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On why the electron doesn't blow up


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I remember when I argued for a structure associated to electrons, I was a number of years ago accused of being a crackpot, despite me giving a number of reasons why there should be in principle. I was even banned from some sites for questioning the conventional view. I qoute Feymann who once said,

"I'd rather have answers which can be questioned, rather than questions that cannot be answered."

I made a lot of keyboard ganster enemies over the years because I argued a physics that wasn't sincere, being blamed that I was misleading others into pseudoscience. How many years have passed since, my knowledge on physics had proven quite rich wereas my advetsaries knowledge appears to not have progressed much.

There are three strong reasons why electrons must have a structure vs. the pointlike dogma taught to students. They go like this:

1. From the formula, I understand that the mass is always proportional to m∝1/r. Since mass is encoded in the description of energy, it would mean that as  r→0 to r=0 then m→∞ is of course [not] physically possible. This is called the self-energy problem of the electron, and as Lawrence Krauss himself had admitted, while physicists have tried to do away with the physical singularity, it seems ad hoc and uses the controversial renormalization process. A mathematician is not a physicist and some physicists rely on mathematical magic, rabbit-out-of-hat stuff which can be disputed by pure physics. Some of the greatest physicists objected to the course of what physics was going to undertake because of mathematical hocus pocus doctrine. I'll write a fuller description of this problem in the notes at the end.

2. There is a scientific bias. String theory predicts an energy rescalling of interactions so that strings act like they are pointlike in collision experiments, yet strings are spatially extended and therefore are not pointlike. Morever, the older classical physics also demonstrated, that below a certain threshold, tiny objects would always be observed to act pointlike, even if they physically were not.

3. Electrons may not even be fundamental, an experiment has managed to split an electron into three further constituent particles: Theoretically, as wiki also admits, an electron can be thought of as being made up of these particles https://en.m.wikipedia.org/wiki/Spin–charge_separation Any system made up of other systems can always be regarded as a spatially extended single system.

With any notion of an extended electron mass, we immediately solve the divergence problem of the electron self energy. But another problem persists, what stops an electron from blowing up due to negative self-energy?

Poincare suggested, very early on that there had to be additional stresses inside an electron capable of neutralizing the divergence, a theoretical model which bares his mame, the Poincare stress, and at a time, was intimately linked to other ideas concerning how much of the energy was attributed to an electron called the electromagnetic mass. Contrary to many sources, the electromagnetic self energy had not been superceded and in fact, some scientists still investigate the concept. Further contrary to what wiki says here, https://en.m.wikipedia.org/wiki/Electromagnetic_mass electromagnetic mass theories haven't actually been abandoned. The late Feynmann himself in his famous lectures added that there is strong evidence to suggest that electromagnetic forces must contribute to the self energy of particles.

One very string example he gave, was a proton and neutron had almost similar masses. He argued, if the neutron is has a neutral electric charge, then why was it only slightly heavier than a proton, surely then it would mean that the electromagnetic mass hypothesis breaks down?

But oh no, it didn't because he went on to explain, while the neutron is not electrically charged, it had a charge distribution inside of it, making it not only a complicated object, but that such a distrinution inside of it made it slightly heavier.

Let's suggest the most simplest mathematical picture for an electron where the self energy of a rest electron is U(self) = mc^2 and the Coulomb force (electrostatic energy) inside of it has a negative pressure. We might then extrspolate from classical equations that we can deal with them as conducting spheres of a homogeneous charge distribution

=1/2e^2/4πϵ R

However if one calculates the momentum in the field of a moving electron then one finds that the total mass in the field is given by:

 

m=2/3 e^2/(4πϵ0c^2R)
m =2/3 k (e^2/ c^2 R)

This yields a discrepancy in the energy given by:

 
E=1/6 k e^2/ 4πϵ R
where the constant is the usual
k    1/ 4πϵ

Poincare hypothesised that there must be stresses holding the electron together against the electrostatic repulsion of the charge on its surface. 

