Why is the maximum speed of the universe the speed of light? Maxwell’s equations explained and visualized. Why is light so fast? What is light made of? Almost all modern technology is based on Maxwell’s equations.
Not only do they describe every electrical and magnetic phenomenon, but hidden within these equations is a fundamental truth about the nature of light, and why it is the ultimate speed of the universe. We are going to visualize the equations with graphics.
Objects have something called a charge. This is a property of matter like mass is a property of matter. If you have a static object with a charge, it will affect only other charges. And if you have a static magnet, it will affect only other magnets. But if you have a moving charge, it will affect a magnet. And if you have a moving magnet, it will affect a charge. That’s what the four equations are telling us.
A charge is the source of an electric field. If I have another charge, you can understand exactly what force it will feel. The first equation is a formula that tells us how electrical charges create electrical fields. It is based on concepts developed by Carl Friedrich Gauss. Permittivity of free space is required in the equation. It is the resistance of free space against the formation of electric fields.
The second equation is called Gauss’s law for magnetism. It says that if you had the same sphere but it was a magnet, you will never find a configuration where the magnetic lines of force always point outward, or always point inwards. In other words, a magnet will always have two poles. There are no magnetic monopoles.
The third equation is called faraday’s law. This law says that if move a magnet, you will create an electric field. This equation tells engineers how to generate electricity from a generator.
The fourth equation is Ampere’s law. It says that if you have moving charge through a wire, or an electrical current, you generate a magnetic field. This requires a constant of nature called mu naught. This is the permeability of free space. This is the ability of free space to allow magnetic lines of force to go through it. Note that there are two terms in this equation, one term tells you the moving electrical charges can create magnetic fields, and the second term tells you that moving electrical fields can also create magnetic fields. This idea of magnetic fields being created from electric fields was Maxwell’s addition to Ampere’s law.
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Both of these constants have to be measured, since they are inherent properties of nature. They are not derived from anything. What does this have to do with light?
If I take an electric charge and put it on a pole, and I just move it up and down, what will this cause? According to ampere’s law, if an electric field moves or changes with time, it would create a magnetic field perpendicular to that.
And because of the changing movement, the magnetic field would also be changing with time. And according to Faraday’s law the moving magnetic field lines would create another new set of electric field lines.
Now, since the same thing is happening to these new electric field lines, that is, they are changing over time, they would in turn create new magnetic field lines. And the new moving magnetic field lines would create yet more electric field lines. You have just created a self propagating wave.
What is the speed of this wave? You find this using advanced multivariable calculus which Maxwell was very good at. He comes up with is 1/V^2 = epsilon naught * Mu naught. Solving you get Velocity = Sq root (1/epsilon naught * Mu naught). So what the equations are saying is the velocity of this wave is inversely proportional the permittivity and permeability of free space. It makes sense that the velocity of any wave would be inversely proportional to the resistance of the substance it is traveling in.
You might ask, well why are mu naught and epsilon naught those exact values? No one knows why. These are just the constants of nature.
Now we take the measured values of these two constants, and do some simple math. The speed of the wave is about 300,000 km per second. Maxwell realized that light must be an electromagnetic wave.
About 40 years later another great scientist by the name of Einstein did his own thought experiments inspired by Maxwell’s equation. And his thought experiment was based on one simple assumption. He asked if the speed of light is an inherent property of space, why would this speed be any different based on the speed of the observer?
And it was from this simple assumption, that he came up with the special theory of relativity in 1905 which changed our ideas about the nature of time.
