Quantum Field Theory
Quantum mechanics was born at the turn of the twentieth century when physicists realized that the behavior of the particles of matter--the atoms composing Max Planck's classic black body, for example--did not obey Isaac Newton's classical laws. Field theory is more than half a century older. Michael Faraday introduced the field concept in 1831.
Unwilling to accept the notion of "action-at-a-distance" to describe the electrostatic interaction between two charges, Faraday postulated the existence of the "electric field" filling all space around the particles. Electric charge both creates the field--it is the field's "source"--and reacts to the presence of a field. The electric force felt by a charge is a measure of the field's strength at that point in space.
By 1926 Paul Dirac, Werner Heisenberg, Erwin Schrödinger, and others had formulated non-relativistic quantum mechanics, the quantum analog of classical mechanics. Describing the low-energy interactions between the fundamental particles of matter, the theory worked incredibly well. By the mid-1920s, then, theoretical physics handled well the regimes in which most interactions took place. Classical mechanics provided the correct description for interactions between large, slow-moving bodies. Quantum mechanics (which subsumed, rather than replaced classical mechanics) was employed when bodies were small and slow-moving. Relativistic mechanics--which also subsumed classical mechanics--yielded the correct description for large, fast-moving bodies. But the story could not end there. What if one wished to describe interactions between small, fast-moving bodies (the subject matter of what is today called "high-energy physics")? A new model was needed, one which combined both quantum mechanics and special relativity.
Such a theory is required for consistency as well. Particles interact with one another through the mediation of a field, for example, the electromagnetic field. Non-relativistic quantum mechanics treats these two entities in fundamentally different ways--the particles are "quantized," but the fields are treated classically. Consequently, non-relativistic quantum mechanics violates the principle of relativity. While Maxwell's equations describing the field are Lorentz invariant, the quantum mechanical Schrödinger equation is not.
So, how, exactly, does quantum field theory differ from quantum mechanics? The crucial difference is this: Einstein's mass-energy equivalence implies that energy can be converted into mass (particles) and vice versa. Thus, the number of particles is not constant during a high-energy interaction. (Or, as a physicist would say, particle number is not conserved.)
Consider an example: in 1911 Ernest Rutherford deduced the existence of the atomic nucleus by bombarding a thin gold foil with low-energy alpha particles, and observing how the alphas were "scattered" (deflected from their original paths) by their electromagnetic interaction with the gold atoms. The initial state of the system contains two particles, the incoming alpha and the target gold nucleus, and the final state also contains two particles, the gold nucleus and the scattered alpha. There is insufficient energy involved in the collisions to produce (i.e., be converted into) new particles. Schrödinger's equation, which treats the matter particles quantum-mechanically (they are represented by wavefunctions) and the electromagnetic field classically, provides an adequate description of this low-energy interaction.
But high-energy interactions are much more complicated. Neither the number, nor the type of particles need be conserved. An electron and a positron (the electron's antiparticle) can collide and wind up with, say, an electron and a positron, or with two muons, or with an electron and a positron and two muons. Or it finish with no matter particles at all, only photons (the "quanta" of the electromagnetic field). The number of "final states" is limited only by the initial energy of the system.
In order to deal with this, an inherently democratic theory emerges. In the spirit of Niels Bohr's principle of complimentarity, in quantum field theory all entities--matter and fields--are quantized, and thus posses both wavelike and particlelike properties. Formally, matter "particles" and fields alike are represented by "field operators," called such because they perform the operation of creating or destroying the quanta of the field. The quanta of the electron field are electrons, the quanta of the positron field are positrons, and the quanta of the electromagnetic field are photons. Interactions are represented by products of these operators, which change the initial state of the interacting system into the final state--which may differ in both the number and type of particles present.
The new synthesis was brought to fruition by a number of physicists, most notably the Americans Richard Feynman and Julian Schwinger, and the Japanese Shin-Ichiro Tomanaga, who shared the 1965 Nobel Prize in physics for their work. The prototypical quantum field theory, it is called "quantum electrodynamics." The accuracy of the theory is staggering. For example, the measured value of the electron's magnetic moment (since an electron is charged, and possess "spin," it acts like a tiny bar magnet), and the theoretical value agree to within one part in one hundred billion. A measurement of the distance between New York and San Francisco, performed to this accuracy, would be off by the thickness of a human hair. This extraordinary level of agreement between theory and experiment provides powerful justification for belief in both the correctness of the principle of relativity, and the description of particle interactions in terms of quantum field theories.
This is the complete article, containing 848 words
(approx. 3 pages at 300 words per page).
