[samcottle (OP)]

Hi, I thought I'd post a bit of a draft paper I'm working on trying to summarise a few years' independent work on the problem of quantum gravity. I've come at the problem very much from a philosophy/humanities background with about the same level of mathematical sophistication as Michael Faraday, i.e. not much. I reasoned that, while a huge amount of mathematical excellence has been thrown at this problem of quantum gravity, not a huge amount of progress has been made. I thought maybe it'd take someone who could, so to speak, see the wood for the trees might have a better chance (no offence to anyone's mathematical abilities). Here's the paper:

A Gravitoelectroweak Hypothesis?

By Mr. SP Cottle.


Abstract:

If a unification exists between electromagnetism and the weak nuclear force, it follows that there may exist some extension to that framework incorporating gravity. The resulting ‘gravitoelectroweak’ interaction would manifest as the summed exchanges, between bodies consisting of atomic material, of W+ and W- particles with tunneling electrons in the background. These background electrons would form something akin to the spin foams (or spin networks) of loop quantum gravity and would lead to a Dirac Sea permeating space. Therefore, the loop quantum gravity model would be supported as would Felix Finster’s suggestion of a causal fermion system. The specifics, however, of how gravity would be transmitted between particles at distance comes from the tunneling of electromagnetic particles (electrons) exchanging W particles with protons and other positively-charged particles. The impact of these electrons on subatomic particles could be tested by, for instance, testing the g-factor of the muon in space. According to this hypothesis, in microgravity, the g-factor of the muon ought to roughly accord with the predictions of the standard model.


Introduction: Electron Densities and Gauge Fields.

The interaction that would lead to the macroscopic force of gravity is the exchange of a W- for a W+ between a foreign electron and a local proton. The electron would tunnel from one atom, at a distance separate from the atom containing the proton, and exchange the W- for a W+ leading the two atoms (to which the foreign electron and local proton belong) moving closer together. Therefore, as an atom (containing a proton) falls into a foreign electron density (gravitational field) it experiences the exchange of several W- particles for several W+ between its own proton and the electrons in the gravitational field into which it’s falling. The greater the density of electrons, the greater the macroscopic force of gravitation. Hence, in regions of high gravitational potential such as near the event horizon of a black hole, we find a greater number of these background, or gravitational, electrons. These electrons diminish in inverse proportion to the square of the distance from the surface of the object to which they belong.

The electrons comprising the gravitational field also, of course, reflect light and give rise to the reflective capacity of bodies as established in the theory of general relativity. For instance, in a system that causes the gravitational lensing of light around an object, the photons would be hitting electrons and become trapped between electrons in the gravitational field; probability would dictate that most photons would be deflected either towards, or away from, the object in question, though a certain number would be channeled around the object for us to observe as this effect of gravitational lensing. A number of other macroscopic effects could also be anticipated in this theoretical framework, such as the accelerating expansion of the universe; the universe would be reflecting photons between galaxy clusters and photons would be building up between galaxy clusters as a result, and the radiation pressure from these buildups would then be leading to the expansion of the observed universe.

Another intriguing facet of this model is that the simultaneous exchange of a W+ and W- between a proton and a gravitational electron would create a massless, spin-2 gauge field in the interstitial space between the electron and proton. However, this gauge field would exist only for the briefest of moments at an incredibly small length scale (never greater than the electroweak range). Though the W particles, when observed in particle accelerators, have mass, in this scenario their like-signed charges cause their masses to cancel. There is an admittedly obscure relationship in this regard between mass and charge, however, to clarify things I’ll suffice it to say that the attraction and repulsion between charges gives rise to the resistive quality associated with mass and gravitation; the clouds of electrons I describe surrounding massive bodies give rise to a force of attraction over other atomic material traveling through them, though they also create resistance due to the mutual repulsion between the gravitational electrons and the electrons comprising the foreign atomic materials. The mutual attraction of the W+ and W- can be seen as two naked charges of exact equivalence canceling one another; it’s important to note however that the electron is still attracted to the W+ and the proton is still attracted to the W-; as such, in this four-body system, there is still the net tendency for the electron and the proton to move towards one another.