Some have suggested the electron can be modelled by a conducting spherical shell with a vacuum inside it.

Presumably the vacuum would lead to a negative pressure on the charged shell due to the Casimir effect and it is this "quantum foam" on the shell that provides a pressure that must balance the electrostatic repulsion of the charged shell.

According to cosmological models and more generally relativity for any fluid equation of state is given by:

p=ρc^2
 
But this equation is maybe too simple. In a true cosmological equation, any pressure is not directly equal to the negative density but in fact is an additive feature. For instance, the effective density is 
 
(R'/R)^2 = K ρ
with K ≝ 8πG/3
 
where (R'/R)^2 is called the fluid expansion parameter and K is some constant. The whole thing is a direct solution of Einsteins field equations. 
 
And even with a negative sign attached to the density, doesn't always mean that it has intrinsic repulsion as a Zeta expansion on a simikarly related subject of the Casimir force results in a positive attraction. 
 
Ignoring the hypothesis of ground state fluctuations being the physical explanation of the quelling of electrostatic repulsion, it's wise to note that the equation 
 
(R'/R)^2 = K ρ
 
must have a relativistic correction, where any true equation of state will satify for an object like an electron with some volume as really
 
ρ + 3P
 
Where the first term (density) and the last term (pressure) have the same units for simplicity if energy density. 
 

This expression can be justified on the grounds that the stress-energy tensor of the vacuum must be Lorentz invariant.

I'm going to propose that we give up on the idea of the vacuum field contribution for a simpler idea. Going back to the simple picture of the self energy, we had

U = mc^2

And we argue now that we rewrite the energy as the negative density inside of it representing loosely the electrostatic charge as

U = - ρV

remember, we can talk about energy density in this case heuristically as it encodes a volume, so multiplying the RHS with a volume gives us back the energy. According to relativity, the crucial correction is made of the form

U = - (ρ + 3P)V

= - mc^2 + 3P/c^2

This correction to Einsteins celebrated E = mc^2 (even though this identity was discovered by several authors before him) means that we invite a correction to it using the additional feature of a pressure. The interpretation of this pressure may be taken as the long sought after missing Poincare stress acting as a balancing agent to the electrostatic forces caoable of ripping an electron sphere to shreds.

The only downfall is that it requires a fine tuning. The pressure featured here has to be of the same strength as the negative density component so that it is [exactly] fine tuned. It's only a problem because we don't know why certain fine tunings exist in nature like they do, but many phenomena exist in nature which is in equilibrium, and while there are over 120 accepted fine tuning constants in nature, they still remain a mystery to us. Such phenomenon literally borders on a type of intelligent design designated in nature. Finally, the effective density parameter is encoded in the stress energy tensor belonging to Einsteins own work

T = ρ + 3P

meaning that the self energy is more compactly thought of as

E =    T dV

Equations that explore conducting spheres had been investigated even before electrodynamics, and self energy singularities was, and still is, a thorn in its side today. It seemed that working with point particles was a lazy insight from observational experiment and an unfortunate outcome where singularities simply don't exist in nature, so techniques where developed to do away with them in the most ad hoc ways, a prominent physicist, the creator of electrodynamics, Paul Dirac himself was among sone of the notable critics of this mathematical patchwork.

 

(1) - some reading material in conducting spheres https://physics.stackexchange.com/questions/281426/what-does-electrostatic-self-energy-mean

notes

1.

The simple equation for the energy of a rest electron is

U = 1/2 k e^2/R

k is the Coulomb constant.

With an integration of r= 0 gives a physically forbidden value of U = ∞

2.

While I suggest a correction to Einsteins rest energy with the nee parameter

U = - (ρ + 3P)V 

= - mc^2 + 3PV

The true total energy of a body where v is much less than c, it's more accurate to say its total energy is

E 1/2 mv2 + m0c2

Which is the sum of its kinetic and potential energy.

