This web page contains an explanation of Keith Dixon-Roche's discovery of the real meaning of Henri Poincaré's formula for the terminal speed of an electron; E=mc²
Poincaré proposed this formula as a limiting speed for an electron, but he had no idea what happened at this teminal speed. Keith Dixon-Roche has discovered that it applies to the creation of the neutron.
The potential energy between a force-centre and its satellite in circular orbits is exactly twice the satellite's kinetic energy:
PE = 2.KE = 2 x ½.m.v² = m.v²
When orbiting at the speed of light (c), this formula becomes:
PE = m.c²
which is the speed at which the magnetic attraction between an electron and its proton is greater than the electron's centrifugal force. The two particles come together and create a neutron.
There is absolutely no reason why matter cannot travel faster the speed of light in free-flight.
Kristian Huygens gave us the relationship between acceleration and velocity; v² = 2.a.R
and Henri Poincaré showed us that E = m.c² ⁽¹⁰⁾, which today is generally believed to represent kinetic relativism
but now we know that gravitational energy is twice kinetic energy in circular orbits (e.g. in atoms): PE = 2.KE = m.v²
If we assume a limiting gravitational energy that will trap light, it is probably equivalent to that defined by Henri Poincaré, i.e. for any specified mass; m.c² = m.2.g.R
where 'g' is the gravitational acceleration at its outer surface (at radius 'R')
Therefore, for any specific gravitational energy, according to: E = m.c²
we should be able to find the associated limiting mass with respect to its ability to emit light:
c² = 2.g/R → g = c² / 2.R
E = m.g.R → m.
R.c² / 2. R → ½.m.c² (kinetic energy at light speed)
i.e. if 2.g.R ≥ c² for a given force centre, light will have insufficient energy to escape its surface.
if g = G.m/R² then 2.G.m/R = c² represents the limiting mass
c² in this famous equation therefore represents a limiting gravitational acceleration that may be used to define the gravitational energy required to trap light, and the formula becomes:
E = m.g.R
where the term 'm.g' refers to the gravitational force on light.
'E' in this formula is not kinetic energy, it is gravitational, i.e. Henri Poincaré's famous formula probably wasn't showing us what has euphemistically become relativism;
between them, Isaac Newton and Henri Poincaré were showing us how to size a black hole!
E = m.c² = m.2.R.g
c² = 2.R.g
g = G.m/R²
c² = 2.R.G.m/R² = 2.G.m/R
R = 2.G.m/c²
If 'm' is the mass of a proton:
R = 2.G.m/c² = 2 x 6.67359232004334E-11 x 1.67262164E-27 ÷ 299792459²
R = 2.48396784934951E-54 m
Which is the Scwarzschild radius of a proton confirming that it cannot trap light; i.e. it is insufficiently dense for its size.
If the above is a correct interpretation of E = m.c², mass does not vary with velocity and therefore, the speed of light is not necessarily a limiting velocity for matter.
You will find further reading on this subject in reference publications(68, 69, & 70)