Duality and World Piece
In the northeast Bronx, I walk through a neighborhood that I once feared going into, this time with a big smile on my face. This is because I can quell the bullies with a new slang word in our dictionary "dual". As I approach the 2-train stop on East 225st , the bullies await me. I say, "Yo, whats the dual?" The bullies embrace me with a pound followed by a high five. I make my train.
In physics one of the most beautiful yet underappreciated ideas is that of duality. A duality allows us to describe a physical phenomenon from two different perspectives; often a flash of creative insight is needed to find both. However the power of the duality goes beyond the apparent redundancy of description. After all, why do I need more than one way to describe the same thing? There are examples in physics where either description of the phenomena fails to capture its entirety. Properties of the system 'beyond' the individual descriptions 'emerge'. I will provide two beautiful examples of how dualities manage to yield 'emergent' properties and, end with a speculation.
Most of us know about the famous wave-particle duality in quantum mechanics, which allowes the photon (and the electron) to attain their magical properties to explain all of the wonders of atomic physics and chemical bonding. The duality states that matter (such as the electron) has both wave-like and particle like properties depending on the context. What's weird is how quantum mechanics manifests the wave-particle duality. According to the traditional Copenhagen interpretation, the wave is a travelling oscillation of possibility that the electron can be realized omewhere as a particle.
Life gets strange in the example of quantum tunneling where the electron can penetrate a barrier only because of its 'wave-like' property. Classical physics tells us that an object will not surmount a barrier (like a hill) if its total kinetic energy is less than the potential energy of the barrier. However quantum mechanics predicts that particles can penetrate (or tunnel) through a barrier even when the kinetic energy is less than the potential energy of the barrier. This effect is used every time you use a flash drive or a CD player!
Most people assume that the conduction of electrons in a metal, is a well understood property of classical physics. But when we look deeper we realize that conduction happens because of the wave-like nature of the electrons. We call the collective electron waves that move through the periodic lattice of a metal a Bloch-wave. Qualitatively, when the electron's Bloch waves constructively interfere we get conduction. Moreover, the wave-particle duality takes us further to predict superconductivity, how it is that electrons (and other spin ½ particles like quarks) can conduct without resistance.
Nowadays in my field of quantum gravity and relativistic cosmology, theorists are exploiting another type of duality to address unresolved questions. This holographic duality was pioneered by Leonard Susskind and Gerhard 't Hooft, and later it found a home in the form of the AdS/CFT duality by Juan Maldacena.
This posits that the phenomenon of quantum gravity is described on one hand by a ordinary gravitational theory (a beefed up version of Einstein's general relativity). On the other hand a dual description of quantum gravity is described by a non-gravitational physics with a space-time of one lower dimension. We are left to wonder in the spirit of the wave-particle duality, what new physics we would glean from this type of duality.
The holographic duality also seems to persist in other approaches of quantum gravity, such as Loop Quantum Gravity, and researchers are still in exploring the true meaning behind holography and potential predictions for experiments.
Dualities seem to allow us to understand and make use of properties in physics that go beyond a singular lense of analysis. Might we wonder if duality can transcend its role in physics and into other fields? The dual of time will tell.
