The equation E = mc², made famous by Einstein, equates energy to mass. It tells us that an increase in energy equates to an increase in inertia. It also tells us that this happens at the speed of light, in two dimensions. Hence, the square measure for c.

These are important clues as to the true nature of both energy and inertia.

All energies are equal

First thing to note is that the equation doesn’t distinguish between different types of energy. It doesn’t matter if the energy is kinetic or potential. All energies have the exact same effect on inertia.

An increase in energy results in an increase in inertia regardless of energy type.

Energy is a property of matter

The conclusion to draw from this is that all energies, regardless of type, reside in the particles that make up light and matter.

This makes inertia similar to energy in that it too is a property of matter.

Inertia as time delay

Next thing to note is the relationship to the speed of light, expressed by the constant c.

This is because the speed of light is the speed with which energy is transferred from one object to another. A time delay is experienced for energy transfers to and from inertial matter, and it’s this time delay that we call inertia.

Energy as size

Furthermore, if energy is size at the subatomic, then inertia must increase with an increase in energy.

We get that:

1. Energy and inertia are directly related.
2. Inertia is related to the speed of light.

That’s exactly what E = mc² is telling us.

Pinning down size

Finally, we can pin down what sort of size we’re talking about. It is, as we have suspected all along, the surface area of subatomic particles.

We arrive at this by considering what happens to a subatomic particle hit by an impulse.

Imagine the particle as a ball. When an impulse hits this ball, energy is distributed over it’s surface. The impulse spreads across the surface like a ripple in water. The pressure wave moves at the speed of light, but in two dimensions. Hence, the square measure for c.

Relationship between energy and inertia

We can now construct our energy distribution formula from the model described above.

We have:

1. Energy ‘E’ as surface area
2. Inertia ‘m’ as time delay in energy distribution across a surface area
3. The speed ‘c²‘ with which energy is transferred from one particle to another

Note that:

1. E equates to length ‘l’ squared: l²
2. ‘m’ equates to time delay ‘t’ squared: t²

From this we get:

1. ‘E’ is equivalent to area, with meters squared as units: m²
2. ‘m’ is equivalent to time squared, with seconds squared as units: s²
3. ‘c²‘ has units: m²/s²

When we plug this into the equation E = mc², we get:

• l² = t²c², with units m², s² and m²/s² respectively
• the unit m² equals s² times m²/s²

We get the correct units. We can therefore conclude that E = mc² equates to l² = t²c² at the subatomic.

Conclusion

The principle of mass-energy equivalence, as expressed by the equation E = mc², is fully compatible with the idea that energy is stored as size in subatomic particles.

Furthermore, the size referred to here is surface area. The more surface area a particle has, the more energy it contains.

Subatomic particles: neutrino, photon, electron, proton