Inertia and Relativity

DaveC426913 said:
Hansda: my kitchen collander passes grains of sand. That puts an upper limit on grains of sand of about .5cm.
Can we now conclude grains of sand are about .5cm in diameter?
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I think hansda got confused a few lines above the one I just quoted:
In classical physics, the angular momentum and magnetic moment of an object depend upon its physical dimensions. Hence, the concept of a dimensionless electron possessing these properties contrasts to experimental observations in Penning traps which point to finite non-zero radius of the electron. A possible explanation of this paradoxical situation is given below in the "Virtual particles" subsection by taking into consideration the Foldy-Wouthuysen transformation.

The issue of the radius of the electron is a challenging problem of the modern theoretical physics. The admission of the hypothesis of a finite radius of the electron is incompatible to the premises of the theory of relativity. On the other hand, a point-like electron (zero radius) generates serious mathematical difficulties due to the self-energy of the electron tending to infinity.
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I think hansda saw that completely unsourced line about the Penning traps (which appears to be talking in terms of classical physics anyway), and ran with it. In doing so, (s)he forgot to read the rest of that section, where it clearly explains it's an unsettled issue.

Edit: Interestingly enough, there's similar discussions on the talk page:
https://en.wikipedia.org/wiki/Talk:Electron#Radius
https://en.wikipedia.org/wiki/Talk:...g_"caused_by"_virtual_photons,_"causes"_spin?
But there too, the statement is unsourced.

Edit2: Yes, it's a fully unsourced addition:
https://en.wikipedia.org/w/index.php?title=Electron&diff=prev&oldid=633949990
Thus it can safely be disregarded.
 
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NotEinstein said:
I think hansda got confused a few lines above the one I just quoted:

I think hansda saw that completely unsourced line about the Penning traps (which appears to be talking in terms of classical physics anyway), and ran with it. In doing so, (s)he forgot to read the rest of that section, where it clearly explains it's an unsettled issue.

Edit: Interestingly enough, there's similar discussions on the talk page:
https://en.wikipedia.org/wiki/Talk:Electron#Radius
https://en.wikipedia.org/wiki/Talk:...g_"caused_by"_virtual_photons,_"causes"_spin?
But there too, the statement is unsourced.

Edit2: Yes, it's a fully unsourced addition:
https://en.wikipedia.org/w/index.php?title=Electron&diff=prev&oldid=633949990
Thus it can safely be disregarded.
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Good. Atleast you could find that statement.
 
https://en.wikipedia.org/wiki/Compton_wavelength . Compton wavelength $$ \lambda=\frac{h}{mc}$$ can be derived from my equations.

From my equation $$ E=mc^2=hf=Iw^2k_2=Lwk_2$$ . we can write $$ hf=Lwk_2$$ or $$hf=L2\pi fk_3k_2 $$ or $$ h=L2\pi k_3k_2$$ . Now we can consider $$ mc^2=Lwk_2$$ or $$mc=\frac{Lwk_2}{c}=\frac{Lwk_2}{k_1rw}=\frac{Lk_2}{rk_1} $$ . So we can write $$ \lambda=\frac{h}{mc}=\frac{L2\pi k_3k_2}{\frac{Lk_2}{rk_1}}=r2\pi k_1k_3 $$ . Here $$k_1 , k_2 , k_3 $$ are constants. $$c=k_1rw$$ , $$ w=2\pi fk_3$$ and $$L=Iw $$ .

From my equation of compton wavelength $$\lambda=\frac{h}{mc}=r2\pi k_1k_3 $$ , we can see that compton wavelength is function of radius. $$\lambda=f(r)$$ . Electron has compton wavelength. So, we can say it has non-zero radius.
 
From my equations classical electron radius $$ r_e$$ also can be related with its actual radius $$ r$$. https://en.wikipedia.org/wiki/Fine-structure_constant .

