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Jarek wrote:To get total energy you have to integrate energy density. Integrating energy density of electric field from distance lower than 1.4fm one exceeds mc^2 of electron - nonsense.
That's the big charge regularization problem, officially still unresolved, requiring deformation of standard EM energy density.
https://physics.stackexchange.com/quest ... int-charge

No you don't have to integrate energy density to get total energy. I already have total energy mc^2 without integrating. We have resolved the regularization problem. It's simple. You don't have to regularize. The electron is cut off at a finite length near Planck length. No more regularization, no more renormalization is required!!!!
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If you want the energy density, just work it backward from the total energy.
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Yes, rho(r) describing energy density around electron is what many people are interested in - please just write the formula or show some plot from your approach.

Jarek wrote:Yes, rho(r) describing energy density around electron is what many people are interested in - please just write the formula or show some plot from your approach.

I don't care about the energy density. If you want the energy density, just work it backwards from the total energy.
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We know well the total energy: 511keV for electron, don't know how it is distributed - please show if you know.

Jarek wrote:We know well the total energy: 511keV for electron, don't know how it is distributed - please show if you know.

Oh, I thought you knew. I don't know and don't care how it is distributed.
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FrediFizzx wrote:

Jarek wrote:We know well the total energy: 511keV for electron, don't know how it is distributed - please show if you know.

Oh, I thought you knew. I don't know and don't care how it is distributed.
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How far away from an electron do you think its coulomb field becomes effectively zero? 1 meter? Less? More?
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Electric field is generally believed to have infinite range - in theory charge of single electron contributes rho~r^-4 to energy density of the Universe (with finite propagation speed).
The big problem is with small distances - making that such energy density integrates to a total energy not exceeding 511keVs for electron.

Jarek wrote:Electric field is generally believed to have infinite range - in theory charge of single electron contributes rho~r^-4 to energy density of the Universe (with finite propagation speed).
The big problem is with small distances - making that such energy density integrates to a total energy not exceeding 511keVs for electron.

Ya didn't answer my question. One meter away, the energy is down to 10^-15 MeV. Close enough to zero?
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It is close to zero, but cannot be neglected: can add to non-negligible contributions in arbitrarily large distance ... gravity is muuuuch weaker and adds to essential contributions in cosmological scales deciding evolution of the Universe.
And generally there is no problem with long-range behavior, only short-range: we don't know what is energy density e.g. 1fm from electron - we need rho(r) energy density function.

Jarek wrote:It is close to zero, but cannot be neglected: can add to non-negligible contributions in arbitrarily large distance ... gravity is muuuuch weaker and adds to essential contributions in cosmological scales deciding evolution of the Universe.
And generally there is no problem with long-range behavior, only short-range: we don't know what is energy density e.g. 1fm from electron - we need rho(r) energy density function.

Have you ever heard of the Cluster Decomposition Principle? Electrons in one room don't affect don't affect electrons in another room.
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E.g. wireless charging allows electrons from one room to affect those in another ... and all electrons gravitationally affect evolution of our Universe ...
But the question here is energy density in small e.g. fm-scale distance ... I didn't get anything from you about.
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Jarek wrote:E.g. wireless charging allows electrons from one room to affect those in another ... and all electrons gravitationally affect evolution of our Universe ...
But the question here is energy density in small e.g. fm-scale distance ... I didn't get anything from you about.
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I should have specified that SINGLE electrons in one room don't affect single electrons in another room.
More later; very busy on another project.
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It is generally believed that interaction between multiple e.g. electrons is sum of interactions between single ones, e.g. through Biot-Savart/Jefimenko: https://en.wikipedia.org/wiki/Jefimenko's_equations
But once again: there is no problem with large distances here, only with tiny especially femtometer-scale.

FrediFizzx wrote:

Jarek wrote:E.g. wireless charging allows electrons from one room to affect those in another ... and all electrons gravitationally affect evolution of our Universe ...
But the question here is energy density in small e.g. fm-scale distance ... I didn't get anything from you about.
Best

I should have specified that SINGLE electrons in one room don't affect single electrons in another room.
More later; very busy on another project.

Fred, I understand that you would like to believe that, but how do you know that nature really is that way? I understand that it is absolutely natural to take that as something with a very high prior probability. But isn't it possible that nature could teach us that it's just not true? What evidence would convince you?

@gill1109 There is nothing that would convince me that all action in Nature isn't local. Particle physics demands it.
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gill1109 wrote:

JohnDuffield wrote:However it’s a pity that it says “the vacuum isn’t empty, but seething with activity. So-called virtual particles pop in and out of existence all the time”. It isn’t true. Vacuum fluctuations aren't the same thing as virtual particles.

I would say that vacuum fluctuations generate real particles. In a non-local, irreducibly random, way.

Pfft!

FrediFizzx wrote:@gill1109 There is nothing that would convince me that all action in Nature isn't local. Particle physics demands it.

Maybe particle physics is not quite right?

gill1109 wrote:

FrediFizzx wrote:@gill1109 There is nothing that would convince me that all action in Nature isn't local. Particle physics demands it.

Maybe particle physics is not quite right?