# What is the meaning of this "let there be light" joke?

Someone across the restaurant is wearing this shirt, and I certainly don't get it.

## Update

• Those are the equations governing electromagnetism. Aug 29, 2014 at 22:45
• The version I am familiar with was more explicit. It says "And God said", followed by Maxwell's equations, followed by … "and there was light.". A direct play on Genesis 1:3 ("And God said, “Let there be light,” and there was light.") Aug 30, 2014 at 0:52
• You must have had a really good camera to get a very detailed (and creepy) picture of a middle school teacher (don't know how you knew it was a middle school teacher) from across the street. Oh, the wonders of modern technology (and physics, light physics)! Aug 30, 2014 at 2:53
• – user10851
Aug 30, 2014 at 3:55
• God may not have said that, for God would probably not likely to use SI unit. Instead, he would prefer the "God given units". Jun 22, 2015 at 8:16

## 2 Answers

As most people know, "let there be light" is a famous biblical quote, from Genesis. Now, on to the teacher's shirt.

Those equations on his back are Maxwell's equations. "Let there be light" is a joke, because Maxwell's equations describe electromagnetic fields, and light is a form of electromagnetic radiation, so the equations can be used to describe light.

So, as a physicist, one could (jokingly) say that God's "let there be light" refers to him 'inventing' Maxwell's equations.

The Divergence of the Magnetic field (B) in vacuum is $0$. $$\nabla\cdot B=0$$

The Divergence of the Electrical field (E) in vacuum is $0$.$$\nabla\cdot E=0$$ The Curl of the Electric field in Vacuum is equal to minus the rate of change of the magnetic field with time.$$\nabla\times E=-\frac{dB}{dt}$$ The Curl of the Magnetic field in Vacuum is equal to the Permeability of free space times the Permissivity of free space times the rate of change of the electrical field with time. $$\nabla\times B=\mu_0\nu_0\frac{dE}{dt}$$

That established: The curl of the curl of a Vector field is equal to the Gradient of the Divergence of the Field minus the laplacian operator of that field $$\nabla(\nabla\cdot A)-\nabla^2A$$ so we have $$\nabla \times{\nabla\times E}=0-\nabla^2(E)$$

$$\nabla\times -\frac{dB}{dt}=-\frac{d(\nabla\times B)}{dt}$$

$$=- \mu_0\nu_0\frac{d^2(E)}{dt^2}$$ so we have $$\nabla^2{E}= \mu_0\nu_0 \frac{d^2(E)}{dt^2}$$ Which is the form of the wave equation. Specifically, this tells us that it defines a wave with a speed of over the square root of the permeability times the permissivity of free space. Which is the speed of light: This equation is thus the equation of the electrical component for the speed of light: You can do exactly the same math for the magnetic field. So we have the equations for light, predicting the speed of light, that were, incidentally, formulated before the speed of light was measured, and predicted it. thus: Let there be light.