User talk:JR137

Dimensionful and dimensionless physical constants

The first two paragraphs in this section are puzzling. Perhaps some improvements could be made.

In the first, it is asserted that the speed of light c is a value that a theory cannot predict, because it is a dimensionful constant. Is it not rather that there is no theory for what the speed of light is? In fact, physical theory can predict the Bohr radius of an atom, which is a dimensionful constant, which suggests that a constant being dimensionful or not is not strictly correlated with whether it can be predicted by a law of physics.

In the second paragraph, the opposite point is made; namely that a dimensionless constant cannot be removed from equations of physics. However, in atomic units, the Schroedinger equation for the hydrogen atom does not contain the dimensionless fine structure constant, which is in disagreement with that point.

The dimensional constants are not arbitrary, as that discussion suggests. The speed of light is a very specific speed and can be measured in any unit system. The number may be different depending on the units in which it is expressed, but the physical quantity is the same. This is true of many dimensional physcal constants. Another example is the Planck constant, which is two times the basic unit of angular momentum in quantum mechanics.

Again, there is no theory for why the Planck constant is what it is. However, there is no doubt that it is a fundamental property of nature.

JR137 (talk) 23:37, 30 April 2009 (UTC)