I really took the time to compose this post; basically it is not extremely difficult to understand. Everybody who once has done matrix diagonalization and is still familiar with the diverse concepts and ideas around that can understand what we are doing here.
It is the fact that it is seven dimensional that makes it hard to write down the calculations in a transparent manner. I think I have succeeded in that detail of transparency because at the end we have to multiply three of those large seven by seven matrices with each other and mostly that is asking for loosing oversight.
Luckily one of those matrices is a diagonal matrix and with a tiny trick we can avoid the bulk of the matrix calculations by calculating the conjugate of the number tau.
Just like in the complex plane where the conjugate of the number i equals -i, for tau goes the same.
Basically the numbers tau are always the logarithm of the first imaginary component. But check if the determinant is one because you can use the tau to craft an exponential curve that will go through all basis vectors with determinant one.
This post is 10 pictures long (size 550 x 775), in the beginning I use an applet for the numerical calculation of the matrix representation of the first imaginary unit in 7D space, here is the link:
Two years back in 2015 after I found the five dimensional numbers tau every now and then I typed in a higher dimensional imaginary unit and after that only staring at the screen of the computer: How to find those numbers as the log applet says…
The method as shown here can be applied in all dimensions and you now have a standard way of crafting exponential curves in all spaces you want. This method together with the modified Dirichlet kernels that provide always a parametrization of the exponential curve form a complete description.
Ok ok those modified Dirichlet kernels always have period pi while this way to calculation the log of the first imaginary unit is always related to the dimension (recall that the 7D first imaginary unit l has the property l^7 while for the complex multiplication in 7D space we have l^7 = -1), but it is very easy to fix the Dirichlet kernels to the proper period in the time domain you want.
The most difficult part of this post is in understanding the subtle choice for the eigenvalues of tau = log l, or better; choosing the eigenvalues of the matrix representation involved. That makes or breaks this method, if done wrong you end up with a giant pile of nonsense…
Have fun reading it and if this is your first time you encounter those matrices with all these roots of unity in them, take your time and once more: take your time.
If you have never seen a matrix like that it is very hard to understand this post in only one reading…
I am glad all that staring to those numerical values is over and we have the onset of analytical understanding of how they are in terms of the angle 2 pi over 7.
The result is far from trivial; with the three or five dimensional case you can use other ways but the higher the dimension becomes the harder it gets.
This method that strongly relies on finding the correct diagonal matrix only becomes more difficult because the size of the matrices grows. So only the execution of the calculation becomes more cumbersome, the basic idea stays the same.
I have no idea what the next post is going to be, may be a bit of magnetism because a few days back I got some good idea in explaining the behaviour of solar plasma included all those giant rings that shoot up and land in another spot of the sun.
And we also have those results from the Juno mission to Jupiter where the electrons also come from Jupiter itself without the guidance of electrical fields. But in the preprint archive I still cannot find only one work about it, that might be logical because often people do not write about stuff they don’t understand…
Ok, that was it. I hope you liked it & see ya around.
All details will be in the next post but I succeeded into using matrix diagonalization in order to find this seven dimensional number tau.
For people who do not understand what a number tau is, this is always the logarithm of an imaginary unit. Think for example at the complex plane and her imaginary unit i. The number tau for the complex plane is log i = i pi/2.
The problem with finding numbers tau becomes increasingly difficult as the number of dimensions rise. I remember back in the year 2015 just staring at all those matrices popping up using internet applets like the next one:
Yet back in the year 2015 I was riding on my noble iron horse (a cheap bicycle) through the swamps surrounding the village of Haren and suddenly I had a good idea. Coming home I tried the idea of matrix diagonalization out in 3 dimensions and it worked.
Now I think that most readers who visit this website are familiar with the concept of finding a diagonal matrix D containing all eigenvalues of a given matrix M. Once you have the eigenvalues you can calculate the eigenvectors and as such craft your matrix C containing all eigenvectors.
You can write the stuff as next: D = C^-1 M C.
Suppose you don’t know what M is but I give you the matrices D, C and the inverse of C. Can you find the matrix M?
Yes that is a beerwalk, all you have to do is calculate M = C D C^-1 and you are good to go.
But with the logarithm comes a whole lot of subtle things for making the right choice for the eigenvalues that you place inside the diagonal matrix D. It turns out you only get the desired result if you use arguments in the complex plane between minus and plus pi.
This is caused by the fact that you always need to make a cut in the complex plane if you want to work with the complex logarithm; but it is a bit surprising that only the cut where you leave out all real negative numbers (and zero of course) makes the calculation go perfect and in all other cases it ends in utter and total disaster.
In the next three pictures I show you some screen shots with numerical values of matrix representations and the logarithm of those matrix representations.
The goal is to find mathematical expressions for the observed numerical values that are calculated via the above mentioned de Pade approximation. We don’t want only numerical approximations but also catch the stuff in a mathematical formulation.
At the end of the third picture you see the end result.
So it took some time to find this result, I wasted an entire week using the wrong cut in the complex plane. And that was stupid because I had forgotten my own idea when riding my noble iron horse through the Harener swamps…
The result for the seven dimensional number tau (circular version) as calculated in the next post is a blue print for any dimension although I will never write stuff down like in a general dimension setting because that is so boring to read.
In part this post picks up where I left the stuff of the missing equations back in the year 2015. The missing equations are found inside the determinant equation; for this to succeed we must factorize determinant of the matrix representations of higher dimensional numbers. A well known result from linear algebra is that the determinant is also the product of the eigen values; so we need to craft the eigen value functions that for every X in our higher dimensional number space give the eigen values.
