:

(a) the photon’s mass is variable: it changes during interaction with other particles, and

(b) the mass of a photon does not have the property of inertia, and it does not have inertia because its mass is variable.

Since a photon is an elementary manifestation of existence (let us say so: an existence-embryo), it can be described as follows: photon is proto-particle (or, embryo-particle), which has proto-mass (embryo-mass), and at the same time, it is also the proto-wave (embryo-wave).

In the next post, we will see what essentially is that what we call matter, and why it does have inertia and charge.