Our Mathematical Universe: My Quest for the Ultimate Nature of Reality

by Max Tegmark

These electric and magnetic fields can be elegantly unified into what’s known as the electromagnetic field, represented by six numbers at each point in spacetime. As we discussed in Chapter 7, light is simply a wave rippling through the electromagnetic field, so if our physical world is a mathematical structure, then all the light in our Universe (which feels quite physical) corresponds to six numbers at each point in spacetime (which feels quite mathematical). These numbers obey the mathematical relations that we know as Maxwell’s equations, shown in Figure 10.4. There’s a caveat here: what I’ve just described was our understanding of electricity, magnetism and light in classical physics. Quantum mechanics complicates this picture, but without making it any less mathematical, replacing classical electromagnetism with quantum field theory, the bedrock of modern particle physics. In quantum field theory, the wavefunction specifies the degree to which each possible configuration of the electric and magnetic fields is real. This wavefunction is itself a mathematical object, an abstract point in Hilbert space.