# Fine structure constant meaning

I admit that I have always seen this number as a simple proportionality constant relating other constants and units. But there is a long tradition attributing it all kinds of deep physical and even mystic significance, what do you think?

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bhobba
Mentor
I admit that I have always seen this number as a simple proportionality constant relating other constants and units. But there is a long tradition attributing it all kinds of deep physical and even mystic significance, what do you think?
Its easy to be caught up in this kind of numerological rubbish - Eddington did - but its just that - rubbish.

If i remember correctly Feynman commented on its seductiveness - I will see if I can dig up what he said.

Thanks
Bill

kith
Constants like c, h or e depend on the units i.e. on the definitions of how we measure things. The fine structure constant doesn't because it is dimensionless. The numerical values of c, h and e are historical while the value of the fine structure constant is fundamental to the electromagnetic interaction.

Khashishi
The only thing mystical about the fine structure constant is that we have no theory on why it has the value it does. It seems to be a property of our universe that just is. So people, being imaginary creatures, imagine universes with different values of fine structure constant. It could simply be that we haven't yet discovered the underlying theory for the value. Maybe it really is a random number, with no underlying reason.

The significance of the fine structure constant is that it is a dimensionless measure of the strength of electromagnetism. So it is a very important quantity. Other than particle masses, it is the only free parameter in quantum electrodynamics, our modern theory of electromagnetism. "Fine structure constant" is a bad name that is used only for historical reasons; it obscures the true meaning of the constant, which is that it is a measure of how strongly charges interact with electromagnetic fields.

If we assume the elementary charge to be equal to 1, then the fine structure constant can be viewed as the strength of the electromagnetic interaction.

But we can to it the other way around. We can assume that the "fine structure constant" equals 1 and the charge of the electron has some numeric value. Viewed this way, fine structure constant is related to the charge of electron in natural units.

The significance of the fine structure constant is that it is a dimensionless measure of the strength of electromagnetism. So it is a very important quantity. Other than particle masses, it is the only free parameter in quantum electrodynamics, our modern theory of electromagnetism. "Fine structure constant" is a bad name that is used only for historical reasons; it obscures the true meaning of the constant, which is that it is a measure of how strongly charges interact with electromagnetic fields.
But there are several things here that you might want to clarify wrt its significance. For instance dimensionless quantities are usually considered scale independent, but alpha has an energy dependence. Also if one takes the view that it is really measuring something like the interaction of charges and EM field shouldn't it be dimensionful and define some units. To me it looks like a simple ratio of other dimensionful quantities, but then again in that case it seems it should be independent of scale. As mentioned in the post above mine it might be traded then with other quantity like charge and it would be this latter the significant one instead.