Point Charges Implement Asymptotic Safety

Imagine two point charges orbiting in a circle and located across from each other on the diagonal. In Euclidean time and space the speed of electric and magnetic fields is @. The electric field emitted from a point charge at coordinates described with $\mathbb{R}4$ in Euclidean time and space and expands spherically at an axial speed @.

$electric\;field\;speed= @$

Imagine the case where the circular orbital speed of a point charge approaches or reaches a factor of $\frac{\pi}{2}$ times @

$point\;charge\;speed = \frac{\pi}{2}@$

Imagine the wavefront emitted by a point charge at time T₀.

The distance across the orbit on the diameter is d = 2r.

$distance = diameter = 2 r$

The field front is a spherical surface expanding at @.

Likewise the field moves across the diagonal at speed @.

We know speed = distance/time.

$speed = \frac{distance}{time}$

How long does it take for the field to travel on the diameter?

$time = \frac{distance}{speed}$

$time = \frac{2r}{@}$

Meanwhile, where is the point charge that emitted the field?

It is traveling on a circular path with orbit r at a speed @pi/2.

How far has it traveled at time 2r/@?

$distance = \left ( {speed} \right ) \left ( {time} \right )$

$distance = \left ( {\frac{@\pi}{2}} \right ) \left ( {\frac{2r}{@}} \right )$

$distance = \pi r$

The particle arrives exactly exactly across the diameter of the orbit at the same time as it’s own field. The point charge perceives itself acting upon it across the diameter. Like point charges repel. Asymptotic safety. Q.E.D.

Ok, not so fast, what is happening with it’s partner charge and its field in this case? We know that the point charge perceives itself across the diameter and that the electrino and positrino point charges are physically one half a revolution away in Euclidean time and space, or directly opposed across the diameter. This is true at any point in the orbit due to the symmetry of a circular orbit.

Aside. Someday scientists will come along and enhance the model with distorted perturbed orbits and the exact dynamics during the application of work to transfer h-bar. It is all fairly easy to model. I tend to focus on the circular and spherical orbits and momentum conserving transformations and the planar orientation in a Noether core, so a very geometrical model. In reality this is all

It turns out that the point charge perceives it’s partner to be approaching the same location, in the limit, as the point charge itself!

It is kind of weird to think about the case where the shadow of our partner charge is in the same location as the self charge. We are really talking only about the field that it emits as is always the case. Might the radius of that emitted field be zero (0) at that point? The field literally has not yet been emitted. Hmmm. Does that make any sense? Meh. It is sort of undefined and chancy and magical. Nature has been logical so far, let’s keep looking for a solution that feels natural, meaning it can be scientifically and mathematically shown to be an emergent behaviour.

We could also guess that the maximum frequency is F_p – 1. Perhaps achieving F_p is never quite reached, the asymptotic safety kicking in. That seems more intuitive to me. I need to noodle on this while I write out all the math.

Noodling : In the case above, each point charge perceives its partner charge to be in the same location as itself. So how should that be interpreted? One Hz prior and one h-bar less energy the partner point charge was perceived to be leading ever so slightly and exerting an intense attractional force. So what happens when that final gap is closed and each point charge appears to be in the same location as it’s opposite partner? Do we consider the partner to not yet have emitted it’s field? Even if it had, with r=0 then it would point in all directions.

Another point here is that the limit on size is emergent from first principles. The Planck frequency is simply the case where the math works out that a point charge can race around a half circle and be acted upon by its own field. If it were to try to orbit faster than $\frac{\pi}{2}@$ then the chord would shorten again and the radius would change and it’s just not possible to add more energy at this limit. The math makes this impossible.

Ok, so now we can embark on the formal geometry. I think I understand enough to start writing down the math and figuring out all the electromagnetic action along the chords from the perceived history of partner and self. That math should lead the way to figuring out any remaining issues. After all we do have a quasi-magnetic North in terms of the GR and QM if we need those life lines. The electromagnetic forces from the partner charge and from self-action will be on a vector direction along a chord of the orbit from the field emission point in history to the action point on each point charge when the field intersects the orbit. Chord length looks like an interesting formula. So we have a system in F_p equations. We want to solve for the radius of orbit, r and the range from r_min to r_max. As mentioned before, there will be a low energy and a high energy solution for each radius r, corresponding to either side of Wien’s peaks.

TL;DR

I figured out how a pair of opposite point charges orbiting in a circle implement asymptotic safety, i.e., immutability at a radius near the Planck length. Start with Euclidean space and a natural law that the electric field implemented by a point charges expands spherically with a radial speed of @ from every location (x,y,z,t) in R4 in the particles history. If each point charge is traveling at an orbital speed of @pi/2 then it will actually perceive itself diametrically opposed. Since like particles repel, so does self-action.

This means that the field of physics can now officially take the minimal step to resurrect point charges and start thinking about them seriously.

Note :The value of @ is nearly the same as c in low energy Minkowski/Einstein spacetime, and we’re talking below photons here, so I needed a new symbol.

This is all part of discovering the math of the point charge dipole. I’ve been determining the approach to the math for years, and I think it is going well. The last few issues are falling into place.

I think the behaviour of the orbiting point charge dipole will come evident with the math. It is a matter of finding the equations that reveal which partner history fields and which self history fields impact the actual point charges. Is it possible that multiple history fields could arrive at the same time when the point charge is moving at faster than @ on its circular path? I do think this is a linear control system so as work is done on the dipole the angle to the history shadows change. Each h-bar causes the radius to change and then the angle relaxes again. We will see…

J Mark Morris : Boston : Massachusetts