Testing for Tolerance

[Aetherwizard]

23 minutes ago, Phi for All said:

!

Moderator Note

You say this as if nobody mentioned specific faults with your concept. It's not unwillingness when flaws in your equation are pointed out. It seems like you're unwilling to answer questions about the flaws, and instead claim the responses are simply hidebound denials. 

Help us all progress in understanding. You're trying to persuade us that your idea has merit, and others are asking about the points where your ideas and what we observe don't match. It's part of the process, and it's not helped by claiming these questions are merely denial. Nobody is claiming you're wrong just because. They've been very specific, so please drop this line of argument, and please answer the questions. 

 

What questions relative to my theory do you want to see answered?

[swansont]

2 hours ago, Aetherwizard said:

The weak interaction is "unitless," yet you have no problem calling it a "force." I show the weak interaction as the ratio of the electrostatic force to the magnetic force. 

Did I call it a force? Did I say anything about the weak interaction at all in this thread?

2 hours ago, Aetherwizard said:

I show the fine structure as a ratio between solid angle, one-spin electrostatic charge, and steradian angle, half-spin magnetic charge. It is hardly unitless.

And yet mainstream physics says it’s unitless. If you’re going to use terminology, the default is that it means what is in common use.

You agree the constant you want to use is not unitless, so you must mean something else. Come up with a new name for it.

 

2 hours ago, Aetherwizard said:

Yes, it is my contention that the fine structure constant is different for protons and neutrons. And don't tell me that neutrons have no electrostatic charge.

Then come up with a model and a way to test it, or evidence from existing experiments

2 hours ago, Aetherwizard said:

A neutron is a magnetically bound electron and proton as evidenced by beta decay.

That’s more speculation on your part. There’s already a model in use that’s different, and having a bound electron in this way is not consistent with known physics. Plus you need to account for the antineutrino 

So, again, we need a model and evidence. This is not true just because you say so.

 

2 hours ago, Aetherwizard said:

The fact that their electrostatic charges neutralize each other does not mean the electron and proton have given up their electrostatic charges.

I’m not aware that anyone claims this to be the case.

2 hours ago, Aetherwizard said:

I hypothesize these electrostatic charges still interact with the electron and proton magnet charges.

Great. Let’s see the model.

42 minutes ago, Aetherwizard said:

What questions relative to my theory do you want to see answered?

We want the theory, for starters.

[exchemist]

43 minutes ago, Aetherwizard said:

What questions relative to my theory do you want to see answered?

Just read the posts made in response to you up to this point and look for the sentences with a question mark at the end. 

[swansont]

2 hours ago, Aetherwizard said:

I only have so much time in my life.

As is true for everyone 

2 hours ago, Aetherwizard said:

Applying my theory to all physics branches and reexamining the basis of all physics is on my to-do list. You have to start somewhere. It would go a lot quicker for me if I didn't meet with so much senseless cynicism and unwillingness to explore simple concepts first. You won't take the time to learn what I am presenting, and instead, your reaction is to deny anything you do not already know. Have you heard the lament about people who are smart but not intelligent?

Likewise, we’d like to know your ideas are on solid footing before we waste time learning the subsequent details. 

e.g. you claim a neutron is an electron magnetically bound to a proton. If that’s a basis for your ideas, I’d like you to justify it. Because if you can’t, i.e. it’s bogus, then anything built on it is bogus as well. 

[Mordred]

3 hours ago, Aetherwizard said:

 

Set aside your to-do list of questions you want to be answered for the moment. Instead, look at my presentation and see if it warrants further development. Perhaps you will discover insights or fix genuine problems in my theory. 

 

I have looked at your literature. The lack of any relationships beyond magnitude only values is a HUGE lack in regards to your goals. You cannot accurately describe anything involving kinetic energy and momentum terms including force of anything particle related without it. You cannot describe the relationship between the E and B fields without using vectors and spinors either. 

They are essential. That is precisely why the majority of particles physics including the Feymann path integrals include the dot and cross product terms. It does so through the Euler-Langrangian equations combined with the probably functions of the Schrodinger equation for QM and the Klein-Gordon equations of QFT.

I can't even confirm any accuracy of any of your equations if you didn't apply those vectors and spinors.

