3 ms·

You've got the right intuition here. The unitless part is key for several reasons. It means that the number itself is meaningful. In your example, the ratio of

You've got the right intuition here. The unitless part is key for several reasons. It means that the number itself is meaningful. In your example, the ratio of 1.7 long/wide would be the same no matter what units used to make the measurement. (Obviously, the units DO have to actually cancel cm/inches doesn't work). The number for the speed of light (299 792 458 m/s) is a defined property, so that number doesn't mean anything deeply. However, 1/137... itself is directly meaningful. This is why people who work in fundamental constant research use dimensionless ratios. Now for a piece that's more interesting. The fine-structure constant (alpha) is the coupling constant that sets the strength of electromagnetism. This means that its value is the thing that matters in the equation: e^2/\hbar c. Each of the other values is a derived quantity. Further, to speak a bit loosely, only changes in alpha matter -- in the sense that if the speed of light (c) changes, but the other constants (e and \hbar) change in a way that keeps alpha the same, then you wouldn't be able to tell with an experiment that anything has changed. Contrast this situation w/ a change in alpha -- a table-top experiment would be able to detect the change (given that it's large enough, and we have methods of measuring changes on year-time scales that are a few parts in ~10^-18 (Rosenband, 2008)), as it would mean that physics has changed in a fundamental way. http://phys.columbia.edu/~millis/1900/readings/Science-2008-Rosenband-1808-12.pdf http://phys.columbia.edu/~millis/1900/readings/Science-2008-...

raattgift 11y ago
Uh, pardon the stupid question, but isn't it safer to consider the fine structure constant to be the IR fixed point of \alpha (i.e. \alpha(\mu = m_e)^-1 = 137...)? \alpha(\mu = M_Z) is about 128. But m_0(photon), h, and e are the same at both energy scales (we can determine the numerical values experimentally). To the best of our ability to measure, none of them (including, if we ignore the main posting, \alpha_em) varies anywhere in a background fixed by the isometry group of SR (where we find c as the sole free parameter, corresponding to the speed of a particle where m_0(particle) = 0). So I'm having trouble understanding your assertion that "Alpha is the fundamental physical constant: c, e and \hbar are the derived quantities" (in your other comment, but also reflected in your second paragraph above). I think we both totally agree that varying \alpha_em at different points in space or time leads to a mess.

raattgift 11y ago

Uh, pardon the stupid question, but isn't it safer to consider the fine structure constant to be the IR fixed point of \alpha (i.e. \alpha(\mu = m_e)^-1 = 137...)? \alpha(\mu = M_Z) is about 128. But m_0(photon), h, and e are the same at both energy scales (we can determine the numerical values experimentally). To the best of our ability to measure, none of them (including, if we ignore the main posting, \alpha_em) varies anywhere in a background fixed by the isometry group of SR (where we find c as the sole free parameter, corresponding to the speed of a particle where m_0(particle) = 0). So I'm having trouble understanding your assertion that "Alpha is the fundamental physical constant: c, e and \hbar are the derived quantities" (in your other comment, but also reflected in your second paragraph above). I think we both totally agree that varying \alpha_em at different points in space or time leads to a mess.