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- Joined
- 6 Mar 2011
- Posts
- 140
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- Scotland, UK
You and I have the same surname!Someone went back in time and killed your apostrophes!
I think without context the statement is a poor one, be it from Hawking or Bob the Builder.I suppose you could say Hawking is an armchair physicist. I was after-all quoting him on infinity. I'll make sure I pass on your comments.
The manner in which renormalisation deals with infinities is a consistent one. It isn't infinity - infinity = 5, that is just pulling numbers out your backside, it first 'controls' the infinity.Have you heard of renormalization? I assume you have as you appear to be much smarter in this subject than I, and that's not sarcasm. But don't flatter yourself too much as I also find your comments a touch patronising.
Just to summarise, when inifinites enter euqations they are a nuisance, and subsequently theorists come up with ways to deal with them. I've never liked the notion since how can an equation be effective when part of it has been born out of frustration to some degree or at best elimintates the annoyance which is infinity.
Many of the infinities in scattering amplitudes come from the fact they include the term Gamma(-D/2) where D is the number of dimensions and Gamma is the Gamma function. If D=4 Gamma(-2) is infinite. However, if you consider D=4+x for small x then you get an expansion of the form Gamma(-D/2) = A/x + B + O(x). In the limit of x->0 the O(x) terms vanish. The A/x term blows up and thus needs to be removed by a counter term. This leaves B, which is the 'prediction'. The decomposition of the expression into the A and B is well defined, you can't fiddle it. It is what is known as a Laurent expansion, a generalisation of Taylor expansions. As such the B prediction is from the theory, not what something you put in by hand.
And I should clarify that the second half of my last post wasn't aimed at you, more a comment in general.