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Fine structure constant

Feynman:

“It [the Fine Structure Constant alpha] has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.”

In classical physics, you can calculate the radius of an electron as a spherical object. In quantum mechanics, you can calculate the average radius of the smallest atom. If an electron is entirely converted to electromagnetic radiation, you can calculate the wavelength of that photon. All these numbers are related to each other by that dimensionless number, the Fine Structure Constant. Thus, the classical, quantum and relativistic realms are connected by it.

Where this number comes from is still a mystery, but it is the easiest way a layman can realize that something lies beneath QM and relativity. If its value were different, then chemistry and colors as we know them would not exist. If it were larger, electrons would be bound too tightly to the nucleus; if it were smaller, electrons would easily fly away. The balance is critical for the chemistry in which we exist. This number so far cannot be derived from first principles; it is almost like a parameter in a simulation for it to be productive.

विश्वास-टिप्पनी

Proof of the Gods?

In classical mechanics by taking electron to be a sphere one can compute its radius r_e. If the rest mass of an electron is converted to electromagnetic radiation, the corresponding photon would have the reduced Compton wavelength $\bar{\lambda}_c$. The average radius of the smallest atom (Hydrogen) is given by the Bohr radius _a_₀.

The Fine-structure Constant is a dimensionless number $\alpha \approx \frac{1}{137.036}$

Then the relationship of the classical radius of the electron r_e, the reduced Compton wavelength $\bar{\lambda}_c$, and the Bohr radius of a hydrogen atom _a_₀ is:

$$ a_0 = 137.036 \times \bar{\lambda}_c = (137.036)^2 \times r_e $$