# QED electron radius

1. Mar 19, 2009

### Orion1

Penning trap upper limit for the electron particle radius:
$$r_e \leq 10^{-22} \; \text{m}$$

QED Compton wavelength electron radius:
$$\boxed{r_e = \alpha_e \overline{\lambda}_c}$$

QED Compton electron radius:
$$\boxed{r_e = \frac{\hbar \alpha_e}{m_e c}}$$

QED electron fine structure constant:
$$\alpha_e = \frac{r_e}{\overline{\lambda}}_c = \frac{m_e c r_e}{\hbar}$$

$$\boxed{\alpha_e = \frac{m_e c r_e}{\hbar}}$$

Weak nuclear fine structure constant:
$$\alpha_w = \sqrt{ \frac{T_{\Delta}}{T_{\Sigma}}} = 2.738 \cdot 10^{-7}$$
$$T$$ - Delta and Sigma particle lifetimes

$$\boxed{\alpha_e = 2.589 \cdot 10^{-10}}$$
$$\boxed{\alpha_w = 2.738 \cdot 10^{-7}}$$

The QED electron fine structure constant magnitude corresponds with the weak nuclear fine structure constant.

How is $$\alpha_w$$ measured via weak $$\beta$$ decay?

Are these equations correct?

Reference:
http://en.wikipedia.org/wiki/Electron#Fundamental_properties"
http://en.wikipedia.org/wiki/Weak_nuclear_force" [Broken]
http://hyperphysics.phy-astr.gsu.edu/HBASE/forces/couple.html#c4"
http://hyperphysics.phy-astr.gsu.edu/HBASE/particles/weastr.html#c1"

Last edited by a moderator: May 4, 2017
2. Mar 19, 2009

### malawi_glenn

what do you want?

3. Mar 19, 2009

Staff Emeritus
No, it's not. It's $\alpha/\sin^2\theta_w$.

No, it's not. That doesn't even make any sense, as QED doesn't know anything about the weak nuclear force.

4. Mar 19, 2009

### Orion1

Vanadium, that is an element, not an equation.

Is this the equation that you attempted to define?

Weak nuclear fine structure constant:
$$\alpha_w = \frac{\alpha}{\sin^2 \theta_w}$$
$$\theta_w$$ - Weinberg angle (weak mixing angle)

Please state the numerical value for that solution and cite a reference.

Have you examined my references in post #1?

Why is the university level hyperphysics weak nuclear fine structure constant equation incorrect?

Reference:
http://en.wikipedia.org/wiki/Weinberg_angle" [Broken]

Last edited by a moderator: May 4, 2017
5. Mar 19, 2009

### malawi_glenn

Look in mandl's textbook in Quantum Field theory for instance. Or any book that contains the gauge theory of the electroweak unification.

Also, what is the purpose of your original post? Are you asking something?

6. Mar 19, 2009

### Orion1

Have you examined my references in post #1?

Are my equations listed in post #1 correct?

Anyone have mandl's textbook in Quantum Field Theory?

Last edited: Mar 19, 2009
7. Mar 19, 2009

### malawi_glenn

as Vanadium pointed out, no.

The QED fine structure constant is 1/137

why are you doing all this?

A good, easy, reference on this, I consider particle physics by Martin

And yes, Manls textbook on QFT is quite common to have... your Library should definitely have one copy. Otherwise, there should be millions of tutorials on www, try search for "Antonio Pich" on ArXiV

Your references in post 1 is wikipedia and hyperphysics, what should I say?... they are not rigour

8. Mar 19, 2009

### Orion1

Vanadium only stated one equation as incorrect. You are now stating all the equations are incorrect? Including the university level hyperphysics equations?

Negative, that value for $$\alpha$$ is not 'rigorous'.

malawi_glenn, you are unable to state a numerical value for Mandl and Martin's $$\alpha_w$$.

rig·or·ous:
. precise
. severely accurate

malawi_glenn, based upon the 'incorrect' equations in post #1, what is the numerical value for the electron radius if the QED fine structure constant for electromagnetism is used?

And why exactly do all these equations fail dimensional examination?

Last edited: Mar 19, 2009
9. Mar 19, 2009

### malawi_glenn

why would anyone use "electron radius" since it is not a 'real' concept, just a unit?

ok, the fine structure constant is 1/137.03599907 which is a numerical value of 2.39934 e-4

If you want to define a constant which has the units of length by introducing $$r_e = \alpha \lambda_r$$ you are free to do it, it is just a unit, nothing 'physical'

The relation between 'the classical electron radius' and the electron comptonwavelngth is: $$r_e{\text{ }}_{class} = {\alpha \lambda_e \over 2\pi} = \alpha^2 a_0$$

where a_0 is the bohr radius.

The weak 'fine structure' constant is $\alpha _W \approx 0.58\alpha$ (martin)

in QED, the electron is a point-particle, so don't call it "QED electron radius"..

Last edited: Mar 19, 2009
10. Mar 19, 2009

### Orion1

And why exactly do all these equations fail dimensional examination?

The Penning trap experiment that determined the electron radius upper limit considers the electron as a QED point-particle.

malawi_glenn, then by your own supposition:
$$\alpha_w = \frac{\alpha}{\sin^2 \theta_w} = 0.58 \cdot \alpha = 4.232 \cdot 10^{-3}$$

A rigorously determined value: (Martin)
$$\alpha_w = 4.232 \cdot 10^{-3}$$

Is this equation correct?

malawi_glenn, based upon the 'incorrect' equations in post #1 and post #9, what is the numerical value for the electron radius if the QED fine structure constant for electromagnetism is used?