 

Edited May 10 by Mordred

[Aetherwizard]

For all those complaining about not knowing enough about my theory, the forum rules prevent me from providing links to relevant texts. If you ask me for equations, I have to reformat them for ASCII characters, which is too time-consuming for my present schedule. If you want to learn it bit by bit, that is fine, but be patient. It is a vast theory with many differences from the Standard Model. And no, it does not answer every question physicists have asked or will ask. 

1 hour ago, exchemist said:

Just read the posts made in response to you up to this point and look for the sentences with a question mark at the end. 

Those questions directly related to my theory were answered. Notice that with all the answers I gave, nobody has commented on the theory presented. Does anybody here know anything about the quantum Hall effect? Not a single word. If you want to know a prediction my theory makes that is verified through experiment, then follow me in the discussion about magnetic charge.

To progress in my theory, it is essential to see the magnetic charge's validity. If you want to learn my theory, engage me regarding the magnetic charge and the equations I produce using it. The theory goes much deeper than just a line of text. 

[Ghideon]

2 hours ago, Aetherwizard said:

What questions relative to my theory do you want to see answered?

https://www.scienceforums.net/topic/133936-testing-for-tolerance/?do=findComment&comment=1266513
https://www.scienceforums.net/topic/133936-testing-for-tolerance/?do=findComment&comment=1266462

 

[exchemist]

1 hour ago, Aetherwizard said:

For all those complaining about not knowing enough about my theory, the forum rules prevent me from providing links to relevant texts. If you ask me for equations, I have to reformat them for ASCII characters, which is too time-consuming for my present schedule. If you want to learn it bit by bit, that is fine, but be patient. It is a vast theory with many differences from the Standard Model. And no, it does not answer every question physicists have asked or will ask. 

Those questions directly related to my theory were answered. Notice that with all the answers I gave, nobody has commented on the theory presented. Does anybody here know anything about the quantum Hall effect? Not a single word. If you want to know a prediction my theory makes that is verified through experiment, then follow me in the discussion about magnetic charge.

To progress in my theory, it is essential to see the magnetic charge's validity. If you want to learn my theory, engage me regarding the magnetic charge and the equations I produce using it. The theory goes much deeper than just a line of text. 

I’m interested in the same question as @Ghideon, which you have yet to answer: how would chronovibration be measured? What would the experimenter need to do in order to demonstrate that chronovibration is real? This has been asked more than once now in this thread and your answers have not been very clear.

[Mordred]

6 hours ago, Aetherwizard said:

 

Yes, it is my contention that the fine structure constant is different for protons and neutrons. And don't tell me that neutrons have no electrostatic charge. A neutron is a magnetically bound electron and proton as evidenced by beta decay. The fact that their electrostatic charges neutralize each other does not mean the electron and proton have given up their electrostatic charges. I hypothesize these electrostatic charges still interact with the electron and proton magnet charges.

Lets look at charge directly regardless if it's magnetic or otherwise. Charge requires divergence ie source and sink of a field the magnetic field itself isn't divergent. The magnetic moment is.

[joigus]

On 5/8/2024 at 10:57 AM, joigus said:

Does that same ratio hold for every charged particle in the universe?

On 5/9/2024 at 4:49 PM, Aetherwizard said:

Yes, but more than that.

I'm afraid that wouldn't work in keeping with what we know about electromagnetism.

If the ratio of magnetic to electric charge is the same in all particles in the universe, you can then rotate every (electric, magnetic) pair to a new definition,

\[ \left(\textrm{new electric quantity}\right)=\cos\alpha\left(\textrm{electric quantity}\right)-\sin\alpha\left(\textrm{magnetic quantity}\right) \]

\[ \left(\textrm{new magnetic quantity}\right)=\sin\alpha\left(\textrm{electric quantity}\right)+\cos\alpha\left(\textrm{magnetic quantity}\right) \]

And the new magnetic charge can be defined to be zero, with all the physics being the same. The Lorentz force law that @Mordred mentioned would have to be re-defined to be,

\[ \boldsymbol{F}=q_{e}\left(\boldsymbol{E}+\boldsymbol{v}\times\boldsymbol{B}\right)+q_{m}\left(\boldsymbol{B}+\boldsymbol{v}\times\boldsymbol{E}\right) \]

These are called duality transformations for the electromagnetic field. Unfortunately, neither the Wikipedia article, nor the Scholarpedia one, do a very good job of explaining what it is.

If you're interested, I can do more, or suggest more material as an exercise. It's not hard.

