# 137 what could it mean

1. Jan 11, 2005

### The_Thinker

i'm positive all of you have heard about the number 137 and i really don't know where to put this thread because of it... it seems to involve everything so i put it here....

Anyways, i've been thinking since 137 is a number and it's dimensionless maybe its the maximum number of atoms that can possibly be made using them, whether man-made or natural, it is the number of atoms that can be be made period! Think of it doesn't it make perfect sense, the probability that an electron will either absorb or emit light, inversely is also symetrically the number which is kept as the constant of the maximum number of atoms that can be formed...

So what do u guyz think?

2. Jan 11, 2005

### mathman

137 is (approximately) the reciprocal of the fine structure constant. Eddington did some numerology and convinced himself that it was exact. However, current measurements give a value of 137.0373.

3. Jan 11, 2005

### rbj

This could be a little more accurate. The most current measurement of the Fine-structure constant at NIST, http://physics.nist.gov/cgi-bin/cuu/Value?alphinv, is:

$$\alpha = \frac{e^2}{\hbar c 4 \pi \epsilon_0} = 1/137.03599911$$

There is a British mathmatician that had come up with an interesting mathematical formula for the Fine-structure constant at http://www.fine-structure-constant.org/

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

that used to be within the tolerances (until they recently revised $\alpha$, now it is slightly outside of the tolerance, but who know? Someday they may revise the measurement and put $\alpha$ back to the previous value.

But I am suspect of its meaning. I think it's numerology rather than physics. Maybe not.

r b-j

Last edited: Jan 11, 2005
4. Jan 11, 2005

### matt.o

and there are some astrophysicsts who have found $$\alpha$$ may have been different in the early universe!

Last edited: Jan 11, 2005
5. Jan 11, 2005

Staff Emeritus

6. Jan 11, 2005

### matt.o

"may have been". emphasis on that!

7. Jan 11, 2005

### JesseM

This page says that in CGS units, $$\alpha = e^2 / \hbar c$$...since Planck's constant has dimensions of (mass*length^2)/time, and c has dimensions of length/time, does this mean that in these units, charge has dimensions of (mass^1/2*length^3/2)/time? Or is $$\epsilon_0$$ still supposed to be in there, but with a value of 1 in these units?

Last edited: Jan 11, 2005
8. Jan 11, 2005

### rbj

the electrostatic cgs units define the unit charge so that

$$F = \frac{Qq}{r^2}$$

effectively defining the Coulomb Force Constant $1/(4 \pi \epsilon_0)$ to be 1.

Last edited: Jan 11, 2005
9. Jan 12, 2005

### JesseM

So $$\epsilon_0$$ is just a dimensionless number 1, rather than 1 (esu^2*second^2)/(cm^3*gram)?

Last edited: Jan 12, 2005
10. Jan 12, 2005

### JesseM

Yeah, my question was a little confused, I wasn't referring to the Coulomb force constant but rather to the permittivity of free space $$\epsilon_0$$, which in MKS units has dimensions of (coulomb^2*second^2)/(kg*meters^3). But in cgs units this constant doesn't appear in the expression for the dimensionless constant $$\alpha$$, which is why I wondered if it was still there "invisibly" as 1 (emu^2*second^2)/(grams*cm^3), or if the electron charge $$e$$ had units of squareroot(grams*cm^3)/second in this system of units so that $$\alpha$$ would still be dimensionless.

Last edited: Jan 12, 2005
11. Jan 12, 2005

### marcus

yeah I saw that just a moment ago, so I removed my post.
just disregard it
you were talking about epsilon-naught, not the coulomb const

12. Jan 12, 2005

### marcus

BTW my impression is that in those systems of units where
it looks like epsilon-naught does not exist
then it actually doesnt exist (isnt needed) and that it is
not, as you suggested might be a possibility, "invisibly there".

pity RBJ is not online, I think he has more expertise

I have a hard time keeping all the varieties of CGS straight,
Gaussian CGS, electrostatic CGS,....

13. Jan 12, 2005

### marcus

this is just my opinion but I think you are right, that is:

in any system where alpha is defined to be e2/(hbar c)

it is the case that the dimension of electric charge is

sqrt( energy x length)

because the dimension of ( hbar x c) is (energy x length)

and alpha is a dimensionless number

this may seem a bit odd but is not the end of the world

14. Jan 12, 2005

### JesseM

15. Jan 12, 2005

### dextercioby

According to the theory developed by P.A.M. Dirac in 1928,the spin relativistic effects would not allow for an atom to have a nuclear charge larger than 137.However,Dirac's theory has a major fault.It assumes the nucleus to be motionless (that can be fixed),but POINT PARTICLE.Taking into account that for large number of nuclons,the dimensions of the nucleus cannot be neglected anymore,the "crytical" number 137 has been increased to an approximate value of 169.Even if this too would prove itself to be smaller than the actual maximal number,i (and not only me) am sure that the maximal nuclear charge must be finite.

Daniel.

16. Sep 18, 2009

### diazona

Yeah, that's my understanding as well. Saying that the permittivity doesn't appear in the formula at all is like saying that the speed of light doesn't appear in Maxwell's equations or the Lorentz transformations at all. (Which I guess could be a valid viewpoint, if you're the type who measures everything in, say, GeV) Just as the speed of light is a natural unit of speed, a.k.a. a conversion factor between time and length, so the vacuum permittivity is a natural unit of permittivity, a.k.a. a conversion factor between charges and energies.

If you don't omit any constants,
$$\alpha = \frac{1}{4\pi\epsilon_0}\frac{e^2}{\hbar c}$$
This is the most general expression for $\alpha$ in any unit system, as far as I know.

P.S. For what it's worth: I see no reason to believe that the numerical value of $\alpha$ has any special meaning. If it were exactly 1/137, then I'd be curious, but in reality, it just looks like an arbitrary decimal number that simply happens to have a reciprocal which is close to an integer.

Last edited: Sep 18, 2009
17. Sep 18, 2009

### Bob_for_short

Let me remind that alpha is the coupling constant: it couples the mechanical and wave equations. For example, it determines the efficiency of transformation of charge acceleration into electromagnetic waves. In a compound system the physical meaning of dimensionless coupling constant is simple and natural, and it is just the ratio of masses, like m2/Mtot in a compound system (see my IR thread for details).

Last edited: Sep 18, 2009