The Primary and Secondary electron density.

This has thus far been one of the more unpopular ideas of this hypothesis. However, as a pedagogical mechanism, and a general aid to clarifying these ideas and separating which electrons form the gravitational field and which electrons’ influence are directly canceled by the presence of a nuclear proton, I’ve come to refer to primary and secondary electron densities. For instance, those electrons that appear up to and including the Van der Waals radius of an atom would be part of the primary electron density whereas any that exist (for a given time) beyond that point would be part of the secondary electron density. The secondary electron density contains gravitational electrons and the electrons comprising the primary electron density do not, as such, have any input into the force of gravity. That said, from a certain philosophical perspective; and from the perspective of unifying forces; we might say that the primary density electrons exert a force of gravitation over the proton in the nucleus of the atoms to which they belong. This is only if we’re conflating the force of electromagnetism with the force of gravity. I grant that, in doing so, we’d be extending our understanding of the force of gravity (and probably also of electromagnetism), but the idea that they’re one and the same force in a total sense is somewhat beyond the scope of this paper.

To calculate the number of electrons comprising the secondary electron density, and thereby contributing to the force of gravity as it’s classically understood, one must first take the number of atoms (since this applied to objects formed of atomic materials), multiply that by the average atomic number of the materials in question, and then divide by the ratio between the force of gravity and the force of electrostatic repulsion. The resulting equation is:

 (eq.1)

This equation can also be made time-dependent and, in some circumstances, this is necessary since for certain bodies a non-sensible number of electrons in the secondary density will be derived using this method. For example, if you were to impute the number of atoms and average atomic number for a hydrogen atom, you’d end up with a number far smaller than one; this is ok for certain calculations, but others require the time-dependent equation. The amount of time an electron remains in a given position is equal to the amount of time it can remain at a given location in space without interacting with another particle. Given that we clearly live in a soup of quantum particles, I’ve estimated this number to be the Plack time; i.e. the smallest amount of time with any physical meaning. The time-dependent equation is:

 (eq.2)

One can use this first equation then, with Coulomb’s law, to produce a figure for the force of gravity between two hydrogen atoms that differs only slightly from the results obtained using Newton’s law for universal gravitation. The reason for the slight variance in the results is the influence of radiation pressure between two bodies. Newton’s constant and Newton’s law are derived from the observation of massive bodies and hence account implicitly for the influence of radiation pressure whereas Coulomb’s law does not. Through exploring this relationship, and symmetry, between Coulomb’s Law and Newton’s, we might come to a clearer understanding of how gravity unifies with electromagnetism. It takes the problems here in a seemingly somewhat back-to-front manner, however, following from establishing the relationship between the two laws and how they interrelate, we can then integrate the weak force into the picture relatively easily through considering the beta decay of the neutron.

[Origin]

This is nothing but word salad.

I did get a kick out of equations 1 & 2.  Mathematical equations generally are mathematical equations not a paragraph of text.

[Bored chemist]

This is nothing but word salad.

I did get a kick out of equations 1 & 2.  Mathematical equations generally are mathematical equations not a paragraph of text.

I suspect that the cut and paste operation decided to save us the trouble of reading the equations.
It may have been wise.

[alancalverd]

The test of a hypothesis is the accuracy of its predictions. I don't see any.

[Bored chemist]

The test of a hypothesis is the accuracy of its predictions. I don't see any.

To be a hypothesis, it needs to be meaningful.
I think it fell at the zeroth hurdle.

[Kryptid]

The electron would tunnel from one atom, at a distance separate from the atom containing the proton, and exchange the W- for a W+ leading the two atoms (to which the foreign electron and local proton belong) moving closer together.