Edited by Dubbelosix
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Now it's all very good to state the physical problems of why an electron cannot be pointlike in the set of arguments above, but are there any huge implications of this being the case? You betcha!

Because physicists where totally adament that electrons where pointlike, the classical notion of spin haf to be done away with. You might ask why, and the reason isn't because points cannot have a real physical rotation property, its becsuse that rotation is very peculiar. You can rotate a sphere 360 degrees and it will come bacm to its original orientation. But a point has to rotate 720 degrees just for it to come back to that original orientation.  For physicists it was a deplorable phenomenon, so they beliecved they could do away with spin by stating it was "an intrinsic effect." An intrinsic property. It's not very well explained outside of this, such as how something can have an intrinsic spin. It just [is] to the physicist. Then came along an interesting experiment. Physicists attempted to measure the shape of an electron, and surprisingly all these tests hinted that the electron had a miniscule shape that was spherical! Even the basic student knows, anything spherical must havr a finite volume. Surpringly theze results didn't spark to any widdr audience that maybe the pointlike picture was wrong

https://www.scientificamerican.com/article/electron-spherical-electric-dipole-moment/#:~:text=Electrons are traditionally thought of,they would be slightly squashed.&text=The Standard Model of particle,dipole moment for the electron.

What they really mean, is that the electron was a smear of charge distribution in space that appeared to be spherical. Nevertheless, charge distribution or not, it auggesta strongly a far cry from the pointlike picture that conventional models regurgitate endlessly. 

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In fact, I can quickly demonatrate this 1/5 factor from a previous article I wrote on thw dipole of a sphere with homogeneous charge distribution.

When modelling it for a sphere of evenly distributed mass m and charge e, we know the equations from literature that can describe the magnetic moment from spin. The volume element is

V= 4/3 πR^3

And it's differential charge element is

de = (de/(4/3 πR^3))dV

The current

dj = de/dt

For the same element is

dj = (3e/(4/3 πR^3)) dVdt

I won't write all the math, you can follow it here to save me some time

https://www.toppr.com/ask/content/concept/magnetic-dipole-moment-due-to-rotation-sphere-209751/

What is the magnetic dipole moment of the sphere?

Such that the equation we seek is

μ = eR^2ω/5

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On 8/14/2021 at 12:54 PM, Dubbelosix said:

I remember when I argued for a structure associated to electrons, I was a number of years ago accused of being a crackpot, despite me giving a number of reasons why there should be in principle. I was even banned from some sites for questioning the conventional view. I qoute Feymann who once said,

"I'd rather have answers which can be questioned, rather than questions that cannot be answered."

I made a lot of keyboard ganster enemies over the years because I argued a physics that wasn't sincere, being blamed that I was misleading others into pseudoscience. How many years have passed since, my knowledge on physics had proven quite rich wereas my advetsaries knowledge appears to not have progressed much.

There are three strong reasons why electrons must have a structure vs. the pointlike dogma taught to students. They go like this:

1. From the formula, I understand that the mass is always proportional to m∝1/r. Since mass is encoded in the description of energy, it would mean that as  r→0 to r=0 then m→∞ is of course [not] physically possible. This is called the self-energy problem of the electron, and as Lawrence Krauss himself had admitted, while physicists have tried to do away with the physical singularity, it seems ad hoc and uses the controversial renormalization process. A mathematician is not a physicist and some physicists rely on mathematical magic, rabbit-out-of-hat stuff which can be disputed by pure physics. Some of the greatest physicists objected to the course of what physics was going to undertake because of mathematical hocus pocus doctrine. I'll write a fuller description of this problem in the notes at the end.

2. There is a scientific bias. String theory predicts an energy rescalling of interactions so that strings act like they are pointlike in collision experiments, yet strings are spatially extended and therefore are not pointlike. Morever, the older classical physics also demonstrated, that below a certain threshold, tiny objects would always be observed to act pointlike, even if they physically were not.

