Quanta and Fields: The Biggest Ideas in the Universe

by Sean Carroll

set of discrete solutions. The quantumness of quantum mechanics, including quantum field theory, comes from solving the equations, not from the fundamental nature of the ingredients we use to construct the model.

(7.2)

1 eV ≈ 10‒33 grams 1 eV‒1 ≈ 10‒5 cm 1 eV‒1 ≈ 10‒15 sec (7.3)

(As the physicist John Wheeler once advised, “Never make a calculation until you know the answer.”)

Like most good theorems, you can try to wriggle out of the conclusions by denying some of the assumptions, but the intuition is on the right track.

two kinds of particles making up “matter”: Electrons 250 stable nuclides And we also have two long-range forces that are relevant to macroscopic physics: Electromagnetism Gravity That’s basically it. You and all your friends and loved ones, not to mention your casual acquaintances and sworn enemies, are combinations of these matter particles interacting with each other and these forces according to the rules of quantum field theory.

Equation (A.4) is known as Euler’s formula, after Swiss polymath Leonhard Euler. When we set θ = π, we get eiπ = cos π + i sin π = -1 + 0, which is equivalent to the famous expression (A.5) There’s a good case to be made that 0, 1, i, π, and e are the five most important numbers in all of mathematics. This formula relates them in a stylish way.