Quote:
Originally Posted by skwinty
The issue I have is that the mathematicians like to get rid of infinities in their equations via renormalisation. This then makes the infinity dissappear.
However, the confusion I have is that some theories/equations are unrenormalisable. So, in some cases you cant get rid of the infinity in the equations.
General Relativity is one of these.
But still the mathematicians apply renormalisation to these and I would like to know why? 
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Mathematicians don't renormalise, theoretical physicists do.
General Relativity as a stand alone theory in fact doesn't require renormalization.
The problem with Quantum field theory as opposed to QM is that in order to predict the interaction between particles or particles with electromagnetic fields etc, theoretical physicists have to rely on Perturbation theory.
http://en.wikipedia.org/wiki/Perturb...m_mechanics%29
In simplest terms this means you allow the basic QM operators to deviate (perturb) under the influence of an external field.
The solutions to these Quantum field equations are expressed as a mathematical series. The series can be infinite for having an infinite number of terms, one or more of the coefficients are infinite, or both. Renormalization occurs if one is able plug back certain physical constants back into mathematical series and reorganize the series so that the infinite terms cancel out and/or truncate the number of terms in the series.
Getting back to GR, from a QM viewpoint, GR cannot be renormalized because as a gravity field theory the mathematical series is infinite. It would require an infinite number of steps to renormalize the series.
Regards
Steven