3. Electrons may not even be fundamental, an experiment has managed to split an electron into three further constituent particles: Theoretically, as wiki also admits, an electron can be thought of as being made up of these particles https://en.m.wikipedia.org/wiki/Spin–charge_separation Any system made up of other systems can always be regarded as a spatially extended single system.

With any notion of an extended electron mass, we immediately solve the divergence problem of the electron self energy. But another problem persists, what stops an electron from blowing up due to negative self-energy?

Poincare suggested, very early on that there had to be additional stresses inside an electron capable of neutralizing the divergence, a theoretical model which bares his mame, the Poincare stress, and at a time, was intimately linked to other ideas concerning how much of the energy was attributed to an electron called the electromagnetic mass. Contrary to many sources, the electromagnetic self energy had not been superceded and in fact, some scientists still investigate the concept. Further contrary to what wiki says here, https://en.m.wikipedia.org/wiki/Electromagnetic_mass electromagnetic mass theories haven't actually been abandoned. The late Feynmann himself in his famous lectures added that there is strong evidence to suggest that electromagnetic forces must contribute to the self energy of particles.

One very string example he gave, was a proton and neutron had almost similar masses. He argued, if the neutron is has a neutral electric charge, then why was it only slightly heavier than a proton, surely then it would mean that the electromagnetic mass hypothesis breaks down?

But oh no, it didn't because he went on to explain, while the neutron is not electrically charged, it had a charge distribution inside of it, making it not only a complicated object, but that such a distrinution inside of it made it slightly heavier.

Let's suggest the most simplest mathematical picture for an electron where the self energy of a rest electron is U(self) = mc^2 and the Coulomb force (electrostatic energy) inside of it has a negative pressure. We might then extrspolate from classical equations that we can deal with them as conducting spheres of a homogeneous charge distribution

=1/2e^2/4πϵ R

However if one calculates the momentum in the field of a moving electron then one finds that the total mass in the field is given by:

 

m=2/3 e^2/(4πϵ0c^2R)
m =2/3 k (e^2/ c^2 R)

This yields a discrepancy in the energy given by:

 
E=1/6 k e^2/ 4πϵ R
where the constant is the usual
k    1/ 4πϵ

Poincare hypothesised that there must be stresses holding the electron together against the electrostatic repulsion of the charge on its surface. 

Some have suggested the electron can be modelled by a conducting spherical shell with a vacuum inside it.

Presumably the vacuum would lead to a negative pressure on the charged shell due to the Casimir effect and it is this "quantum foam" on the shell that provides a pressure that must balance the electrostatic repulsion of the charged shell.

According to cosmological models and more generally relativity for any fluid equation of state is given by:

p=ρc^2
 
But this equation is maybe too simple. In a true cosmological equation, any pressure is not directly equal to the negative density but in fact is an additive feature. For instance, the effective density is 
 
(R'/R)^2 = K ρ
with K ≝ 8πG/3
 
where (R'/R)^2 is called the fluid expansion parameter and K is some constant. The whole thing is a direct solution of Einsteins field equations. 
 
And even with a negative sign attached to the density, doesn't always mean that it has intrinsic repulsion as a Zeta expansion on a simikarly related subject of the Casimir force results in a positive attraction. 
 
Ignoring the hypothesis of ground state fluctuations being the physical explanation of the quelling of electrostatic repulsion, it's wise to note that the equation 
 
(R'/R)^2 = K ρ
 
must have a relativistic correction, where any true equation of state will satify for an object like an electron with some volume as really
 
ρ + 3P
 
Where the first term (density) and the last term (pressure) have the same units for simplicity if energy density. 
 

This expression can be justified on the grounds that the stress-energy tensor of the vacuum must be Lorentz invariant.

