Friday, October 26, 2012

The quality of agreement and comparisons

Many authors like to make statements such as "our calculated value of 1.23 for X is in excellent agreement with the experimental value of 2 for X".

In contrast, this week I read the modest statement "the DMFT value of 0.66 is in mediocre agreement with the Brinkman-Rice value of 0.47" in this review [below eqn. (266)].

I think the quality of agreement in such comparisons is in the eye of the beholder. Different people can have quite different standards. Furthermore, the level of agreement one might hope for depends strongly on the context and many other factors. e.g., how many free parameters there are, how difficult it is to calculate or measure the relevant quantity, and how sensitive the calculated quantity is to the level of theory.

Let me illustrate with two statements a hypothetical author might write in the future:

"my new formulation of renormalisation in quantum electrodynamics (QED) leads to value for the g-factor of the electron that agrees with experiment to one part in a thousand"

"my new quantum field theory of gravity leads to a value of the cosmological constant which differs from the observed value by a factor of one hundred."

To the novice, 1. sounds very impressive and 2. sounds lame.
However, paper 1. would be ignored and paper 2. may lead to a Nobel Prize!
Existing versions of renormalisation in QED give values of g that agree with experiment to about 15 significant figures!
Existing formulations of the cosmological constant in quantum field theory give values that differ from experiment by about 100 orders of magnitude!
[Weinberg has a nice looking review on this that I hope to read sometime....]

The solution to this problem?
I think we should simply write: "our calculated value of 1.23 for X can be compared with the experimental value of 2 for X".
Let the reader decide for themselves whether they think the "agreement" is excellent, impressive, surprising, disappointing, mediocre, poor, .....

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