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apeiron

Gold Member

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http://en.wikipedia.org/wiki/Physical_constant

Which is the more fundamental and why? And exactly what is the meaning of their difference?

I have my own take of course. My feeling is that a constant is always a measurement of an equilibrium resulting from two processes or actions "in balance". In some sense, it is where a dynamic system settles.

All the constants seem to have this basic duality. So c is a dimensionful constant that relates distance and time. G is a dimensional constant that relates distance and mass.

Dimensionless constants also seem to be constructed from other things in interaction.

Wiki says: "Such a number is typically defined as a product or ratio of quantities that have units individually, but cancel out in the combination."

http://en.wikipedia.org/wiki/Dimensionless

So the essential difference between the two classes of constants would seem to be that the dimensionful are the result of asymmetries - you need measurements of two orthogonal axes of description like distance and time - while the dimensionless are the result of what appear to be symmetries. Measurements are made in the one coin (even if more than one axes is required) and so can be canceled out.

So I think this is an interesting difference. One requires pairs of measurements that remain orthogonal and cannot be reduced further, the other requires pairs which do allow reduction to a naked number.

Is this the right way to look at it and what does it mean?

The fine structure constant alpha is a complicated and key example of a dimensionless constant, which may in fact create problems for my simple analysis.

http://en.wikipedia.org/wiki/Fine_structure_constant

And there may be other good challenges lurking in the considerable list of dimensionless constants given by Wiki.

http://en.wikipedia.org/wiki/Dimensionless