Edited May 10 by joigus
Latex editing

[Aetherwizard]

22 minutes ago, exchemist said:

I’m interested in the same question as @Ghideon, which you have yet to answer: how would chronovibration be measured? What would the experimenter need to do in order to demonstrate that chronovibration is real? This has been asked more than once now in this thread and your answers have not been very clear.

Listen very carefully.

The prevailing view is that a physical linear timeline is real. A physical linear timeline, such that matter could dilate from one time frame to another, requires each time frame to be populated with a complete copy of the physical Universe in each time frame. An object cannot move among time frames unless there is a physical place to arrive at. There is zero physical evidence for physical matter in any other time frame than the present moment. There is much more than can be said about the lack of physical evidence for a physical linear timeline.

You are asking me to provide physical evidence demonstrating that chronovibration is real, but you have no evidence for the prevailing belief.

Chronovibration is proposed as the oscillation of forward and backward time such that the net result is the present moment. Physical observations are made of subatomic particles with half-spin properties, but the half-spin does not apply spatially to rotation or angular momentum. In chronovibration, the half-spin nature of subatomic particles applies to the particles seeing only the forward time direction. This would cause subatomic particles to age in the forward time direction while physically existing in a present moment, a present moment that makes no progress toward the past or future. This is what we physically observe.

No physical matter has ever been observed leaving the present moment or appearing suddenly from a different moment. So, the physical linear timeline concept has zero physical evidence, and the chronovibration concept agrees with the observable physical evidence.

As I mentioned before, and this is my answer to observing chronovibration, the photon speed constant and the Compton wavelength constant are empirically determined. Therefore, the time component, whether linear or cyclical, is automatically inferred as a constant. This type of reasoning occurs throughout physics. 

I do not have access to all the current technology, either physically or in its literature. This leaves the possibility that someone with available resources would be able to devise an experiment that could physically prove or disprove the concept of chronovibration. Please do not impose more upon me than I can handle, especially with my meager finances.

 

19 minutes ago, joigus said:

If the ratio of magnetic to electric charge is the same in all particles in the universe

I didn't claim that the ratio of magnetic to electric charge is the same in all particles. In fact, I disagree with that statement. I said the "mass to magnetic charge" ratio is the same in all particles in the Universe. 

However, I appreciate you applying your skills to what I am presenting, even if you didn't initially understand what I had stated. I am hoping to inspire others with greater skills in electrodynamics to apply Standard Model tools to the new unit system I devised. 

Although the QMU is based on dimensional analysis, the relationships of the units are different from MKS/SI and some mathematical treatments. I suggest that several of the current math operators in electrodynamics should be dimensional units. If the system proves valid, it would greatly simplify physics and open its understanding to more students. 

Maybe my system will crash and burn, but my success with QAHE and the Gamma Ray single peak should spark interest in physicists looking for better ways to quantify physics.

56 minutes ago, Mordred said:

Lets look at charge directly regardless if it's magnetic or otherwise. Charge requires divergence ie source and sink of a field the magnetic field itself isn't divergent. The magnetic moment is.

No, let's not. Yes, it is true that both electrostatic fields and magnetic fields possess divergence. Divergence is not due to the charge; it is a property of the field. Getting into fields is a valid line of inquiry, but let's first gain a common understanding of the geometry of the charges to better understand the fields they produce, at least within my physics theory. 

I already understand the Standard Model narratives about point particles, their vectors, probability functions, etc. If I was here to improve on the Standard Model, I would say so. Instead, I have said that I am proposing a different understanding of fundamental physics. I propose a different paradigm based on the same constants and data but with different ontologies. This results in a modified set of equations with new equations added.

I would not mind sharing my explorations into magnetic moment, but not until we have the same understanding of magnetic charge and its importance in physics.

Please tell me that you can understand how the experimental evidence for the QAHE strongly supports my claim for the existence of magnetic charge. You don't have to say I'm right; acknowledge that you understand the simple math that supports my claim.

[Ghideon]

37 minutes ago, Aetherwizard said:

The prevailing view is that a physical linear timeline is real.

The prevailing view in physics does not assert that a 'physical linear timeline' is real. General relativity is widely accepted and demonstrates that time is relative and not linear (and also absolute). The theory's equations are non-linear.

Edited May 10 by Ghideon

[Aetherwizard]

5 hours ago, Ghideon said:

The following two statements do seem to contradict each other, can you clarify? (In case you missed the question earlier)

On 5/7/2024 at 8:18 PM, Aetherwizard said:

Chronovibration is measured the same way photon speed is measured.

