Some physicists take it that the idea of Poincare stresses must exist because if they didn't a single electron would blow apart because of the electrostatic forces. A solution can exist to quell this by saying there is a fine tuning inside of electrically -charged particles like an electron where the gravitational force inside of them becomes extremely large.

An electro-gravito-magnetic contribution of energy inside a particle of a radius smaller than the classical radius can be found as:

$$E_{GEM} = \frac{1}{2}(\frac{4 \pi \epsilon GM^2}{r_s} + \frac{e^2}{r_s})$$

Where $$r_s$$ is assumed smaller than the classical radius $$(r_s < R)$$ where $$R$$ is equiv to $$\frac{e^2}{Mc^2}$$ (but still a sphere, and $$e^2$$ plays the role of the electric charge).

The inertial mass of a system can be thought of as a charge: In all respects of the math which describes these systems, mass pretty much is a charge $$\sqrt{GM^2}$$.

The charge I once found can be described using some fundamental relationships, important relationships which are believed to be of importance when describing systems under CGM-physics... (CGM-physics is the idea that the universe somehow can be described by the fundamental constants of nature) - in this equation, we have permitivitty and permeability as a part of the structure of the charge itself.

$$\sqrt{G}M = \sqrt{\frac{\pm \alpha \hbar n}{2 \epsilon_0 \mu_0 c}}$$

The problem of internal stresses gave rise to what was called the 4/3 mass problem. (You can read more on the the Poincare Stresses in electromagnetic theories of mass which is a very good article by wiki) > Some physicists still talk about mass in such ways.

The way you can solve the $$\frac{4}{3}$$ mass problem - is by saying there is a contribution $$\frac{4 \pi \epsilon GM^2}{r_s}$$ of the gravitational charge which will play the role of the Poincare Stresses - In essence, we must assume that $$G$$ takes on extremely large values inside of the sphere which help cancel the electrostatic forces believed to rip a particle apart. We can assume $$G$$ takes on an extremely large value by going back to Motz paper where he once admitted it having a large value through

$$G = \frac{\hbar c}{M^2}$$

In which he states that the gravitational constant is taken to be very large inside the sphere of a particle. Adopting this equation then allows us to ignore Poincare Stresses. but does raise an important question of fine tuning since the gravitational constant must be large enough to cancel out the electrostatic (repulsive force).

[some extra equations]

In parallel to the electromagnetic theories which where taken seriously by physicists many years ago and some still today, we can rewrite it as gravitational charge analogues.

The gravitostatic equation of contribution of energy to mass would be

$$E = \frac{1}{2} \frac{GM^2}{r_s}$$

This keeps as the gravitational analogue of

$$E_{EM} = \frac{1}{2} \frac{e^2}{4 \pi \epsilon R_{classical}}$$

The contribution of mass in my equation is found then as

$$M = \frac{1}{2} \frac{GM^2}{r_s c^2}$$

where $$GM^2$$ is the squared gravitational charge (Usually with coefficients $$4 \pi \epsilon$$.

Now going back to a similar process to Wein (1900), the attraction of the gravitational field can be understood as

$$G \frac{\frac{1}{2} \frac{GM^2}{r_s c^2} M}{R}$$

If Lloyd Motz is correct, how much stronger does the gravitational constant require to be to exactly cancel out the electostatic force inside of an electron?

It comes at a value of:

$$10^{40} \cdot G(Newton)$$

Therefore, the right hand side of the equation by Motz

$$G = \frac{\hbar c}{M^2}$$

Needs to satifsy a number which is around this order, if not, exactly this order. If it is exactly this order, we are inducing the idea that there is a fine tuning of particles relative to their internal structures when the electromagnetic and gravitational forces are taken into consideration.

