# Fine structure constant -1/137

1. Mar 9, 2008

### spidey

A lot of scientists say that fine structure constant is still a mystery..one of them was Richard Feynmann...i know fine structure constant is a dimensionless constant and there are many dimensionless constant but why this fine structure constant takes special place?can anyone tell me why this constant is still a mystery and what mystery it has?

2. Mar 9, 2008

### pam

There are not so many dimensionless constants that have no simple math explanation like pi or e. The fsc alpha is the strength of the electromagnetic and weak forces, and is related to the strength of the strong force.
"Still a mystery" is a bit of hyperbole that RF enjoyed, but explaining or understanding its
value 1/137.036... could be the crowning accomplishment of this new century.

3. Mar 9, 2008

### rbj

the NIST site and Wikipedia page answer some of this. the way i like to think of it, from the POV of Planck units, is that $\sqrt{\alpha}$ is the quantitative amount of the Elementary charge as measured in units of the Planck charge. as such, if you consider all charged objects as the same integer multiple of Elementary charges, $\alpha$ represents the relative strength of the E&M interaction, relative to the other forces (like gravity which is normalized to 1 in Planck units). the fact that $\alpha \approx 10^{-2}$ instead of $\approx 10^{-19}$ (which is about the masses of particles in Planck units; the fact that this number is so small is why "gravity is extremely weak") is a matter of curiousity. why is it that, measured in natural units of charge, that the Elementary charge is in the same ballpark? but the masses of particles are not anywhere close to a natural unit of mass?

because we can't, without hand-waving some kinda anthropic principle based argument, have it explained from more fundamental principles. even if you were doing everything in Planck units, $\alpha$ would still be a value that you would have to #define in your C program where you are emulating physical reality from the diff eqs. that are used to describe it.

one guy said that it should be

$$\alpha = \frac{\cos \left(\pi/137 \right)}{137} \ \frac{\tan \left(\pi/(137 \cdot 29) \right)}{\pi/(137 \cdot 29)}$$

but i think his reasoning was only numerological. i don't think that whenever the physics behind the value of the Fine-structure constant are understood, the resulting theoretical value will be the one above. but i dunno, it's worth pondering and speculating about, which is essentially what Feynman was saying.

4. Mar 10, 2008

### spidey

it also says that alpha is the ratio between the velocity of electron and velocity of light...velocity of light is different in different mediums so will this change the value of alpha...Or velocity of light means the velocity of light in vaccuum...

from this shall we say that there exists an upper limit for the velocity of electron....

5. Mar 10, 2008

### dst

There is an upper limit for the velocity of an electron (the speed of light, presumably?). When things are compared to "the velocity of light", usually what is meant is the constant labelled C which is the speed of light in a vacuum.

Don't know where you get this stuff from, an electron can move at any velocity (of course that wouldn't make sense unless you were considering a group/beam of electrons).

6. Mar 10, 2008

### pam

"is the quantitative amount of the Elementary charge as measured in units of the Planck charge."

Since alpha is dimensionless, it equals 1/137 in units of anything.

7. Mar 10, 2008

### rbj

it's from the NIST reference i made. it says

$$\alpha = \frac{e^2}{4 \pi \epsilon_0 \hbar c}$$

$$\sqrt{\alpha} = \frac{e}{\sqrt{4 \pi \epsilon_0 \hbar c}}$$

the denominator is the Planck charge. the ratio $\sqrt{\alpha}$ is of two identically dimensioned quantities, so it's dimensionless and about one 11th.

8. Mar 10, 2008

### spidey

since alpha is also ratio between velocity of electron and light

alpha = v/c=1/137
v/c=1/137
v=c/137

so this should be the upper limit of velocity of electron...am i right...

9. Mar 11, 2008

### pam

No. Your first equation is only for a special case.

10. Mar 11, 2008

### spidey

if it is for special case then wouldnt alpha value change for velocity of electron greater than c/137...

11. Mar 11, 2008

### rbj

no, read what the NIST site says. for the special case of the Bohr hydrogen atom and the electron is in the lowest energy orbit, the fine-structure constant is the ratio of that electron velocity to the speed of light. so, in the Bohr hydrogen atom, the electron's speed is 137 times slower than light.

12. Mar 12, 2008

### spidey

Thanks rbj...

alpha is calculated for velocity of electron in the first orbit of hydrogen atom...so wat is special in this...we can also give so many ratios like this..velocity of electron in second orbit/c and so on and we will get many constants......velocity of anything/ velocity will anything will be dimensionless,so wat is special with this alpha..sorry,i really couldnt understand the mystery here...