[BilboGrabbins (OP)]

Its been long assumed the electron follows a probability fuzz around a nucleus, but the work of Bohr showed remarkable success that orbitals for the hydrigen atom became to be called stationary orbitals that did not radiate. I independently came to the conclysion that these special orbitals could in fact be folliwing the weak ewuivelence of free falling physics, which means the particle free falling would not accelerate in such a way to give off radiation. I later found out that a free falling orbital model was investigated a while ago but appears not to have gained much traction.

First of all, why did I pursue a free falling model of an electron the in the stable orbits of an atom?

1. Electrons cannot be at rest in a stable equilibrium

2. Electrons cannot be in motion pursuing ellipitical orbits

These two basic premises of quantum theory are at odds with each other. One thing was certain, if electrons had motion then Bohr was right:

3. Only non-stable orbits with motion can allow atoms to radiate.

So with the help of quantum theory, Bohr created a model of the atom where electrons followed ''special orbits'' and these ''special orbits'' where the ones where electrons had been able to whizz around without giving off the usual radiation we would expect from a moving charge. Later, the planetary model was superseded by wave mechanics, the idea was simple enough

4. That electrons did not move around the nucleus, instead they existed as a wave spread out statistically in space.

But with this, there was a catch. DeBroglie, the true inventor of the wave particle duality model, for all states of matter, never said that his wave mechanics specifically said this. From experiments, like the photoelectric effect and gamma scattering, we knew the particle had to exist both sometimes as a particle, other times a wave. The inseparability of the wave from the particle, lead to his famous wave hypothesis, stating that the particle was accompanied by wave. The wave itself was unobservable however, only today using very special techniques, computers and special equipment have been able to indirectly see the wave nature inside of particles. It still doesn't tell us at what time the electron would act as a particle, unless directly observed, by which time the wave would collapse and all that would remain, would be the particle. Yeah, quantum theory was weird.

In spirit of deBroglie, I'd like to carry on his strong assertion that particles where guided by waves, so that we can  in some way rationalise the weird nature of quantum mechanics into a regime that is more acceptable for a willing and rational mind. Certainly, why cannot a particle be guided by its wave? Matter was guided by curvature in space, and it was this correspondence of the two ideas where I linked perhaps a unity between the strange wave mechanics of deBroglie to that of GR. One stated that matter told space how to curve and space told matter how to move, whereas particles told waves how to spread, and the waves told particles how to move. Maybe wave mechanics and curvature where closely related. This was my first motivation. We'll learn as my theory progresses, that the orbits described by the moving particle also contain their own curvatures, their own geometries. By inviting the weak equivalence principle, we would further learn how to allow a particle to move in an orbit without giving off any radiation.

So a natural conclusion under the DeBroglie model is that electrons do in fact follow paths inside an atom accompanied by the wave. The waves are not observable but the electron is.

In order to model an electron with any arrangement of orbits, requires the eccentricity. So in my work we will model this eccentricity for a more accurate spin orbit equation.

Quite a bit of a calculus goes into the derivation, of eccentricity, but it wasn't my derivation. My contribution is its direct application to a spin orbit equation, two final forms came as



where is the gravimagnetic field, we identify torsion as encoded in this as being part of the central potential , its full form is



and



and



Is the eccentricity. In a later post Ill show how you derive the full result from calculus, but its ugly and complicated so I'm not doing that today. The main point is we have a correction term on the spin orbit equation, the deviation of the orbit described by the eccentricity. It shows how much it will deviate from a perfect circle so has real world applications, even inside of the interior of atoms.

The alternative formula is



And is the total angular momentum. You get the first equation by plugging in the inverse Bohr mass



into the standard spin orbit equation, which is,



Ironically, I found that it didn't matter whether I used Bohrs inverse mass or inverse radius, they both produced the same equation, so they are not too much different animals.

In this post I'll explain quickly the calculus used to derive the eccentricity. Its all standard, it's not something I derived myself, whoever did, was doing this stuff at high level university stuff, it was the insight I had where we could use it to describe the radius of curvature. Hopefully I put it here in an understandable way, my only contribution, as its a bit complicated. We start off with a Langrangian



We are able to define the shape of the orbit from



The angle is defined by a succinct integral equation as



The r-integration is followed by making



and



This gives



So pretty complicated stuff tracking these variables, a lot more complicated than Id mess around with normally outside of mathlab. Next we can make from this,



and also



So that the final orbit of curvature can be taken, with eccentricity as

[Kartazion]

Hello.