I just want to write a very simple definition of the Poincare stress from an online source

''Non-electric forces postulated to give stability to a model of the electron. Because of the difficulties in regarding an electron as a point charge it is possible to postulate that the electron is a charge distribution with a nonzero radius. However, an electric charge distribution alone is unstable. In 1906 Henri Poincaré postulated unknown non-electric forces, now called Poincaré stresses, to give stability to the electron. Considerations such as these are now thought to be irrelevant(?),

First of all, the distribution of a charge within a non-zero radius is not invalidated. It has been validated with great success but at the expense of ignoring that particles may actually behave pointlike at a certain threshold. Below this threshold, sphere-like particles which have a radius smaller than your normal classical radius could very well always behave like pointlike particles by those who measure it. A similar rule exists for the 1 dimensionally extended objects of strings (in string theory, these strings are the particles just like an electron). It's sort of not fair to think that a rule exists for string theory particles which clearly are not treated as 1-dimensional objects and that in the more accepted standard model, particles are pointlike and that is the end of the story.

I also bolded a misconception in the article quote.

''

Yet there is an overseen problem - that is in physics, we also have semi-classical models. Parts of these models can be described very successfully in non-classical theories, while the same theory can still have elements of it which retain totally classical. So the ''consensus'' that particles in quantum electrodynamics should be described by non-classical means might not be totally the right way to describe nature since you can have very successful theories which mingle classical and non-classical aspects... rather well.

...The biggest problem believing that the electron truly is pointlike is that the equations describing them with a radius going to zero would actually yield an infinite energy when no one is watching the pot boil.

The equation which describes this is

$$U = \int_{|r| \leq R} \frac{\epsilon_0}{2} \mathbb{E}^2 d \vec{r} = \int_{R}^{\infty} \frac{e^2}{8 \pi \epsilon_0 r^2} dr = \frac{e^2}{8 \pi \epsilon_0 R}$$

The equation basically says, if $$R = 0$$ then the energy of the electron $$U$$ goes to infinity.

Infinities are strange things, none have ever been observed in nature, so you may take this to mean that the equation is wrong. But that requires on to be biased that non-classical electrodynamics completely runs the show and that renormalization techniques can solve this problem. Or one can argue, that it is actually indicating particles are not truly pointlike and that is the stance I take in this work.

I am curious at the comments this might receive. I don't proclaim this is the answer to problem of anything here but I am offerring it out there to find some intelligible comments to see whether there is anything wrong with my analysis of the equations and my understanding of the Poincare Problem.

Thanks for hearing me out!

Chessmaster

An electro-gravito-magnetic contribution of energy inside a particle of a radius smaller than the classical radius can be found as:

$$E_{GEM} = \frac{1}{2}(\frac{4 \pi \epsilon GM^2}{r_s} + \frac{e^2}{r_s})$$

Where $$r_s$$ is assumed smaller than the classical radius $$(r_s < R)$$ where $$R$$ is equiv to $$\frac{e^2}{Mc^2}$$ (but still a sphere, and $$e^2$$ plays the role of the electric charge).

The inertial mass of a system can be thought of as a charge: In all respects of the math which describes these systems, mass pretty much is a charge $$\sqrt{GM^2}$$.

The charge I once found can be described using some fundamental relationships, important relationships which are believed to be of importance when describing systems under CGM-physics... (CGM-physics is the idea that the universe somehow can be described by the fundamental constants of nature) - in this equation, we have permitivitty and permeability as a part of the structure of the charge itself.

$$\sqrt{G}M = \sqrt{\frac{\pm \alpha \hbar n}{2 \epsilon_0 \mu_0 c}}$$

The problem of internal stresses gave rise to what was called the 4/3 mass problem. (You can read more on the the Poincare Stresses in electromagnetic theories of mass which is a very good article by wiki) > Some physicists still talk about mass in such ways.

The way you can solve the $$\frac{4}{3}$$ mass problem - is by saying there is a contribution $$\frac{4 \pi \epsilon GM^2}{r_s}$$ of the gravitational charge which will play the role of the Poincare Stresses - In essence, we must assume that $$G$$ takes on extremely large values inside of the sphere which help cancel the electrostatic forces believed to rip a particle apart. We can assume $$G$$ takes on an extremely large value by going back to Motz paper where he once admitted it having a large value through

$$G = \frac{\hbar c}{M^2}$$

In which he states that the gravitational constant is taken to be very large inside the sphere of a particle. Adopting this equation then allows us to ignore Poincare Stresses. but does raise an important question of fine tuning since the gravitational constant must be large enough to cancel out the electrostatic (repulsive force).