The probability of an electron tunneling over astronomical distances is absurdly unlikely, so that doesn't make for a good explanation for how planets can stay in orbit around a star.

[samcottle (OP)]

The electron would tunnel from one atom, at a distance separate from the atom containing the proton, and exchange the W- for a W+ leading the two atoms (to which the foreign electron and local proton belong) moving closer together.

The probability of an electron tunneling over astronomical distances is absurdly unlikely, so that doesn't make for a good explanation for how planets can stay in orbit around a star.

Can you tell me how unlikely it is? It's unlikely in any case that the electron would tunnel beyond the Van der Waals radius, though (contrary to what you might think) the unlikelihood of something happening doesn't mean that it never happens; it means that it happens with regularity only not very often. If you then take into consideration the unfathomable numbers of electrons in say this galaxy then you'd get a clearer picture of how the probabilities and unlikelihood of events happening are somewhat absorbed under those very large numbers. Also read Finster's papers on causal fermion systems, they are very enlightening (as is a good book on LQG), and not all that far away from what I've proposed here. Try to post something more helpful next time (I have, of course, thought about this). I'm sorry you people failed to understand something, but there's no reason I ought to have to tolerate gaslighting and abuse, like some of the comments here.

[samcottle (OP)]

The test of a hypothesis is the accuracy of its predictions. I don't see any.

I stated in the abstract that this hypothesis predicts that the g-factor of the muon would accord with the predictions of the standard model in microgravity. I predicted a while ago that the deviations from the standard model predictions are accounted for due to the experiments being carried out in Earth's gravity well and that the observed differences in the g-factor between locations can be accounted for considering the differing heights above sea level at the locations where the experiments were carried out (i.e. at Fermilab versus the Lawrence Livermore National Laboratory).

[Bored chemist]

Can you tell me how unlikely it is?

Practically impossible.
Could it happen once... yes.
Twice... maybe.
Often enough to be a significant factor in how the universe works,,, no.

[samcottle (OP)]

This is nothing but word salad.

I did get a kick out of equations 1 & 2.  Mathematical equations generally are mathematical equations not a paragraph of text.

Word salad. Or you're too stupid to understand the words and so revert to discrimination and gaslighting.

[Kryptid]

Let's not hurl insults.

Can you tell me how unlikely it is?

The distance factor in the tunneling probability equation is actual an exponent, so increases in length scale massively decrease tunneling odds: https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.07%3A_Quantum_Tunneling_of_Particles_through_Potential_Barriers#:~:text=L%3De24%CF%80,it%20is%20to%20tunnel%20through.

That website does some example calculations. For barrier of 1 nanometer, the calculated probability for the low energy electron is 1.7% x 10^-4. When that barrier distance is increased to 5 nanometers, the probability drops drastically to 2.1% x 10^-36. If I plug a micrometer distance into the equation (1,000 nanometers), then the probability I get drops profoundly to 1.792% x 10^-7,709. There very probably has never been such an unlikely event to occur in the history of the visible Universe. That's just a micrometer. Millions of kilometers is just not feasible.

[Origin]

Or you're too stupid to understand the words and so revert to discrimination and gaslighting.

Pointing out that you have no clue what you are talking about is not discrimination.

[samcottle (OP)]

Let's not hurl insults.

Can you tell me how unlikely it is?

The distance factor in the tunneling probability equation is actual an exponent, so increases in length scale massively decrease tunneling odds: https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.07%3A_Quantum_Tunneling_of_Particles_through_Potential_Barriers#:~:text=L%3De24%CF%80,it%20is%20to%20tunnel%20through.

That website does some example calculations. For barrier of 1 nanometer, the calculated probability for the low energy electron is 1.7% x 10^-4. When that barrier distance is increased to 5 nanometers, the probability drops drastically to 2.1% x 10^-36. If I plug a micrometer distance into the equation (1,000 nanometers), then the probability I get drops profoundly to 1.792% x 10^-7,709. There very probably has never been such an unlikely event to occur in the history of the visible Universe. That's just a micrometer. Millions of kilometers is just not feasible.