If we were to rely on the probability of the electron-density distribution in a atom, then we would see that its density is greater at the nucleus than in upper n-shell orbits. It would be interesting to be able to interpret where are the links between this electron-density distribution at Kepler's orbits.

[Origin]

But with this, there was a catch. DeBroglie, the true inventor of the wave particle duality model, for all states of matter, never said that his wave mechanics specifically said this. From experiments, like the photoelectric effect and gamma scattering, we knew the particle had to exist both sometimes as a particle, other times a wave.

That is not correct.  If we do an experiment to detect a particle we will detect a particle and if we do an experiment to detect a wave we will detect a wave.  That doesn't mean sometimes it's a particle and sometimes it's a wave.  This only means an electron had aspects of waves and particles.  It is actually neither.  An electron is nothing like you have ever seen and as such any attempt to visualize it is bound to fail.

[Bored chemist]

 People seem to think that an electron (or a photon etc) is either  a particle or a wave or some sort of mixture.

This is a picture of a quagga

Quagga.JPG (94.61 kB . 805x590 - viewed 3305 times)

When examined from the front, it looks like a zebra.
And when examined in a different way, it looks like a horse.

This does not mean that it is both a zebra, and a horse.
It does not mean that it's a zebra and it does  not mean that it is a horse.

What it shows is that it can not be a zebra or a horse.

In the same way, because an electron sometimes looks like a wave, and sometimes looks like a particle, we know that it is neither.


(and yes, I know, technically a quagga is a type of zebra, but that's not the point)

[BilboGrabbins (OP)]

But with this, there was a catch. DeBroglie, the true inventor of the wave particle duality model, for all states of matter, never said that his wave mechanics specifically said this. From experiments, like the photoelectric effect and gamma scattering, we knew the particle had to exist both sometimes as a particle, other times a wave.

That is not correct.  If we do an experiment to detect a particle we will detect a particle and if we do an experiment to detect a wave we will detect a wave.  That doesn't mean sometimes it's a particle and sometimes it's a wave.  This only means an electron had aspects of waves and particles.  It is actually neither.  An electron is nothing like you have ever seen and as such any attempt to visualize it is bound to fail.

Well, we can refer to the double slit experiment. We can say it acts like a particle, as we detect it on the screen. Before this observation has been made, it will diffract as though it once acted like a wave, so we can technically say it sometimes acts like a wave or a particle. They key aspect though os that the particle may indeed be accompanied by a wave, so it has a dual aspect. In other words, it always (is) a particle and it just so happens that a wave guides it.

[BilboGrabbins (OP)]

Hello.

If we were to rely on the probability of the electron-density distribution in a atom, then we would see that its density is greater at the nucleus than in upper n-shell orbits. It would be interesting to be able to interpret where are the links between this electron-density distribution at Kepler's orbits.

It would be interesting, in the model I propose, all stable n-orbits are following a free falling trajectory. It's density is always greater near the nucleus, but it might be more accurate to say the distribution must fluctuate around the area which is prescribed by the square of its wave function.

[Bored chemist]

They key aspect though os that the particle

Which part of "it is not a particle" did you not understand?

[BilboGrabbins (OP)]

They key aspect though os that the particle

Which part of "it is not a particle" did you not understand?

The part where you say it isn't a particle. I hope you're not suggesting particles don't really exist, because evidence would suggest greatly in favor against such philosophical nonsense.

[Bored chemist]

because evidence would suggest greatly

OK, let's look briefly at the evidence.
Electrons sometimes behave like waves; we can do electron diffraction experiments.
A particle can't behave like a wave.
So we know that electrons are not particles.

As Origin said.

This only means an electron had aspects of waves and particles.  It is actually neither.  An electron is nothing like you have ever seen and as such any attempt to visualize it is bound to fail.

And, as I said

 People seem to think that an electron (or a photon etc) is either  a particle or a wave or some sort of mixture.

[BilboGrabbins (OP)]

because evidence would suggest greatly

OK, let's look briefly at the evidence.
Electrons sometimes behave like waves; we can do electron diffraction experiments.
A particle can't behave like a wave.
So we know that electrons are not particles.

As Origin said.

This only means an electron had aspects of waves and particles.  It is actually neither.  An electron is nothing like you have ever seen and as such any attempt to visualize it is bound to fail.

And, as I said

People seem to think that an electron (or a photon etc) is either  a particle or a wave or some sort of mixture.

"A particle can't behave like a wave.
So we know that electrons are not particles."