[some extra equations]

In parallel to the electromagnetic theories which where taken seriously by physicists many years ago and some still today, we can rewrite it as gravitational charge analogues.

The gravitostatic equation of contribution of energy to mass would be

$$E = \frac{1}{2} \frac{GM^2}{r_s}$$

This keeps as the gravitational analogue of

$$E_{EM} = \frac{1}{2} \frac{e^2}{4 \pi \epsilon R_{classical}}$$

The contribution of mass in my equation is found then as

$$M = \frac{1}{2} \frac{GM^2}{r_s c^2}$$

where $$GM^2$$ is the squared gravitational charge (Usually with coefficients $$4 \pi \epsilon$$.

Now going back to a similar process to Wein (1900), the attraction of the gravitational field can be understood as

$$G \frac{\frac{1}{2} \frac{GM^2}{r_s c^2} M}{R}$$

*So*If Lloyd Motz is correct, how much stronger does the gravitational constant require to be to exactly cancel out the electostatic force inside of an electron?

It comes at a value of:

$$10^{40} \cdot G(Newton)$$

Therefore, the right hand side of the equation by Motz

$$G = \frac{\hbar c}{M^2}$$

Needs to satifsy a number which is around this order, if not, exactly this order. If it is exactly this order, we are inducing the idea that there is a fine tuning of particles relative to their internal structures when the electromagnetic and gravitational forces are taken into consideration.

*Why do we think particles are pointlike exactly?*I just want to write a very simple definition of the Poincare stress from an online source

''Non-electric forces postulated to give stability to a model of the electron. Because of the difficulties in regarding an electron as a point charge it is possible to postulate that the electron is a charge distribution with a nonzero radius. However, an electric charge distribution alone is unstable. In 1906 Henri Poincaré postulated unknown non-electric forces, now called Poincaré stresses, to give stability to the electron. Considerations such as these are now thought to be irrelevant(?),

**as it is accepted that an electron should be described by quantum electrodynamics rather than classical field theory**.First of all, the distribution of a charge within a non-zero radius is not invalidated. It has been validated with great success but at the expense of ignoring that particles may actually behave pointlike at a certain threshold. Below this threshold, sphere-like particles which have a radius smaller than your normal classical radius could very well always behave like pointlike particles by those who measure it. A similar rule exists for the 1 dimensionally extended objects of strings (in string theory, these strings are the particles just like an electron). It's sort of not fair to think that a rule exists for string theory particles which clearly are not treated as 1-dimensional objects and that in the more accepted standard model, particles are pointlike and that is the end of the story.

I also bolded a misconception in the article quote.

''

*As it is accepted that an electron should be described by quantum electrodynamics rather than classical field theory*''Yet there is an overseen problem - that is in physics, we also have semi-classical models. Parts of these models can be described very successfully in non-classical theories, while the same theory can still have elements of it which retain totally classical. So the ''consensus'' that particles in quantum electrodynamics should be described by non-classical means might not be totally the right way to describe nature since you can have very successful theories which mingle classical and non-classical aspects... rather well.

*And if you are still not convinced*...The biggest problem believing that the electron truly is pointlike is that the equations describing them with a radius going to zero would actually yield an infinite energy when no one is watching the pot boil.

The equation which describes this is

$$U = \int_{|r| \leq R} \frac{\epsilon_0}{2} \mathbb{E}^2 d \vec{r} = \int_{R}^{\infty} \frac{e^2}{8 \pi \epsilon_0 r^2} dr = \frac{e^2}{8 \pi \epsilon_0 R}$$

The equation basically says, if $$R = 0$$ then the energy of the electron $$U$$ goes to infinity.

Infinities are strange things, none have ever been observed in nature, so you may take this to mean that the equation is wrong. But that requires on to be biased that non-classical electrodynamics completely runs the show and that renormalization techniques can solve this problem. Or one can argue, that it is actually indicating particles are not truly pointlike and that is the stance I take in this work.

**PS.**I am curious at the comments this might receive. I don't proclaim this is the answer to problem of anything here but I am offerring it out there to find some intelligible comments to see whether there is anything wrong with my analysis of the equations and my understanding of the Poincare Problem.

Thanks for hearing me out!

Chessmaster

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