As per the above link $$ \alpha=\frac{r_e}{r_Q}$$ and $$L=r_Qm_ec $$ . From my equations earlier we have seen that $$ mc=\frac{Lk_2}{rk_1}$$ or $$ L=\frac{mcrk_1}{k_2}$$ . Considering this a case for electron, $$m=m_e $$ and we can write $$ L=r_Qmc=\frac{mcrk_1}{k_2}$$ . From this we can see $$ r_Q=\frac{rk_1}{k_2}$$ . Putting this value in the first equation, we can write $$ \alpha=\frac{r_e}{r_Q}=\frac{r_e}{\frac{rk_1}{k_2}}$$ or $$r_e=\frac{\alpha rk_1}{k_2} $$ . From this we can see that $$r_e=f(r) $$ . From this also we can conclude that electron radius $$ r$$ is non zero.
 
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hansda said:
Good. Atleast you could find that statement.
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And now please explain how an anonymous user posting an unsourced statement on Wikipedia was enough to convince you of its truth.

hansda said:
https://en.wikipedia.org/wiki/Compton_wavelength . Compton wavelength $$ \lambda=\frac{h}{mc}$$ can be derived from my equations.

From my equation $$ E=mc^2=hf=Iw^2k_2=Lwk_2$$ . we can write $$ hf=Lwk_2$$ or $$hf=L2\pi fk_3k_2 $$ or $$ h=L2\pi k_3k_2$$ . Now we can consider $$ mc^2=Lwk_2$$ or $$mc=\frac{Lwk_2}{c}=\frac{Lwk_2}{k_1rw}=\frac{Lk_2}{rk_1} $$ . So we can write $$ \lambda=\frac{h}{mc}=\frac{L2\pi k_3k_2}{\frac{Lk_2}{rk_1}}=r2\pi k_1k_3 $$ . Here $$k_1 , k_2 , k_3 $$ are constants. $$c=k_1rw$$ , $$ w=2\pi fk_3$$ and $$L=Iw $$ .

From my equation of compton wavelength $$\lambda=\frac{h}{mc}=r2\pi k_1k_3 $$ , we can see that compton wavelength is function of radius. $$\lambda=f(r)$$ . Electron has compton wavelength. So, we can say it has non-zero radius.
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hansda said:
From my equations classical electron radius $$ r_e$$ also can be related with its actual radius $$ r$$. https://en.wikipedia.org/wiki/Fine-structure_constant .

As per the above link $$ \alpha=\frac{r_e}{r_Q}$$ and $$L=r_Qm_ec $$ . From my equations earlier we have seen that $$ mc=\frac{Lk_2}{rk_1}$$ or $$ L=\frac{mcrk_1}{k_2}$$ . Considering this a case for electron, $$m=m_e $$ and we can write $$ L=r_Qmc=\frac{mcrk_1}{k_2}$$ . From this we can see $$ r_Q=\frac{rk_1}{k_2}$$ . Putting this value in the first equation, we can write $$ \alpha=\frac{r_e}{r_Q}=\frac{r_e}{\frac{rk_1}{k_2}}$$ or $$r_e=\frac{\alpha rk_1}{k_2} $$ . From this we can see that $$r_e=f(r) $$ . From this also we can conclude that electron radius $$ r$$ is non zero.
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So how do you resolve the incompatibility with the premises of the theory of relativity?
 
NotEinstein said:
And now please explain how an anonymous user posting an unsourced statement on Wikipedia was enough to convince you of its truth.
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Wikipedia is read by lot of people world over. Anybody can find any anomaly. If you have observed any anomaly, you can point out. It is user friendly and easy reference.

NotEinstein said:
So how do you resolve the incompatibility with the premises of the theory of relativity?
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I think, I already explained earlier that Lorentz Transformations are basically quantum phenomena.
 
hansda said:
Wikipedia is read by lot of people world over. Anybody can find any anomaly. If you have observed any anomaly, you can point out. It is user friendly and easy reference.
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If you don't want to answer the question, just say so.

hansda said:
I think, I already explained earlier that Lorentz Transformations are basically quantum phenomena.
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So you have no idea how to resolve the incompatibilities.

Also, in your first derivation, by assuming $$L$$ to be non-zero, you've assumed that the electron has a non-zero radius; that's how the definition of angular momentum works. Your entire calculation is thus circular reasoning.
And this is in fact explicitly stated in the exact section of the fine-structure constant you are referring to. So for your second derivation, you are also assuming a non-zero radius to derive a non-zero radius: circular reasoning.
How do you resolve that circular reasoning?
 