And yet they do. I don't know what physics you've been reading, but electrons contrary to what you think, do behave like waves. There's over a dozen well-known founded reasons in physics to support this. Its also known from Brownian motion, from photoelectric phenomenon and many other experiments they show clear corposcular behaviour. Even the double slit experiment unifies both these known facts. This experiment proved that electrons appeared to show wavelike behaviour but when they reached the detector, showed they were particles.

So I'm sorry for disagreeing, electrons are particles and either they act as waves or are guided by them. I suggest you go back to basics to learn the science of this because I'm dumbfounded by the statements you are making.

[BilboGrabbins (OP)]

In fact, to be blatantly honest with you, to say an electron is neither a wave or a particle, is so psuedoscientific that it beggers belief. We know they are particles, we just don't know for certain whether the wave is intrinsic to particle motion in space or whether the wave guides the particle, the latter being the DeBroglie interpretation. But to say it's not a particle goes against a hundred years of physics which claims otherwise.

[Bored chemist]

I suggest you go back to basics to learn the science of this because I'm dumbfounded by the statements you are making.

Am I right in thinking that only one of us is actually a scientist?

[BilboGrabbins (OP)]

I suggest you go back to basics to learn the science of this because I'm dumbfounded by the statements you are making.

Am I right in thinking that only one of us is actually a scientist?

If you are a scientist, I'd hate to be taught under you to be quite frank. Nearly any textbook will disagree with your skewered view on the non-existence of the corposcular nature of particles. I'd expect maybe a crank to deny the particle nature of quantum physics, but not an actual scientist. Instead of having some contest, it might serve your reputation better to explain only one of the experiments I have elucidated upon. Say, the photoelectric effect. How would you explain it if electrons were not actually particles...? Now be careful, because it's pretty much the bread and butter argument for the particle claim, so I'd be all ears to hear an alternative explanation, so long as its not cranky.

[Bored chemist]

If an electron was a particle, it would have a radius.
Attempts to measure that have, so far, given a result of "too small to measure, and quite possibly zero".

How can a thing with zero size have a wavelength or an amplitude?

The wave function for a particle can have those properties, but it's a mathematical abstraction; it isn't the electron itself.

[BilboGrabbins (OP)]

If an electron was a particle, it would have a radius.
Attempts to measure that have, so far, given a result of "too small to measure, and quite possibly zero".

How can a thing with zero size have a wavelength or an amplitude?

The wave function for a particle can have those properties, but it's a mathematical abstraction; it isn't the electron itself.

You really are digging a hole here, particle doesn't mean it has to have a radius, though, I often wonder if it does, but that's irrelevant. You clearly don't know what particle means, its a discrete packet of quanta. It's so recognised as the explanation, that it's foundation cannot be challenged in any rigourous way and Einstein was the first to notice that photons had to come in discrete packets, and the same rule applies to the rest of all fundmental particles. Here wiki explains exacty that, "Because a low-frequency beam at a high intensity could not build up the energy required to produce photoelectrons, as it would have if light's energy were coming from a continuous wave, Albert Einstein proposed that a beam of light is not a wave propagating through space, but a swarm of discrete energy packets, known as photons."

[BilboGrabbins (OP)]

Also, a wavelength does indeed describe the theoretical length of the packet, but this hits at the root of a different theoretical issue, not the issue of particle nature. Again, a particle has wave properties, but when it is observed, a collapse in the wave function occurs and all we observe is a discrete packet of quanta aka. A particle.

[BilboGrabbins (OP)]

I'll say a few words though on the nature of a possible electron radius. But even if it had none, it's still called a pointlike particle regardless.

[BilboGrabbins (OP)]

Anyway, as I explained, a poinlike particle is one without a radius. An electron with a radous would still be a particle. I wrote on this subject not long ago and here you can read some theoretical objections against a pointlike structure.

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 name, 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 strong example he gave, was a proton and neutron had almost similar masses. He argued, if the neutron 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 distribution 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

E =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 capable 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.

[Bored chemist]

it's still called a pointlike particle regardless.

So, how come we can diffract it?

[Bored chemist]

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

Nice idea, but you got it wrong.
He actually said “I would rather have questions that can't be answered than answers that can't be questioned.”

And yet you tell me that I should believe what it says in the textbooks.

Nearly any textbook will disagree with your skewered view on the non-existence of the corposcular nature of particles.

Did you understand the quote from R.F.?
Telling me that the textbook is right  makes it "an answer which can not be questioned"; exactly what Feynman said we shouldn't want.