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!

Gravity is Weak Because of Light Speed

According to the above video, gravity lives outside our universe in a higher dimension or parallel universe. It then leaks into our universe. By the time it gets to us, it has a weak signal. However, using extra dimensions and universes to explain what we don't understand only increases the overall mystery. It also increases the burden of proof of the scientists who postulate such a hypothesis. Surely higher dimensions and parallel universes are more poorly understood than the gravity we can actually observe and measure. For these reasons, they make a poor hypothesis.

Today we are going to explain the weakness of gravity using what we already know. First we define the variables we will be using:

Time for a thought experiment. Imagine a cubic section of our universe. Divide this cube into two halves: A and B. A and B contain a vacuum with a few photons whizzing around with momentum p. A and B each have fairly equal numbers of these photons.

From another part of our universe we take mass m and add it to section B:

At equation 1 above we add section B's momentum and mass energies. It's obvious that A's total energy is less than section B's (see inequality 2 below):

Now, look what happens when we divide both sides by p^2:

Number 3 above is an absurdity. How can light speed (c^2) be less than another speed? According to Einstein, light speed is the maximum speed limit in our universe. Maxwell showed mathematically that light is an electromagnetic wave. The speed of light is a function of the permittivity and permeability of free space. Since these values are constant, light speed is also constant in a vacuum.

To date, no particles have been discovered that can exceed the speed of light. But is light speed really the top speed? The inequality at 3 suggests otherwise. Here's why we currently believe nothing goes faster than light in a vacuum. Below is a Minkowski-ish spacetime diagram.

Velocity vector A is at rest; it is moving through time (t'), so its velocity is zero (see equation 3b). B is moving through both time and space, so its velocity is greater than zero (see 3c). C is moving through space only. It's proper time (t') is zero and its velocity ... are you ready for this? ... is infinite (see 3d).

Of course this infinite speed is from the photon's point of view. We calculate what an observer sees at 3e above. At 3f, we assert that light speed is infinite speed if proper time is used. Can't beat infinity, therefore light speed is the top speed.

Since light speed is the top speed, the inequality at 3 is wrong. Equation 4 below makes better sense:

Notice we simply included a reduction factor of epsilon^2. What can we learn from this? We learn that the full energy of section B does not come into play. It is weakened by the fact that nothing can go faster than light. To restore equilibrium completely, let's multiply the left side by a time-dilation ratio. (To see how this ratio was derived, click here.)

From equation 5 we can derive equation 7 below (Newtonian gravity). Equation 9 reveals the nature of the reduction factor.

Equation 9 tells us that gravity is weak due to time dilation and the ratio of section A momentum to section B momentum. In particular, gravity is weak because momentum p is weak. Why is p so weak? It's the momentum you find in the vacuum of space (with a few photons thrown in). Where there is low vacuum energy there is weak gravity.

The Essence of Time

What exactly is time? Is it just an abstract idea? Or does it exist independently of human imagination and perception? Atomic clocks reveal that the rate of time appears to run slower on the earth's surface than way out in space. Assuming time is a real entity, what is it made of? What is its essence? We start our investigation by defining some variables:

We know that nothing goes faster than light in a vacuum. If we add velocity (v) to velocity (c) we still get the speed of light (c).

Equation 1) above seems absurd. When we combine velocities, we should get a higher velocity than c ... unless ... the rate of time (t') shrinks. Equation 2) below works:

And from equation 2) we can derive the famous Lorentz equation:

When velocity (v) increases, time (t') shrinks, but something else happens that's also strange: mass (m') increases. We can verify this if we start with Einstein's energy equation below.

From equation 6) we can derive the relative mass equation:

Equation 13) confirms that when velocity (v) is increased, mass (m') increases. Now, let's take equation 10) and derive equation 14) below:

Equation 14) shows why increased velocity increases mass. When the velocity of a system increases, velocity (u) decreases. To conserve momentum, mass (m') must increase. We start with momentum (mc) and end up with (m'u). Of course m'u must always equal mc. But what exactly is this velocity u? I call it the velocity of time.

The rate of time is the relative speed (u) of a photon or (c^2-v^2)^.5. If a system is moving at velocity (v) and we assume that system is at rest, then the photons in that system may still appear to be moving at c, but relative to v they have slowed to velocity u. Since photons are bosons, their relative speed (how fast they carry force) will determine how fast or how slow the system evolves. If the system is your watch, your watch will noticeably slow down if it moves at a significant fraction of light speed. This suggests that time is real and not just a concept. After all, the original concept of time was that the rate of time is fixed.

Below is a Feynman diagram where velocity v is zero, so velocity u equals velocity c. At the beginning of time (t), two electrons colide. Next, a photon is emitted, then the electrons fly apart.

In the next diagram imagine that the entire diagram is moving through space at velocity v. If we assume the diagram is at rest, the emitted photon will be relatively slower and the measure of time will also be slower:

The electrons in the above diagram are moving faster, but photons can't increase their speed, so, relative to the electrons, the photon is slower. This seemingly slow moving photon is the time we measure or proportionate to the time we measure. Now, just for fun, what happens if the electrons go faster than light?

Time reverses! Your watch is now running backwards. In the diagram above, the particles fly apart, then comes the photon, and finally, the particles collide.

Before we conclude that time is (or is proportionate to) the speed of photons relative to the other particles in a system, let's look at how gravity impacts time, and take a closer look at light, i.e., electromagnetic waves. Once again we define some variables:

We include the variables for permittivity and permeability. Taken together, they determine the speed of an electromagnetic wave. A photon's relative speed (u) has its own corresponding permittivity and permeability. Free space is a vacuum. That is where light has a velocity of c. If the permittivity of free space, for example, had a lower value, light would go faster. Increasing velocity v causes permittivity and permeability to increase (so does additional mass/energy). As a result, EM waves (light) slow down or are relatively slower. The mathematical proof below provides further insight into the essence of time:

Equations 23) and 24) show that time is the reciprocal of frequency. Equations 24) and 26) define the rate of time (with variable t[sub o] set to 1) in one of two ways: The ratio of the relative speed (u) of a photon to light speed (c); or, the ratio of permittivities and permeabilities. Both ways are equivalent. To put it more simply, time (at the quantum level) is the measure of the rate bosons can carry force between particles. If that process is disrupted by high speeds or increased mass/energy, that process will slow down. Anything that is a function of that process will also slow down--including your watch.

Update: Quantum particle-waves are transverse waves: their oscillations are perpendicular to their propagation direction. The following is a mathematical proof that shows that the Lorentz equations above work for transverse waves.

Equation 37) is the formula used to calculate the velocity of a transverse wave. We were able to derive it from the Lorentz equation for relative mass. This shows that the two are intrinsically connected. Equation 39) predicts what we expect: increased mass (m') reduces the time rate (t').