Planck Scale Physics in Our Low-Energy World

A big success of quantum electrodynamics was due to the introduction of the renormalization scheme. Briefly speaking, quantum electrodynamics (QED) is in a sense not a fundamental theory, but a fundamental constraint. 

A fundamental theory is such a theory that being formulated in terms of certain laws and certain parameters produces a result in terms of those fundamental parameters. Such a view on QED has failed because of divergences. 

Indeed, in reality everything in physics should be finite, but we know that we possess only some knowledge on asymptotic low-energy behavior of various physical quantities. Very often applying asymptotics beyond their applicability one goes into unphysical behavior of various results and, sometimes, to divergences. To make divergences finite one has to use a complete description, not its asymptotics, with exact laws instead of their asymptotic forms. 

The problem of QED is that we cannot learn anything about the complete description and exact laws, because they are related to physics beyond our reach. Using different models for this physics (i.e. different regularizations) we arrive at different results. 

Power of the renormalization procedure is in the treatment of QED as a fundamental constraint, not as a theory. We can calculate a long-range Coulomb-like interaction (which determines an observable value of the electric charge), we can study electron s kinetic (or complete) energy (which determines an observable value of the electron s mass) and we can measure a number of other properties such as the anomalous magnetic moment of an electron and the Lamb shift in the hydrogen atom. The constraint means that they are correlated and we can calculate the correlation. Learning some of these values from experiment, we can predict the others. 

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