I'm going to propose that we give up on the idea of the vacuum field contribution for a simpler idea. Going back to the simple picture of the self energy, we had

U = mc^2

And we argue now that we rewrite the energy as the negative density inside of it representing loosely the electrostatic charge as

U = - ρV

remember, we can talk about energy density in this case heuristically as it encodes a volume, so multiplying the RHS with a volume gives us back the energy. According to relativity, the crucial correction is made of the form

U = - (ρ + 3P)V

= - mc^2 + 3P/c^2

This correction to Einsteins celebrated E = mc^2 (even though this identity was discovered by several authors before him) means that we invite a correction to it using the additional feature of a pressure. The interpretation of this pressure may be taken as the long sought after missing Poincare stress acting as a balancing agent to the electrostatic forces caoable of ripping an electron sphere to shreds.

The only downfall is that it requires a fine tuning. The pressure featured here has to be of the same strength as the negative density component so that it is [exactly] fine tuned. It's only a problem because we don't know why certain fine tunings exist in nature like they do, but many phenomena exist in nature which is in equilibrium, and while there are over 120 accepted fine tuning constants in nature, they still remain a mystery to us. Such phenomenon literally borders on a type of intelligent design designated in nature. Finally, the effective density parameter is encoded in the stress energy tensor belonging to Einsteins own work

T = ρ + 3P

meaning that the self energy is more compactly thought of as

E =    T dV

Equations that explore conducting spheres had been investigated even before electrodynamics, and self energy singularities was, and still is, a thorn in its side today. It seemed that working with point particles was a lazy insight from observational experiment and an unfortunate outcome where singularities simply don't exist in nature, so techniques where developed to do away with them in the most ad hoc ways, a prominent physicist, the creator of electrodynamics, Paul Dirac himself was among sone of the notable critics of this mathematical patchwork.

 

(1) - some reading material in conducting spheres https://physics.stackexchange.com/questions/281426/what-does-electrostatic-self-energy-mean

notes

1.

The simple equation for the energy of a rest electron is

U = 1/2 k e^2/R

k is the Coulomb constant.

With an integration of r= 0 gives a physically forbidden value of U = ∞

2.

While I suggest a correction to Einsteins rest energy with the nee parameter

U = - (ρ + 3P)V 

= - mc^2 + 3PV

The true total energy of a body where v is much less than c, it's more accurate to say its total energy is

E 1/2 mv2 + m0c2

Which is the sum of its kinetic and potential energy.

Dubbel, I demand applications, hard applications what do you think this knowledge could be used for? Are you telling me we can blow up electrons without the usage of anti-particles or large particle accelerators?

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Posted (edited)

No,the equations means that the electron classically is instable without a poincare stress so long as it isnt a pointlike particle. And even then pointlike particles are unstable because a zero radius means they would blow up in quantum theory without renormalization. To satisfy a solution, the equation for rest energy can have a correction of pressure to stabilise it, in the form of +PV on mc^2. General relativity further says a density is also added to it.

Edited by Dubbelosix
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Posted (edited)

The video hits on the adpects I spoke about. But he seems to ignore the troublsesome divergence energy of a pointlike electron. Classically, a sphere, no matter how small we make it, will always avoid it. The fact we can measure the electron charge distribution as having a spherical shape is at massive odds to saying it is pointlike. Further, making electron pointlike just because experiments from scattering suggests it acts like it, is also at odds with string theory, which are subject to being spatially extended objects, and therefore, not pointlike. It's an area of physics that I think has been promoted in favor of a pointlike model in a bias way, from prominant physicists some dared not to argue with. But you can argue the spherical structure of an electron, but it seems we don't because it's not fashionable. Physicists rarely go back to badics to temry and prove something wrong, because they hate not to be right.

Edited by Dubbelosix
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  • 3 weeks later...

It's interesting that Poincare, and Lewis Carroll, and Riemann, and other "traditional" personalities, already knew so much about quantum mechanics and relativity 200 years ago.  I think it's essental to not throw away old knowledge when clearly new discoveries are supplementing it and not destroying its basis.  As for applications some more of those will come in a few more hundreds of years' time.  The exploring and experimenting and the exercises in interpreting, are vital practice for us.

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  • 1 month later...

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