# Why Is the Fine Structure Constant Still a Mystery?

• spidey
In summary: From this, we can say that there exists an upper limit for the velocity of electron. However, this limit is relative to other mediums and will change based on the velocity of light in different media.
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?

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.

spidey said:
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?

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?

can anyone tell me why this constant is still a mystery and what mystery it has?

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.

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...

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).

"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.

dst said:
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).

it's from the NIST reference i made. it says
... The quantity $\alpha$, which is equal to the ratio v1/c where v1 is the velocity of the electron in the first circular Bohr orbit and c is the speed of light in vacuum, appeared naturally in Sommerfeld's analysis and determined the size of the splitting or fine-structure of the hydrogenic spectral lines...

pam said:
"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.

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

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

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

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...

spidey said:
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...
No. Your first equation is only for a special case.

pam said:
No. Your first equation is only for a special case.

if it is for special case then wouldn't alpha value change for velocity of electron greater than c/137...

pam said:
No. Your first equation is only for a special case.

spidey said:
if it is for special case then wouldn't alpha value change for velocity of electron greater than c/137...

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.

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 couldn't understand the mystery here...

## 1. What is the fine structure constant -1/137?

The fine structure constant, also known as the Sommerfeld constant, is a dimensionless quantity that characterizes the strength of the electromagnetic interaction between elementary particles. Its approximate value is 1/137 or 0.0072973525664.

## 2. How was the value of the fine structure constant -1/137 determined?

The value of the fine structure constant was first calculated by the German physicist Arnold Sommerfeld in 1916, based on experimental data collected by physicist Albert Einstein. It was later refined by British physicist Paul Dirac in 1937 and is now considered one of the fundamental constants of nature.

## 3. What is the significance of the fine structure constant -1/137 in physics?

The fine structure constant is a fundamental constant in physics that plays a crucial role in the theory of quantum electrodynamics (QED), which describes the interactions between charged particles and electromagnetic fields. It also appears in other physical theories such as the Standard Model of particle physics.

## 4. Is the value of the fine structure constant -1/137 constant?

According to current scientific understanding, the value of the fine structure constant is considered to be a fundamental constant of nature and thus remains constant throughout the universe and across time. However, some theories suggest that it may vary slightly in extreme conditions such as near black holes or during the early stages of the universe.

## 5. How does the fine structure constant -1/137 relate to the concept of alpha particles?

The fine structure constant can be thought of as the square of the coupling constant, or alpha, which describes the strength of the interaction between charged particles and electromagnetic fields. This relationship is a fundamental part of the theory of QED and helps to explain the behavior of alpha particles in various physical phenomena.

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