[ExI] Renormalization (was End of time?)
The Avantguardian
avantguardian2020 at yahoo.com
Sat Oct 2 00:37:47 UTC 2010
From: Adrian Tymes <atymes at gmail.com>
>To: scerir <scerir at libero.it>; ExI chat list <extropy-chat at lists.extropy.org>
>Sent: Wed, September 29, 2010 9:15:20 AM
>Subject: Re: [ExI] End of time?
Adrian wrote:
>The author is confusing senses of "infinity". There are (infinitely) many
>grades of
>"infinity" for precisely this reason. Take a, the number of people who play
the
>lottery and win, and b, the number of people who play the lottery and lose.
>Let's
>say this lottery only happens every time there is an exact multiple of 100
>players,
>and that the odds of winning are 1%. Thus, a = 99 * b. Therefore, a > b.
This
>relationship holds true even if b becomes infinite.
I too call bullshit on this paper. First off, I agree with Adrian that they
don't know what they are talking about when it comes to probability. The
frequency at which an event occurs in an infinite number of trials
is practically the *definition* of probability.
Secondly their use of the word "regulate" in the abstract tips you off that they
are using the process of renormalization or regularization to get rid of
infinities in their computations. For those who don't know what that means, it
means using somewhat arbitrary mathematical means to get rid of infinities from
a calculation in order to get a finite answer. This happens all the time in
Quantum Field Theory and String Theory and I think it is bogus. What they did
was they took an infinite model of space-time, artificially drew a border around
a subset around it that they call a "geometric cutoff" so that they could do
math with finite values, and then turned around and claimed that the geometric
cutoff was a *real* physical entitity.
This is no different than the sailors of ancient times thinking that if they
sailed past the borders of their map, they would fall off of the edge of the
world.
I am very suspicious of the idea of regularization that string theorists and
other modern physicists so blithely use. For example, they use theorems from
math that were used to rigorously assign values to the sums of divergent series
and then treat those values as actual sums. What do I mean by this?
Take for example, the series {1+1+1 . . .} for example. The partial sums of this
series are simply the natural numbers. The sum of one term is 1. The sum of two
terms is 2. The sum of three terms is 3 and so on. This is what is meant by
divergent series is that the partial sums increase without bound and approach no
limit. Now there is a method called zeta function regularization that allows one
to patch singularities in the zeta function by analytic continuation by
overlaying it with a different function that is isomorphic to the zeta function
everywhere except for at those singularities where it takes on a finite value.
http://en.wikipedia.org/wiki/1_%2B_1_%2B_1_%2B_1_%2B_%C2%B7_%C2%B7_%C2%B7
Using this technique, one gets a value for the *infinite* series {1+1+1 . . .} =
-1/2. If this doesn't make sense to you, it's because it is not a sum in the
commonly accepted sense. And for physicists to call it a sum and treat it as a
sum, is just sloppy math. If you were count 1, 2, 3, 4 and so on forever you
would *never* reach -1/2.
And I am not alone in my misgivings of the practices of the string theorists.
Regarding this practice of "regularization" or renormalization in physics, Dirac
said,
"Most physicists are very satisfied with the situation. They say: 'Quantum
electrodynamics is a good theory and we do not have to worry about it any more.'
I must say that I am very dissatisfied with the situation, because this
so-called 'good theory' does involve neglecting infinities which appear in its
equations, neglecting them in an arbitrary way. This is just not sensible
mathematics. Sensible mathematics involves neglecting a quantity when it is
small - not neglecting it just because it is infinitely great and you do not
want it!"
And Feynman said:
"The shell game that we play ... is technically called 'renormalization'. But no
matter how clever the word, it is still what I would call a dippy process!
Having to resort to such hocus-pocus has prevented us from proving that the
theory of quantum electrodynamics is mathematically self-consistent. It's
surprising that the theory still hasn't been proved self-consistent one way or
the other by now; I suspect that renormalization is not mathematically
legitimate."
Stuart LaForge
"Old men read the lesson in the setting sun.
Beat the cymbal and sing in this life, or wail away the hours fearing death.
Their choice is their fortune." - I Ching
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