I've come across this before. You're using free electrons here as opposed to electrons in their bound state around atomic nuclei, aren't you? There would have to be some special rule/principle governing the behaviour of electrons in orbit around a nucleus allowing them to tunnel to far great distances, or it might be that aspects of quantum theory are incorrect. The explanatory power of this model is too great for me to simply put aside, unfortunately. I think, also, string theory more or less also made the admission that gravitational fields are formed of quanta (particles) of the electrical field (i.e. electrons).

[samcottle (OP)]

Also, the tunneling electrons (from their bound state around atomic nuclei) would encounter potential barriers at some points, but would otherwise largely be tunneling through empty space. I think part of the problem here is that we don't consider electrons in their bound state around atomic nuclei to be tunneling at all, I don't know why either. They certainly don't orbit the nucleus like the Moon orbits the Earth. Hence they must constantly be tunneling to different locations around the nucleus and forming a cloud of probability (that we're familiar with) surrounding atomic nuclei. For reasons, largely due to the composition of the background, I suspect free electrons would, you're right, not be able to tunnel to very great distances.

[Bored chemist]

You're using free electrons here as opposed to electrons in their bound state around atomic nuclei, aren't you?

One of the more memorable mutterings of a Uni lecturer that I recall was one of them saying " you can't paint an electron purple".
He was making the point that you can't label an electron (The proof is to do with exchange proprieties).

So, while it's true that wee are considering free electrons, it's also not relevant.
All electrons behave the same because none of them "knows" that it's free or not.

More importantly, we always do tunnelling experiments with bound electrons, for example the ones in a tunnelling electron microscope tunnel from being bound to the sample to being bound by the probe tip.

This sort of thing (i.e. there are two well known reasons that you are wrong) is why we point out that you are wrong.
That's not "discrimination and gaslighting".

And even if this

Or you're too stupid to understand the words

was true, it would still be your fault for being unclear, wouldn't it?

[samcottle (OP)]

I was referencing the 'word salad' remark, but never mind. Electron microscopes do not use bound state electrons, they fire a beam of electrons through a sample and then detect the electrons. What are you talking about?

[samcottle (OP)]

n.b. just to head you off at the pass, they do not use bound electrons from the probe tip, they pass a current through the sample (i.e. free electrons).

[paul cotter]

BC was referencing the scanning tunnelling electron microscope, not the "regular" electron microscope.

[Origin]

Also, the tunneling electrons (from their bound state around atomic nuclei) would encounter potential barriers at some points, but would otherwise largely be tunneling through empty space.

Electrons don't tunnel through empty space, your statement makes no sense.

They certainly don't orbit the nucleus like the Moon orbits the Earth. Hence they must constantly be tunneling to different locations around the nucleus

Since electrons don't orbit the nucleus like the moon they must be tunneling?  Nope, your wrong.  Electrons are quantum objects and an electrons orbital acts like a standing wave, not a particle tunneling here and there.

I was referencing the 'word salad' remark, but never mind.

The only reason I used the term 'word salad' is because your OP is word salad.  The OP uses a lot of science terms but there is little or no actual science in there.

The explanatory power of this model is too great for me to simply put aside, unfortunately.

I don't see any model (there is zero math, hence no model) just arm waving. 
However I could be wrong, maybe this is some great new idea, so all you have to do is use this 'model' to explain anything.  I look forward to seeing your example.

[Bored chemist]

n.b. just to head you off at the pass, they do not use bound electrons from the probe tip, they pass a current through the sample (i.e. free electrons).

Tunnelling microscopes do use tunnelling.
https://en.wikipedia.org/wiki/Scanning_tunneling_microscope

I personally assisted with the (re)installation of the first (or maybe second) commercial STEM in the UK.
What's your background?