View Full Version : Fine Structure Constant

2006-Aug-20, 10:58 PM
So, how does the Fine Structure Constant (FSC) fit into all of this?

Where does a=~1/137 fit into the Planck size/length/time regime?

In other words the electron is ~10 ^-15 and Planck size is ~ 10 ^-33, so is there a way to compare this to the FSC a= ~1/137 scale?

2006-Aug-21, 01:02 AM
Are you speaking of the electron width and Planck length in meters? If you believe those quantities don't relate well to the larger dimensionless fine-structure constant, why don't you just employ different, smaller unit measures?

That seems too easy. Perhaps I've misunderstood. What do you mean by "fit into all this"?

2006-Aug-21, 01:56 AM
what 01etc said ... alpha (http://en.wikipedia.org/wiki/Fine_structure_constant) is dimensionless (= it's just a number), and relates to one of the four (three) fundamental forces - electromagnetism (electroweak force).

It's one of the ~20 constants that can't be calculated from first principles, using either GR or QED/QCD.

Does this mean that 'observing' it in more detail may shed light on how the universe works, beyond the Standard Model? Maybe.

But perhaps you're asking something completely different?

2006-Aug-21, 10:09 AM
where e is the elementary charge, HBar=h/ (2?) is the reduced Planck's constant, c is the speed of light in a vacuum, and ε0 is the permittivity of free space.

This looks like it is reducing this to the Planck or reduced Planck arena.

I guess what I am really asking is can the FSC a=1/137 be considered to be equivalent to the Higgs Boson/graviton/neutrino or any other qualifying 'tiniest unit', that could be considered for how the elements, electrons/protons/neutrons get their 'mass'?

Thanks for the responses.

2006-Aug-21, 03:52 PM
The so-called "fine structure constant", alpha = 1/137.03599958, is a combination of electrical charge of the electron, the Planck constant and the speed of light. The fine structure constant describes how electromagnetic forces hold atoms together and the way light interacts with atoms.

The fine structure constant can be seen at many places. For example, the (squared) speed of electrons in the hydrogen atom is roughly 1/137 of the (squared) speed of light. As a consequence of this, the spectrum of the hydrogen atoms have the famous lines with energies 1/n², but if you look at the lines with a better resolution, you find out that they are separated to several sublines; they form the so-called fine structure of the Hydrogen spectrum.
The distance between the main lines of the spectrum is 137 times bigger than the distance between the lines in the fine structure; therefore the name.


2006-Aug-21, 09:09 PM

How do you find that alpha is the square of the ratio of the speed of light to the speed of electrons in hydrogen? I get simply a=c/vH.

2006-Aug-21, 10:07 PM
sry, badly worded by me.
Forget that post, this has a better description.

"An important feature of atomic spectra that arises from relativity is fine structure - so called because what at first appears to be a single line in a spectrum is actually seen to consist of two or more closely spaced lines when analysed with high precision. Fine structure arises because the electron has an intrinsic angular momentum or spin that interacts with the magnetic field that is produced, for example, as the electron orbits the nucleus at relativistic speeds. The strength of this interaction is characterised by the fine-structure constant, a, given by e˛/2e0hc, where e is the charge of the electron, e0 is the permittivity of free space, h is Planck's constant and c is the speed of light. This dimensionless constant has a value of around 1/137. The equations for fine structure contain a factor of a˛, so the spacing between the lines is suppressed by over a factor of 10 000."


The H-spectrum can be dominated by a single series formula.
See “Structure and spectrum of the hydrogen atom. Fine structure of its lines”


For any arbitrary length s, the fine-structure constant is the ratio of two energies: (i) the energy needed to bring two electrons from infinity to a distance of s against their electrostatic repulsion , and (ii) the energy of a single photon .


2006-Aug-30, 12:13 AM

If one would consider the stored energy in the electrons spin, not around the nucleus but on it’s own axis, well...hummmmm

2006-Aug-30, 11:11 AM

If one would consider the stored energy in the electrons spin, not around the nucleus but on it’s own axis, well...hummmmm

An electron doesn't really spin around its own axis (or if it does, then that spin can't change). It is considered a fundamental particle: it has but one internal state. You can't put energy in, and you can't take energy out, except for translational energy with respect to other particles. The usual meaning of "spin" is something a bit different.

I remember using the fine structure constant a lot when learning about EPR spectroscopy (http://en.wikipedia.org/wiki/Electron_paramagnetic_resonance) (no relation to the paradox, but closely related to NMR, which is the technique used when you go to the hospital for an MRI scan), but I can't remember the exact relation. The method is, however, based on electron spin excitation.... I think that the usual value of the fine structure constant is actually calculated from measurements of the electron's gyromagnetic ratio.

2007-Apr-02, 07:37 PM
Using relic radiation from the birth of the universe, astrophysicists at the University of Illinois have proposed a new way of measuring the fine-structure constant in the past, and comparing it with today.
By focusing on the absorption of the cosmic microwave background by atoms of neutral hydrogen, the researchers say, they could measure the fine-structure constant during the “dark ages,” the time after the Big Bang before the first stars formed, when the universe consisted mostly of neutral hydrogen and helium.
The fine-structure constant characterises the strength of the electromagnetic force, which is one of the four fundamental forces in physics. But, the fine-structure constant may not be constant. Recent observations of quasars – starlike objects billions of light-years away – have found a slightly different value for the fine-structure constant.

Read more (http://www.news.uiuc.edu/news/07/0402wandelt.html)