RE: First collisions at the LHC with unprecedented Energy! (Ask a particle physisicist)
September 2, 2015 at 11:27 pm
(This post was last modified: September 2, 2015 at 11:54 pm by Alex K.)
contd.:
Removing the infinities: so, when you use quantum field theory to calculate anything, many quantities will naively come out infinite. Heisenberg already had sleepless nights over this problem, a generation before Feynman, Schwinger, Tomonaga,Dyson and friends. It was therefore thought that field theory is bunk.
The trick to remedy this is called renormalization. The important insight is that the free parameters of the theory are not themselves observable quantities. People always assumed they were finite numerical quantities and got infinite results for observable values such as particle masses and scattering cross sections. The insight now was that the input parameters are not finite numerical values. By sending them to infinity simultaneously in a controlled fashion, the observable results of the calculations become finite. How one can still specify the free parameters of the theory by specifying numbers one can write down on a piece of paper and do calculations with, is a technical trick - one fixes the scheme of what relatove values one adds to each of the parameters in sending them to the limit ->infinity, and can then specify actual numbers, which are however not meaningful in their own right, but only if one specifies in which manner one had to add "infinity" to each of them in the sense of a mathematical limit.
Removing the infinities: so, when you use quantum field theory to calculate anything, many quantities will naively come out infinite. Heisenberg already had sleepless nights over this problem, a generation before Feynman, Schwinger, Tomonaga,Dyson and friends. It was therefore thought that field theory is bunk.
The trick to remedy this is called renormalization. The important insight is that the free parameters of the theory are not themselves observable quantities. People always assumed they were finite numerical quantities and got infinite results for observable values such as particle masses and scattering cross sections. The insight now was that the input parameters are not finite numerical values. By sending them to infinity simultaneously in a controlled fashion, the observable results of the calculations become finite. How one can still specify the free parameters of the theory by specifying numbers one can write down on a piece of paper and do calculations with, is a technical trick - one fixes the scheme of what relatove values one adds to each of the parameters in sending them to the limit ->infinity, and can then specify actual numbers, which are however not meaningful in their own right, but only if one specifies in which manner one had to add "infinity" to each of them in the sense of a mathematical limit.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition
