# The "computability" of fundamental physical constants

I would like to ask if any of the fundamental physical quantities like the speed of light or plancks constant (all measured according to a common standard of of units) can be classified as computable or non-computable in the sense of of Turing? I don't know if the question makes sense, becuase I have not been training in either theoretical physics or computability theory. But still, the question is relevant in comparing the power of analog vs digital computers, the engineering design of which is the prime concern of EE techies.

• See this Feb 8, 2014 at 16:53
• The the speed of light is integer by definition (en.wikipedia.org/wiki/Speed_of_light). Feb 8, 2014 at 17:02
• 1 kg is the mass of a body of a specified cylindric shape made of a specific platinum/iridium alloy. The Avogadro constant is the number of atoms in 0.012 kg of C$^{12}$. So with a suitably good model of quantum physcs you might compute the Avogadro constant from first principles. But it is a really long way to go (and requires trust in the models being accurate enouhg) Feb 8, 2014 at 17:05

Some of the physical constants are measured, some are defined, and some are computed. The measured ones are just that and have some error attached. The best measured value is a terminating decimal, which is certainly computable. There are (infinitely many) values within the uncertainty range that are not computable. The defined ones again are fixed values with a terminating decimal. For example, the speed of light is defined to be $299 792 458 m/s$ The anomalous magnetic moment of the muon can (in theory) be computed as an infinite sum over all the interaction processes of interest. It can then be compared with experiment. We can imagine computing as many decimals as desired.