Reference:
http://en.wikipedia.org/wiki/Penning_trap" [Broken]

Last edited by a moderator: May 4, 2017
11. Mar 19, 2009

### malawi_glenn

because physics is more advanced then this...

e.g. the bohr radius is just a unit, it is not an orbital radius of the electron in hydrogen (as we know, the radial distance in hydrogen is a probabilistic quantity)

the number 1/137 is more rigour than your $$\boxed{\alpha_e = 2.589 \cdot 10^{-10}}$$ ... rigour in that sense that it is close to the experimental measured value.

I mean, what is the physical (first principle reason) for someone to suggest that the electron radius is alpha time electron Compton wavelength? What is the underlying idea?

12. Mar 19, 2009

### Orion1

malawi_glenn, based upon the 'incorrect' equations in post #1 and post #9, what is the numerical value for the electron radius if the QED fine structure constant for electromagnetism is used?

And why exactly do all these equations fail dimensional examination?

Last edited: Mar 19, 2009
13. Mar 19, 2009

### malawi_glenn

you don't have a calculator or what?

and "what" electron radius? There are many kinds of electron radii units, you mean your suggestion $$\boxed{r_e = \alpha_e \overline{\lambda}_c}$$? Which you call "QED compton wavelenght radius"?

14. Mar 19, 2009

### Orion1

$$\boxed{r_e = \alpha_e \overline{\lambda}_c}$$

Affirmative.

malawi_glenn, you still have not stated why exactly do all these equations fail dimensional examination?

Negative, that value for $$\alpha$$ is numerology and not 'rigorous' at all.

Negative, that numerical value is incorrect, and certainly not even close to rigorous.

malawi_glenn, what are the physical (first principle reasons) for these equations?

$$r_e =\frac{\alpha \lambda_e}{2 \pi}$$

Rigorous classical electron radius:
$$r_e = \frac{1}{4 \pi \epsilon_0} \frac{e^2}{m_e c^2} = 2.8179402894(58) \cdot 10^{-15} \; \text{m}$$

Negative, the numerical value for the classical electron radius from Wikipedia is excellent, they are both extremely rigorous.

Negative, I do not believe that I am the one that requires a calculator at the moment.

Reference:

Last edited by a moderator: May 4, 2017
15. Mar 19, 2009

### malawi_glenn

roger copral

16. Mar 19, 2009

Staff Emeritus
What in blazes are you talking about?

17. Mar 19, 2009

### malawi_glenn

Only God knows... he usally does this kind of approach =/

1/137 is not rigour, it is just "numerology" LOL

18. Mar 20, 2009

### Orion1

malawi_glenn's numerical value for the electromagnetic fine structure constant is incorrect.

malawi_glenn, you still have not stated a correct numerical value for the electromagnetic fine structure constant.

Vanadium_50, why is the university level hyperphysics weak nuclear fine structure constant equation incorrect?

Vanadium_50, and why exactly do all these equations fail dimensional examination?

Vanadium_50, is the equation and numerical values correct in post #10?

Reference:
https://www.physicsforums.com/showpost.php?p=2123562&postcount=10"

Last edited by a moderator: Apr 24, 2017
19. Mar 20, 2009

### malawi_glenn

orion, in post #9 I gave you a better (closer to experimental) value of alpha (1/137 is a VERY good number for alpha, orion you are a pain in our *** with your style..

the figure 2.39934 e-4 is of course wrong, i made that on purpose LOL, why can't you just take 1/137.03599907 in your own calculator??

This is an open forum, I can answer to anything I want to.

Why do you want to calculate all this crap anyway?

The value hyperphysics gives you for the weak finestructure is just an approximation, the hadrons are composite objects etc, you have to go to elementary particle level to examine the couplings of interactions. If you want the latest values, go to particle data group, not wikipedia or hyperphysics.

You are the one who proposed that a unit called "QED electron radius" should be invented, you have to motivate "why". I am not the guy who should say on what first principles it relies on.

The classical electron radius is something which you evaluate from classical electrodynamics, when you evaluate Thomson scattering etc. It should be done in great detail in e.g. Jackson.

I now invent a thing called "Glenn electron radius"

$$r_e^{\text{Glenn}} = \alpha_e^3 \frac{1}{4\pi\epsilon_0}\frac{e^2}{m_e c^2}$$

And what does it mean? I have no idea, it is just a unit.

You see my point why all your 'effort' is pointless?

20. Mar 20, 2009

### Orion1

Negative, that equation is dimensionally incorrect.

An accurately measured approximation is not a failure in dimensional examination.

malawi_glenn, instead of deliberately introducing known unbalanced and non-formulated dimensionally incorrect equations on this forum without any referencing at all, why not state exactly why do all these equations fail dimensional examination?

malawi_glenn, you have not stated what 'first principle' the classical electron radius is based upon.

$$r_e = \frac{1}{4 \pi \epsilon_0} \frac{e^2}{m_e c^2}$$

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

$$r_e = \frac{1}{4 \pi \epsilon_0} \frac{e^2}{m_e c^2} = \frac{\hbar \alpha}{m_e c} = \alpha \overline{\lambda}_c$$

Electromagnetic fine structure constant:
$$\boxed{\alpha = \frac{e^2}{4 \pi \epsilon_0 \hbar c}} = 7.2973525705 \cdot 10^{-3}$$

$$\boxed{\alpha = 7.2973525705 \cdot 10^{-3}}$$

QED Compton wavelength electron radius:
$$\boxed{r_e = \alpha \overline{\lambda}_c}$$

Reference:
http://en.wikipedia.org/wiki/Fine-structure_constant" [Broken]