 

On 5/9/2024 at 9:49 AM, Aetherwizard said:

the job for directly detecting chronovibration would be for the experts at NIST

Before I could explain anything, you need to explain how these statements conflict. And yes, I missed this post earlier. I answered the other part of your question in another reply.

3 minutes ago, Ghideon said:

The prevailing view in physics does not assert that a 'physical linear timeline' is real. General relativity is widely accepted and demonstrates that time is relative and not linear (and also absolute). The theory's equations are non-linear.

The prevailing view in physics states that time dilation is real. Within Minkowski coordinates, time dilation is defined as moving among time frames, which quantifies a physical linear timeline. If you are going to say there is no movement among time frames, then there is no physical basis for claiming the existence of time dilation. Either physical matter moves among time frames, or it does not.

And don't make the mistake of thinking I disagree with either Special or General Relativity. I fully agree with the equations of both but disagree with the ontologies. 

If there is no physical evidence for a physical linear timeline, then the time dilation ontologies cannot be accurate. Yet the correct ontology could be that space is quantized and experiences density gradients. Clocks orbiting at higher altitudes move through a denser space than at lower altitudes. Thus, clocks at higher altitudes tick more ticks per orbit due to space density gradients than at lower altitudes. Thus, the clocks will lose synchronization exactly as calculated, but they will remain in the present moment and not disappear into a different time frame. No satellite has ever popped out of the present moment or popped in from a different moment, thus falsifying the concept of time dilation.

Chronovibration removes the possibility of time dilation. Physical evidence supports chronovibration, and no physical evidence supports a linear physical timeline. 

[swansont]

3 hours ago, Aetherwizard said:

For all those complaining about not knowing enough about my theory, the forum rules prevent me from providing links to relevant texts. If you ask me for equations, I have to reformat them for ASCII characters, which is too time-consuming for my present schedule. If you want to learn it bit by bit, that is fine, but be patient. It is a vast theory with many differences from the Standard Model. And no, it does not answer every question physicists have asked or will ask. 

Surely there is some basic premise that’s testable. 

Every bit of effort you put into telling us how you can’t present your theory is effort you could have put into telling us your theory.

[Aetherwizard]

23 hours ago, Ghideon said:

The units of Planck's constant and electron's angular momentum are the same and their values differ. Angular momentum of an electron is quantized and depends on quantum numbers.  

They are both angular momentum. hbar is used in probability theories, which I am not presenting.

3 minutes ago, swansont said:

Surely there is some basic premise that’s testable. 

Surely you have seen my posts regarding the prediction of magnetic charge and its tested result in the quantum anomalous Hall effect. 

[swansont]

1 hour ago, Aetherwizard said:

You are asking me to provide physical evidence demonstrating that chronovibration is real, but you have no evidence for the prevailing belief.

Since you have only presented a strawman of the mainstream view, this is moot. Relativity says nothing about “time frames” and copies of the physical universe.

That sounds vaguely like the many-worlds interpretation of QM, but one must note that MWI is an interpretation, and not actually QM. Similarly you seem to be offering an interpretation of the prevailing view, which is not the actual science.

[joigus]

1 hour ago, Aetherwizard said:

I didn't claim that the ratio of magnetic to electric charge is the same in all particles. In fact, I disagree with that statement. I said the "mass to magnetic charge" ratio is the same in all particles in the Universe. 

I'm sorry to say you did. Here it is:

On 5/8/2024 at 3:18 AM, Aetherwizard said:

The magnetic charge of the electron in my work is reciprocal to the electrostatic charge. The relationship is as follows:

e² = 8πα · e_emax²

Here, α is the electron fine structure, e² is the electrostatic charge, and e_emax² is the electron magnetic charge.

(my emphasis) Reciprocal? What does that mean? I would have guessed "inversely proportional", but no. You at least displayed the maths, so there's no doubt what you meant.

So yes, you did claim that, as then I asked,

On 5/8/2024 at 10:57 AM, joigus said:

Does that same ratio hold for every charged particle in the universe?

quoting you, so there could be no ambiguity about what I meant. Then you said,

On 5/9/2024 at 4:49 PM, Aetherwizard said:

Yes, but more than that.

And now you change your statement.

