- #1

nightcleaner

(this post was moved from the Using the Force Constant in Equations thread as it seems to be a branching question.)

I just got off work and I usually like to have something to think about while going about my chores. Cleaning is not very demanding, mentally, and radio is just an irritating noise to me these days. So I find that I like listening to what is going on in my head best.

Well, it seems natural to wonder why 1/137 and not some other number. Why one charge square per 137 separations square? (NIST lists alpha= 7.297352568 10E-3, which makes it 1/137.035999 by my calculator).

NIST also has an explanation under the heading "current advances" which gives the dimensional derivation of alpha as charge squared divided by (h-bar c 4 pi permitivity).

[tex]\alpha=\frac{e^2}{4 \hbar c \pi \epsilon_0}[/tex]

NIST goes on to say that alpha is proportional to e^2, so it is the square of an effective charge "screened by vacuum polarization and seen from an infinite distance." Since alpha depends on the energy at which it is measured, NIST says, it is considered an "effective", or running coupling constant.

Wikipedia sent me the long way around the barn, as usual, but it was an interesting tour. I found little directly on the fine structure constant, but then found the hyperfine structure, which I learned is a small perturbation in Bohr energy levels due to proton-electron dipole moment. Hyperfine structure is much smaller than Lamb shift, which Wiki says is the same as fine structure.

Hyperfine structure is very interesting in itself, which gives the 21 cm line of hydrogen in intersteller medium, a useful tool for radio astronomers. It is also used to define the second (a unit of time, as in 60 seconds per minute) as 9,192,631,770 cycles of the hyperfine structure transition of caesium-133 atoms.

The Lamb shift, which Wiki identified with alpha, is a radio frequency transition between 2s 1/2 and 2p 1/2. The energy change was found to be about 1060 MHz of 2s 1/2 above 2p 1/2. I remember a little about s and p levels from chemistry. S is a spherical shell, p is a double-lobed shape, like a dumb bell, they say, although I have never seen a dumb bell shaped just like that. Two tear drops joined at the narrow end, if you have never seen a picture of it. The Wiki author then goes on to explain that this is a one-loop effect in QED, interpreted as the influence of virtual photons.

Whatis.com said alpha is equal to the ratio of the velocity of an electron in a hydrogen atom to the speed of light. This interested me because I once asked my chemistry prof. about the speed of electrons in orbitals and he assured me that it was a meaningless question, since electrons in orbitals are more like charge density clouds than like particles which can have velocities.

Answers.com said "for any 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 of wavelength s/2pi. Then they noted that it is one of the 20-odd "external parameters" that have to be added manually from experimental data to the standard model of particle physics, and that it cannot be predicted by QED. All interesting stuff, but not really helpful in trying to imagine what alpha actually is.

Then there were a couple of numberology approaches, not very meaningful to me, and finally, Eric Weisstein at Wolfram.com noted that there is a "curious approximation" to alpha in the fact that 44pi - cos^-1 (e^-1)=137.036007939.

So out of all this, my best fix was from NIST, where I got the idea that the fine structure constant is due to shielding of the charges by virtual patricles. In this idea, the charge causes virtual particles near it to rotate, which in turn cause slightly more distant virtual charges to rotate, and this creates a sphere of positive virtual charges around the negative electron charge, and these charges then shield the negative charge. In this way local effects radiate outward to become actions at a distance.

In other news, my friend has decided to buy a feeder pig to raise up on restaurant scraps which I am to supply. I plan to call it "8 piG." If I do not grow too fond of it, it will eventually transition to "ate piG." I am sure this is only a coincidence.

Be well,

Richard

I just got off work and I usually like to have something to think about while going about my chores. Cleaning is not very demanding, mentally, and radio is just an irritating noise to me these days. So I find that I like listening to what is going on in my head best.

Well, it seems natural to wonder why 1/137 and not some other number. Why one charge square per 137 separations square? (NIST lists alpha= 7.297352568 10E-3, which makes it 1/137.035999 by my calculator).

NIST also has an explanation under the heading "current advances" which gives the dimensional derivation of alpha as charge squared divided by (h-bar c 4 pi permitivity).

[tex]\alpha=\frac{e^2}{4 \hbar c \pi \epsilon_0}[/tex]

NIST goes on to say that alpha is proportional to e^2, so it is the square of an effective charge "screened by vacuum polarization and seen from an infinite distance." Since alpha depends on the energy at which it is measured, NIST says, it is considered an "effective", or running coupling constant.

Wikipedia sent me the long way around the barn, as usual, but it was an interesting tour. I found little directly on the fine structure constant, but then found the hyperfine structure, which I learned is a small perturbation in Bohr energy levels due to proton-electron dipole moment. Hyperfine structure is much smaller than Lamb shift, which Wiki says is the same as fine structure.

Hyperfine structure is very interesting in itself, which gives the 21 cm line of hydrogen in intersteller medium, a useful tool for radio astronomers. It is also used to define the second (a unit of time, as in 60 seconds per minute) as 9,192,631,770 cycles of the hyperfine structure transition of caesium-133 atoms.

The Lamb shift, which Wiki identified with alpha, is a radio frequency transition between 2s 1/2 and 2p 1/2. The energy change was found to be about 1060 MHz of 2s 1/2 above 2p 1/2. I remember a little about s and p levels from chemistry. S is a spherical shell, p is a double-lobed shape, like a dumb bell, they say, although I have never seen a dumb bell shaped just like that. Two tear drops joined at the narrow end, if you have never seen a picture of it. The Wiki author then goes on to explain that this is a one-loop effect in QED, interpreted as the influence of virtual photons.

Whatis.com said alpha is equal to the ratio of the velocity of an electron in a hydrogen atom to the speed of light. This interested me because I once asked my chemistry prof. about the speed of electrons in orbitals and he assured me that it was a meaningless question, since electrons in orbitals are more like charge density clouds than like particles which can have velocities.

Answers.com said "for any 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 of wavelength s/2pi. Then they noted that it is one of the 20-odd "external parameters" that have to be added manually from experimental data to the standard model of particle physics, and that it cannot be predicted by QED. All interesting stuff, but not really helpful in trying to imagine what alpha actually is.

Then there were a couple of numberology approaches, not very meaningful to me, and finally, Eric Weisstein at Wolfram.com noted that there is a "curious approximation" to alpha in the fact that 44pi - cos^-1 (e^-1)=137.036007939.

So out of all this, my best fix was from NIST, where I got the idea that the fine structure constant is due to shielding of the charges by virtual patricles. In this idea, the charge causes virtual particles near it to rotate, which in turn cause slightly more distant virtual charges to rotate, and this creates a sphere of positive virtual charges around the negative electron charge, and these charges then shield the negative charge. In this way local effects radiate outward to become actions at a distance.

In other news, my friend has decided to buy a feeder pig to raise up on restaurant scraps which I am to supply. I plan to call it "8 piG." If I do not grow too fond of it, it will eventually transition to "ate piG." I am sure this is only a coincidence.

Be well,

Richard

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