In the academia, I observed that $$ k_1k_3=\frac{1}{4}$$ . With this value you can check proton compton wavelength from my equation. It is coming very close.
 
NotEinstein said:
If you don't want to answer the question, just say so.


So you have no idea how to resolve the incompatibilities.

Also, in your first derivation, by assuming $$L$$ to be non-zero, you've assumed that the electron has a non-zero radius; that's how the definition of angular momentum works. Your entire calculation is thus circular reasoning.
And this is in fact explicitly stated in the exact section of the fine-structure constant you are referring to. So for your second derivation, you are also assuming a non-zero radius to derive a non-zero radius: circular reasoning.
How do you resolve that circular reasoning?
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Electron compton wavelength is known. Considering $$k_1k_3=\frac{1}{4} $$ , a very close value for electron radius can be known.
 
NotEinstein said:
If you don't want to answer the question, just say so.


So you have no idea how to resolve the incompatibilities.

Also, in your first derivation, by assuming $$L$$ to be non-zero, you've assumed that the electron has a non-zero radius; that's how the definition of angular momentum works. Your entire calculation is thus circular reasoning.
And this is in fact explicitly stated in the exact section of the fine-structure constant you are referring to. So for your second derivation, you are also assuming a non-zero radius to derive a non-zero radius: circular reasoning.
How do you resolve that circular reasoning?
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My equations are general equations which should be true for all the massive spinning particles. Applying these equations for electron is only one of the cases.
 
hansda said:
My equations are general equations which should be true for all the massive spinning particles. Applying these equations for electron is only one of the cases.
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Please give your definition of $$L$$, and demonstrate that this definition makes sense for particles with zero radius.
 
hansda said:
$$L=Iw $$ ; $$ I=mr^2k$$ ; $$w=2\pi fk_3 $$ . Here $$k , k_3 $$ are constants.
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So you admit that your definition of $$L$$ excludes the possibility of a zero-radius particle spinning by definition. Because $$L=I\omega$$, where $$I=mr^2k$$, which is $$0$$ when $$r=0$$. In other words, with your definition, a zero-radius particle cannot be spinning. And since you model an electron as a spinning particle, you've implicitly assumed an electron has a non-zero radius. Conclusion, your derivation is circular reasoning.
 
NotEinstein said:
So you admit that your definition of $$L$$ excludes the possibility of a zero-radius particle spinning by definition. Because $$L=I\omega$$, where $$I=mr^2k$$, which is $$0$$ when $$r=0$$. In other words, with your definition, a zero-radius particle cannot be spinning. And since you model an electron as a spinning particle, you've implicitly assumed an electron has a non-zero radius. Conclusion, your derivation is circular reasoning.
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zero radius particle can not exist.
 
hansda said:
https://en.wikipedia.org/wiki/Compton_wavelength . Compton wavelength $$ \lambda=\frac{h}{mc}$$ can be derived from my equations.

From my equation $$ E=mc^2=hf=Iw^2k_2=Lwk_2$$ . we can write $$ hf=Lwk_2$$ or $$hf=L2\pi fk_3k_2 $$ or $$ h=L2\pi k_3k_2$$ . Now we can consider $$ mc^2=Lwk_2$$ or $$mc=\frac{Lwk_2}{c}=\frac{Lwk_2}{k_1rw}=\frac{Lk_2}{rk_1} $$ . So we can write $$ \lambda=\frac{h}{mc}=\frac{L2\pi k_3k_2}{\frac{Lk_2}{rk_1}}=r2\pi k_1k_3 $$ . Here $$k_1 , k_2 , k_3 $$ are constants. $$c=k_1rw$$ , $$ w=2\pi fk_3$$ and $$L=Iw $$ .

From my equation of compton wavelength $$\lambda=\frac{h}{mc}=r2\pi k_1k_3 $$ , we can see that compton wavelength is function of radius. $$\lambda=f(r)$$ . Electron has compton wavelength. So, we can say it has non-zero radius.
Click to expand...

Considering $$k_1k_3=\frac{1}{4} $$, my equation for compton wavelength can be rewritten as $$\lambda=\frac{h}{mc}=r2\pi k_1k_3=\frac{r\pi}{2} $$
 
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