Other members have problems with the way you use units, justify your concept of "chronovibration", and ignore quantum mechanics, so taken as a whole, I'd say I have very well-founded misgivings that your theory could ever be turned into a sound one, considering you only claim to explain the anomalous quantum Hall effect.

You've proven to me you have no understanding of what magnetic charge means in the context of the classical electromagnetic theory.

Edited May 10 by joigus
minor addition

[Mordred]

1 hour ago, Aetherwizard said:

 

No, let's not. Yes, it is true that both electrostatic fields and magnetic fields possess divergence. Divergence is not due to the charge; 

Yes let's as this is incorrect. The B field is non divergent and does not have a point of origin.

The E field is divergent and has a point of origin the B field does not. I thought you claimed to understand the vectors and spinors of the cross product ? 

Of course your likely going to state " Not in my model"

Well that's well described by modern physics via Maxwell equations.

Edited May 10 by Mordred

[exchemist]

1 hour ago, Aetherwizard said:

Listen very carefully.

The prevailing view is that a physical linear timeline is real. A physical linear timeline, such that matter could dilate from one time frame to another, requires each time frame to be populated with a complete copy of the physical Universe in each time frame. An object cannot move among time frames unless there is a physical place to arrive at. There is zero physical evidence for physical matter in any other time frame than the present moment. There is much more than can be said about the lack of physical evidence for a physical linear timeline.

You are asking me to provide physical evidence demonstrating that chronovibration is real, but you have no evidence for the prevailing belief.

Chronovibration is proposed as the oscillation of forward and backward time such that the net result is the present moment. Physical observations are made of subatomic particles with half-spin properties, but the half-spin does not apply spatially to rotation or angular momentum. In chronovibration, the half-spin nature of subatomic particles applies to the particles seeing only the forward time direction. This would cause subatomic particles to age in the forward time direction while physically existing in a present moment, a present moment that makes no progress toward the past or future. This is what we physically observe.

No physical matter has ever been observed leaving the present moment or appearing suddenly from a different moment. So, the physical linear timeline concept has zero physical evidence, and the chronovibration concept agrees with the observable physical evidence.

As I mentioned before, and this is my answer to observing chronovibration, the photon speed constant and the Compton wavelength constant are empirically determined. Therefore, the time component, whether linear or cyclical, is automatically inferred as a constant. This type of reasoning occurs throughout physics. 

I do not have access to all the current technology, either physically or in its literature. This leaves the possibility that someone with available resources would be able to devise an experiment that could physically prove or disprove the concept of chronovibration. Please do not impose more upon me than I can handle, especially with my meager finances.

 

 

I'm not asking you to do the experiments. I'm asking what experiment could, at least in principle, be done to show that Chronovibration is real, and what would one expect to observe? You do not seem able to answer this. 

From your earlier posts you seem to say the frequency of this chronovibration is equal to c/Compton wavelength. As the Compton wavelength of a particle is h/mc, that would mean the chronovibration frequency is c²m/h, i.e. proportional to mass.  Do I have that right?  

If so, is there some way to show that the chronovibration frequency of, say, the electron, is lower than that of the proton, by a factor of 1836?

How could this frequency be detected and measured? 

 

[Ghideon]

1 hour ago, Aetherwizard said:

Before I could explain anything, you need to explain how these statements conflict. And yes, I missed this post earlier. I answered the other part of your question in another reply.

 

On 5/8/2024 at 3:18 AM, Aetherwizard said:

Chronovibration is measured the same way photon speed is measured.

measuring the speed of light (photon speed) is relatively easy and does not require experts at NIST. And hence it contradicts:

On 5/9/2024 at 4:49 PM, Aetherwizard said:

the job for directly detecting chronovibration would be for the experts at NIST 

 

[Mordred]

On 5/7/2024 at 9:22 PM, Mordred said:

Granted there is likely a lot you haven't posted yet with regards to your hypothesis. I will leave the time dilation aspects to others, for the time being. The question I have is how does your theory work with Lorentz force laws? In particular regard to the cross product relations between the two as described by Maxwell equations. I'm hoping you have at some point looked at the E and and B fields under vector/spinor field treatments. Understandably you likely haven't been able to post all the pertinent details to your hypothesis yet. The equations you have posted thus far only provide scalar quantities. 

 So understanding the vector relations between the two fields of your hypothesis would be useful. Well truthfully they will become rather essential. If your hypothesis has different relations this has huge ramifications in terms of the SM model in particular the Electromagnetic stress energy momentum tensor.

