This web page contains an explanation of Keith Dixon-Roche's discovery of the true meaning of Henri Poincaré's formula for the terminal speed of an electron; E=mc²
Poincaré proposed this formula as a limiting speed for matter, 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 velocity at which the magnetic [field] attraction between an orbiting electron and its proton is greater than the electron's centrifugal force. The two particles come together and create a neutron (Fig 1).
Those that believe E = mc² represents a limiting condition for mass travelling in free-flight at the speed of light, or that mass changes to energy with velocity, have been misled.
This formula applies only to the potential energy in proton-electron pairs, nothing else.
There is no reason why matter cannot travel faster than the speed of light.
Kristian Huygens gave us the relationship between acceleration and velocity; v² = a.R
and Henri Poincaré showed us that E = m.c², which today is generally believed to represent kinetic relativism.
But we now know that it defines the potential energy in circular orbits in proton-electron pairs: PE = -2.KE = m.v²
Therefore, the principal argument is as follows;
KE = ½.m.v²
PE = m.g.R = m.(v²/R).R = m.v² = 2.KE
which applies to all circular orbits.
This means that mass (m) in the formula; E = m.c², does not vary with velocity and therefore, the speed of light is not a limiting velocity for matter.
Moreover, as an electron can only collect [kinetic] energy from (EME) whilst partnered with a proton, the faster it orbits, the harder it is to extract. And at the speed of light it will unite with its proton partner to become a neutron. So free-flying electrons cannot possibly travel at light speed (nor anything close); there are no such things as photons.
Actually, Isaac Newton provided us with the mathematical proof of the above 300 years ago.
If we assume a limiting gravitational energy that will trap 'light', it must be equivalent to that defined by Henri Poincaré, i.e. for any specified mass; m.c² = m.g.R
where 'g' is the gravitational acceleration at its outer surface (at radius 'R').
Therefore, Poincaré's formula should enable us to find the limiting mass (of any particular density) to radiate light:
c² = g/R → g = c² / R
E = m.g.R → m.
R.c² / R → m.c² (potential energy at light speed)
i.e. if g.R ≥ c² for a given force centre, light will have insufficient energy to escape its surface.
If g = G.m/R² then G.m/R = c² represents the limiting mass
E = m.c² = m.g.R
c² = R.g
g = G.m/R²
c² = R.G.m/R² = G.m/R
R = G.m/c²
If 'm' is the mass of a proton:
R = G.m/c² = 6.67359232004334E-11 x 1.67262164E-27 ÷ 299792459²
R = 1.24198392467475E-54 m
which is the Schwarzschild radius of a proton confirming that it cannot trap light through gravity; i.e. it is insufficiently dense for its size.
More importantly though, when divided by the coupling ratio, this becomes the neutronic radius; when the electron actually achieves m.c² (Fig 1)
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 wasn't showing us what has euphemistically become relativism;
between them, Isaac Newton and Henri Poincaré were showing us how to size a [fictitious] black hole!
It is important to note, however, that Schwarzschild radius is fictitious as it is based upon light being an electron travelling at the speed of light, which is incorrect; light is electro-magnetic energy.
You will find further reading on this subject in reference publications(68, 69, & 70)