The Elegant Universe - Brian Greene [67]
Quantum Field Theory
Over the course of the 1930s and 1940s theoretical physicists, led by the likes of Paul Dirac, Wolfgang Pauli, Julian Schwinger, Freeman Dyson, Sin-Itiro Tomonaga, and Feynman, to name a few, struggled relentlessly to find a mathematical formalism capable of dealing with this microscopic obstreperousness. They found that Schrödinger's quantum wave equation (mentioned in Chapter 4) was actually only an approximate description of microscopic physics—an approximation that works extremely well when one does not probe too deeply into the microscopic frenzy (either experimentally or theoretically), but that certainly fails if one does.
The central piece of physics that Schrödinger ignored in his formulation of quantum mechanics is special relativity. In fact, Schrödinger did try to incorporate special relativity initially, but the quantum equation to which this led him made predictions that proved to be at odds with experimental measurements of hydrogen. This inspired Schrödinger to adopt the time-honored tradition in physics of divide and conquer: Rather than trying, through one leap, to incorporate all we know about the physical universe in developing a new theory, it is often far more profitable to take many small steps that sequentially include the newest discoveries from the forefront of research. Schrödinger sought and found a mathematical framework encompassing the experimentally discovered wave-particle duality, but he did not, at that early stage of understanding, incorporate special relativity.4
But physicists soon realized that special relativity was central to a proper quantum-mechanical framework. This is because the microscopic frenzy requires that we recognize that energy can manifest itself in a huge variety of ways—a notion that comes from the special relativistic declaration E = mc2. By ignoring special relativity, Schrödinger's approach ignored the malleability of matter, energy, and motion.
Physicists focused their initial pathbreaking efforts to merge special relativity with quantum concepts on the electromagnetic force and its interactions with matter. Through a series of inspirational developments, they created quantum electrodynamics. This is an example of what has come to be called a relativistic quantum field theory, or a quantum field theory, for short. It's quantum because all of the probabilistic and uncertainty issues are incorporated from the outset; it's a field theory because it merges the quantum principles into the previous classical notion of a force field—in this case, Maxwell's electromagnetic field. And finally, it's relativistic because special relativity is also incorporated from the outset. (If you'd like a visual metaphor for a quantum field, you can pretty much invoke the image of a classical field—say, as an ocean of invisible field lines permeating space—but you should refine this image in two ways. First, you should envision a quantum field as composed of particulate ingredients, such as photons for the electromagnetic field. Second, you should imagine energy, in the form of particles' masses and their motion, endlessly shifting back and forth from one quantum field to another as they continually vibrate through space and time.)
Quantum electrodynamics is arguably the most precise theory of natural phenomena ever advanced. An illustration of its precision can be found in the work of Toichiro Kinoshita, a particle physicist from Cornell University, who has, over the last 30 years, painstakingly used quantum electrodynamics to calculate certain detailed properties of electrons. Kinoshita's calculations fill thousands of pages and have