So I'd like to be clear how your model handles the following formula with regards to each field 

 

F⃗ =q(E⃗ +v⃗ ×B⃗ )

 

 

the × is the cross product. Not to be confused with the multiplication symbol " *"

for any posts I make on this thread I will be using vector notation with A⋅b for example being the inner product, the cross product A×B for the cross product. I will likely not need the outer product for this discussion. for multiplication I will use A∗B this is also for the benefit of other readers.

Also for other readers benefit. As magnetic force as per magnetic force law 

 

F⃗ B=qv⃗ ×B⃗ 

 

 

there is 3 key consequences. v⃗  is particle vector

1) As the magnetic force is perpendicular to v⃗  it cannot change the the magnitude of the velocity. 

2) as it does not have force parallel to the particle velocity it does no work.

3) Motion of a charged particle under the action of a magnetic field alone is always motion with constant speed. However it can alter the velocity direction.

same relations apply between E and B.

 

 

Why do you think I mentioned this on page one  had you looked at the cross product term you would have recognized what I stated is precisely what is described by the Lorentz force law. Other applicable laws being the magnetic law and Amperes law.

The cross product term has consequences in regard to the magnetic field that makes it unique from the E field which involves the dot product.

It is also why the magnetic moment becomes critical as it has different vector relations from the magnetic field. It's critical to understanding how magnets work.

Edited May 10 by Mordred

[KJW]

 

2 hours ago, Aetherwizard said:

In chronovibration, the half-spin nature of subatomic particles applies to the particles seeing only the forward time direction.

It's funny that you say this because I have also had the idea that the arrow of time is connected to spinors.

 

 

1 hour ago, Aetherwizard said:

And don't make the mistake of thinking I disagree with either Special or General Relativity. I fully agree with the equations of both but disagree with the ontologies.

If you disagree with the ontology, then in what way are you agreeing with special and general relativity? It seems to me that you think time dilation is a physical effect acting on clocks. This conflicts with the principle of relativity which says that the laws of physics are the same in all frames of reference. This means that an ideal clock ticks at the same intrinsic rate in all frames of reference, and therefore time dilation is the result of something other than a physical effect acting on the clock. You say you agree with the equations, but you seem to disagree with the principles upon which the equations are based. It's as if you think Einstein got lucky with a wrong theory that happens to make correct predictions.

 

 

[Mordred]

8 hours ago, Aetherwizard said:

 

Those questions directly related to my theory were answered. Notice that with all the answers I gave, nobody has commented on the theory presented. Does anybody here know anything about the quantum Hall effect? Not a single word. 

 

little point getting into quantum Hall effect if you can't get the basic relations correct.

classical motion in a magnetic field being

\[m\frac{dv}{dt}=-ev\times B\]

set the magnetic field to the z plane the particle moves in the transverse plane 

so you get using time differentials

\[m\ddot{x}=-eB\\dot{y}\]

\[m\ddot{y}=eB\\dot{x}\]

gives

\[x(t)=X-Rsin(\omega_Bt+\theta)\]

and

\[y(t)=Y+Rcos(\omega_Bt+\theta)\]

cyclotron frequency given by

\[\omega_B=\frac{eB}{m}\]

 

oh look there's that cross product term once again, first equation enough said

If you like I can take this through the Drude model to get the explicit expression for conductivity.

however lets just skip to the conductivity tensor.

\[\sigma \begin{pmatrix}\sigma_{xx}&\omega_{xy}\\-\sigma_{xy}&\sigma_{xx}\end{pmatrix}\]

\[sigma\frac{\sigma_{DC}}{1+\omega^2_B\tau^2}\begin{pmatrix}1&-\omega_B\tau\\-\omega_B\tau&1)\end{pmatrix}\]

with

\[\sigma_{DC}=\frac{ne^2\tau}{m}\]

the off diagonal terms gives rise to the hall effect resistivity being the inverse  of conductivity

here is a peer review coverage.

https://phas.ubc.ca/~berciu/TEACHING/PHYS502/PROJECTS/21-Thomas.pdf

This should show that if you never looked at vectors and spinor relations you could never describe the Hall effect with any degree of accuracy.....

that is the classical treatment I gave the link provides the quantum treatment.

for reference Drude model. 

https://en.wikipedia.org/wiki/Drude_model

Edited May 11 by Mordred