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Feb20-12, 09:32 PM
P: 381
Quote Quote by bhobba View Post
Unfortunately the jig is up on this one - you need some math. Here is the simplest explanation I know:

There is a trick in applied math called perturbation theory. The idea is you expand your solutions in a power series about a parameter that is small and you can calculate your solution term by term getting better accuracy with each term. The issue is the coupling constant is thought to be small so you expand about it. The first term is fine. You then calculate the second term - oh oh - its infinite - bummer. Whats wrong? It turns out the coupling constant in fact is not small - but rather is itself infinite so its a really bad choice. Ok how to get around it. What you do about it is what is called regularize the equations so the equations are of the form of a limit depending on a parameter called the regulator. You then choose a different parameter to expand about called the renormalized parameter and you fix its value by saying its the value you would get from measurement so you know its finite when you take the limit. If you do that you immediately see the original problem - the coupling constant secretly depends on the regulator so when you take the limit it blows up to infinity. The infinity minus infinity thing is really historical before they worked out exactly what was going on and resolved by what is known as the effective field theory approach.

Thanks. I kinda got the concept now. Anyway. In a power series, [itex]y= y_0+ \epsilon y_1+ \epsilon^2 y_2+ \cdot\cdot\cdot [/itex], is "[itex]\epsilon[/itex]" equivalent to the coupling constant which must be very small like 1/137 and present in each series (although I know it is in more complex form)?