IS EINSTEIN'S E=MC^2 CORRECT?

This article was originally published on June 1, 2023.

This is Einstein's famous equation.

E = m c^2

Let's rewrite it in a slightly different form

E = Const^0 m^1 c^2

We have already noticed a very peculiar feature: only three numbers, 0, 1, and 2, appear as powers in that equation. Does the Universe like only small numbers? And only numbers between 0 and 2? Or is this a problem with Einstein's thinking, trying to get things as simple as possible because they are more beautiful that way? There may be an issue.

Let's add units to both sides.

E[kg^1 (m/s)^2] = m[kg^1] c[(m/s)^2]

How might this equation be altered? Suppose that energy isn't an exact quadratic function of the speed of light c. In that case, a Const constant must be added. This constant is non-physical, so let's accept it temporarily. For instance, the Boltzmann and Avogadro constants are non-physical, yet no one objects.

Let's introduce powers of a, b for the Const, y for the mass, and z for the speed of light.

E[kg^1 (m/s)^2] = Const[kg^a (m/s)^b] m^y[kg^y] c^z[(m/s)^z]

For units to work, we have those equations.

kg^1 = kg^a * kg^y

1 = a + y

so a = 1 - y

(m/s)^2 = (m/s)^b * (m/s)^z

2 = b + z

so b = 2 - z

The new equation is now.

E[kg^1 (m/s)^2] = Const[kg^(1 - y) (m/s)^(2 - z)] m^y[kg^y] c^z[(m/s)^z]

Let's assume, as an example, that y=1.02, z=1.97

E[kg^1 (m/s)^2] = Const[(m/s)^0.03 / kg^0.02] m^1.02[kg^1.02] * c^1.97[(m/s)^1.97]

Without units, the modified equation looks like that

E = Const m^1.02 c^1.97

where units are as follows:

E[kg^1 * (m/s)^2] or E[J], Const[(m/s)^0.03 / kg^0.02], m[kg], and c[m/s]. Only mass and the speed of light effects on energy are affected.

In the second example, where y equals 0.97 and z equals 2.04, the influence of mass is diminished, whereas the speed of light plays a more significant role.

E = Const m^0.97 c^2.04

Now we would have E[J], Const[kg^0.03 / (m/s)^0.04], m[kg], and c[m/s].

Could this be true? How do we verify if our ideas are correct?

Deviations from the Einstein equation could show up at relatively high energies. Where to find such examples? Perhaps in some stars or nuclear explosions. People familiar with astronomy can identify potential objects with high energies. Then, pointing a Webb telescope in that direction may surprise us.

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