It once seemed that light had energy but no mass, and matter had mass but no energy, until Einstein found that light had relativistic mass, and matter had a rest energy that a nuclear bomb could release. It then became apparent that mass and energy were somehow related.
Mass was originally defined as weight, that was later refined to be gravitational mass. Newton’s law that mass needed a force to accelerate it also led to the definition of inertial mass. They are different because a weightless object in space still needs a force to move it, so it has inertial mass but not gravitational mass. Momentum is mass times velocity, so a photon with no mass should have no momentum but solar sails move when the sun shines on them, and photons are bent by the sun’s gravity. This meant that a photon with no rest mass gains relativistic mass as it moves, so it has momentum (Note 1).
Light in contrast was originally seen as pure energy, which Planck’s equation related to its frequency. Einstein then did for matter what Planck had done for light, namely define its energy. In 1905, he deduced that the energy of matter is its mass times the speed of light squared, or as he put it: E=mc². This let us build atom bombs but it has never been clear why the energy of matter relates to light at all. If matter is an inert substance, why is its energy based on the speed of light?
If an electron is extreme photons repeatedly running in many channels, the energy of matter is the sum of their energy. Each channel contains a photon at the highest frequency whose energy is given by Planck’s equation. If these photons add to give the electron’s mass, which spreads in two dimensions not one, this predicts Einstein’s equation (Note 2). A processing model predicts E=mc2, which Einstein proved based on how our physical world behaves. It follows that the energy of matter depends on the speed of light because matter is made of extreme light.
Note 1. Relativistic mass is defined by special relativity. Rest mass is mass with no relativistic effects.
Note 2. Let the speed of light c=LP/TP, for Planck length LP and Planck time TP, and a photon’s energy E=h.f, by Planck’s equation. In this model, each electron channel essentially contains an extreme photon at a point with a frequency of 1/TP, so its energy E=h/TP. Now if Planck’s constant (h) is the transfer of one Planck process P over a Planck length in Planck time, h=P.LP/TP. Substituting gives E=P.LP/TP.TP = E=P.c/TP for the energy of one photon. Planck’s relation then also applies to an electron made of photons, except instead of h, the total processing is the electron’s mass me, which transfers over a unit sphere surface in time TP, so the electron’s energy E= me.LP.LP/TP.TP, which is E= me.c2. If all mass arises in the same way, then E= m.c2 in general.