Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

If I were to try to find pi using a ruler and a compass, I would first try to find out how many rational line segments of the diameter I could fit around the interior circumference and then continue to refine until I began converging on some number. Before the foundations of Non-Euclidean geometry were made, people would not have even questioned that the euclidean pi had a unique nature.

Why not think of the standard model parameters in the same light? Just simply as ratios that might change with the geometry of space or some something similar?

share|improve this question
add comment

1 Answer

up vote 1 down vote accepted

The number $\pi$ is a mathematical constant that can be calculated. And indeed, as expected from naturalness, it is of order one, so it is clearly not fine-tuned. So we wouldn't be talking about fine-tuning even if it were just a physical parameter and not a mathematical constant.

Fine-tuning only occurs when a theory requires at least 2 parameters with the same units whose numerical value differs by a big ratio. That's not the case of $\pi$. It is the case of the Higgs mass in the Planck units which is $10^{-15}$, and especially cosmological constant in Planck units which is $10^{-123}$. There are many other less extreme examples.

But if your suggestion is that all such constants should finally be as calculable as $\pi$, that's indeed a classic goal of theoretical physics, one that string theory has the capacity to resolve because everything in string theory is calculable. At the current state of progress, however, there exists a very high - but finite or countable - set of possible vacua where the results of the calculations are different. That's why some people defend the anthropic reasoning.

share|improve this answer
    
Fine tuning and fitting are powerful instruments in describing experimental data. They make it possible to describe good data with a bad theory. If you lack free parameters to fit well the data, expand your coupling and masses in power series and consider each term as a free fitting parameter. Doing so one is bound to describe the data. $\pi$ is also possible to fit, if necessary - the theory must describe data so every means is good nowadays. –  Vladimir Kalitvianski May 26 '11 at 8:21
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.