Why Electromagnetism and Gravity Are Not the Same

According to legend, Einstein was once asked, "How does it feel to be the smartest man alive?" Einstein replied, "I don't know, you'll have to ask Nikola Tesla." Indeed, Tesla was probably the smartest man alive. He even had his own theory of gravity which was brilliantly composed and involved the aether, "ponderable bodies," "mechanical effects," "tubes of force," motion producing the illusion of time, and electromagnetism!

Tesla was also critical of Einstein's theory of gravity: General relativity. He had this to say about the concept of curved spacetime: "If mass curves space then space would have an equal and opposite force and straighten out again!" Remarkably, as brilliant as Tesla was, his theory of gravity never caught on. In this post, we will examine why. Below we define the variables we will use:

Let's take a look at the classical wave equation for both the electric and magnetic fields:

Notice that equation 1 has units of the electric field (E) over distance squared (L^-2). Equation 2 has units of the magnetic field (B) over distance squared. (Also notice the equations equal zero, which implies flat spacetime.) Now, what happens if we totally remove the magnetic and electric fields? In other words, what happens if we remove electromagnetism? We get equation 3:

At equations 4 and 5 we derive something very similar to Einstein's field equations. Notice how equations 3 and 5 have units of L^-2--or units of curvature. When mass is greater than zero, the equation no longer equals zero, i.e., spacetime is curved. We are now in a position to derive Newton's equation of gravitational acceleration:

Check out equation 7 above. It's time to do a shout-out to James Clerk Maxwell who proved that light and electromagnetism are one and the same! Equation 7 shows how the permittivity and permeability of free space equals the reciprocal of light speed squared. Equation 8, of course, is the final solution. The right side is clearly Newton's work. I will also point out that deriving Newton's gravitational acceleration would not have been possible if we didn't eliminate the electric and magnetic fields, i.e., electromagnetism.

Another key difference between electromagnetism and gravity is mass affects the rate of EM acceleration (see equation 11), but mass has no effect on gravitational acceleration (see equation 12).

Electromagnetism is a function of charge, not mass, so a change in mass causes a change in acceleration. Gravity, by contrast, has mass (m) in both the numerator and denominator of equation 12. It cancels itself, so a change in mass does not change the rate of acceleration.

As you can now plainly see, the genius who was fluent in eight languages, who gave the world the gift of alternating current and brought light and power to the world, was simply wrong about gravity. And that other dude with the wild hair was right!