These eigenvalue functions are also the discrete Fourier transform of our beloved higher dimensional numbers and these functions come in conjugate pairs. Such a pair form two factors of the determinant and if we multiply them we can get rid of all complex coefficients from the complex plane.
A rather surprising result is the fact that if we subtract a cone equation from a sphere equation we get a cylinder…
This post is also a way of viewing the exponential circles and curves as an intersection of all kinds of geometric objects like the unit sphere, (hyper) cones, (hyper) planes and (hyper cylinders. Usually I represent it all as some analysis but you can take a very geometric approach too.
I have no idea if the shape of the higher dimensional curves is studied as a geometrical object; I suspect this is not the case since the use of complex numbers outside the complex plane is very seldom observed. The professionals just want their tiny fishing bowl (the complex plane) and declare it an Olympic swimming pool…
Well, let it be because these people will never change.
All in all this post is 20 pictures long (size 550 x 775) so it is a relatively long read.
The pictures of the graphs were all made with an applet named Animated drawing, here is a link and there you can find it under ´Online calculators and function plotters´±
The above thing should give identical zero for all x.
An important feature of exponential curves in spaces with an odd number of dimensions is that they all are inside a hyperplane. The hyperplane says the sum of the coordinates is always 1. If you cut and past the next sum of the five coordinate functions you see that you always get one for all x:
At last the link to the original update from 2015 where I found the missing equations for the first time. But all I knew they were hidden inside the determinant. A few weeks ago I decided to take a better look and the result is this post.
Recently I am working on a relatively long post where I try to take a much more geometric approach to finding exponential circles and exponential curves. That post is also going forward from a few years back when I was searching for the so called missing equations.
The problem of the missing equations does not arise until you start working in five dimensions or higher; the equations as generated by the sphere-cone equations are just not enough to end up with a one dimensional curve.
Back in the time I simply took a few weeks until I had found the answer: The missing equations can be found inside the determinant!
For example if you have a 17 by 17 matrix in 17 variables (the so called matrix representations of 17-dimensional number systems), all you have to do is factorize this determinant and from those factors you can craft the extra needed equations.
Weirdly enough you find a hyper plane and a bunch of hyper-cylinders.
So in the next post I try to show you how you can have a very geometric approach to finding the higher dimensional exponential curves as the intersection of a sphere, a hyperplane, a bunch of cones and a bunch of cylinders.
In my old notes I found a mysterious looking line of squares of cosines with their time lags. That was from before I solved the problem and this ‘solution’ has all kinds of faults in it.
That is this small post; it is about something that does not work.
It is just 3 pictures long (550 x 775 pixels):
It was just over two years back I wrote that long update on the other website about the missing equations, I was glad I took those weeks to solve this problem because it is crucial for the development of general higher dimensional theory on this detail.
I hope next week I am ready with the new long post, after that I will likely pick up magnetism again because I finally found out what the professionals mean when talking about ´inverted V-s’; that means there is also an electric field accelerating the particles in the aurora’s of earth and Jupiter.
Tiny problem for the professionals: At the Jupiter site, regardless of inverted V-s yes or no, the plasma particles get accelerated anyway…
So that looks like one more victory for Reinko Venema and one more silence from the professional professors.
After all that magnetism stuff it is about time to throw in a tiny bit of simple math around how to find the derivative and primitive (the integral) of the inverse of a function.
In most (introductory) textbooks on calculus you will find a nice way of finding the derivative of the inverse of a given function f(x) defined on the real line. For integration where you need to find the anti-derivative there is also a very elegant way of calculating those, but in my life I have never ever seen it in print on paper in an actual existing book.
Now last week I came across a video where another guy claimed that finding the primitive in this way was completely new but within 60 seconds with the help of the Google search engine you can find this is not the case.
According to a wiki on the subject of integration of the inverse of a function, the first know results date back to 1905. This is a remarkably short time ago and for myself speaking I think that many folks found this way too but for some strange reasons it never popped up to the surface. It is strange to observe that for example the method of the calculation of variations was invented included those fine differential equations that form the way to find for example the path of least action or minimal time but somehow those people never found the way to integrate the inverse of a function…
On the other hand, I have seen it myself that there can easily be a complete vacuum in mathematics; in my first year at the university I invented the so called product integral. Normally when you calculate an integral you can view that as adding up all the area under the graph of a certain function, with a product integral you do the same but you do not add it up but you multiply all stuff.
And in it’s most natural setting you do that with raising a function f(x) to the power dx.
That was my invention but although product integration has been studied for over a century, nobody had ever taken a function to the power dx…
Now enough of the blah blah blah done, this post is four pictures long and the wiki stating this cute formula was found in the year 1905 is the next:
This post is four pictures (550 x 775 pixels), here they are:
So that was it for this post, see ya around my dear reader.
Updated on 16 Oct 2017:
Today I found that video back where some guy made those unsubstantial claims that this result was never ever found in the entire history of mathematics. That is not true but it is strange that the derivative is in every introductory course or book while the integral version is always absent.
We can safely jump to the conclusion that the integral version is not widespread known and this causes authors of those books not to include it.
The video goes under the title:
Rare Integration Strategy – You won’t learn this in Calculus.
So that was it for this update on this post, see ya around my dear reader.
In the previous post where I tried to demonstrate that it is impossible to accelerate electrons via exposing them to non-uniform magnetic fields contains a tiny error of 1/2.
I did forget to multiply the Bohr magneton with the electron spin number of 1/2.
Is this a serious problem? Not for me, because now the magnetic dipole moment of the electron is halved you need double the gradient of the applied magnetic field. So we need a spatial gradient of only 10 million Tesla per meter in order to accelerate the electron by 1/10 of the gravitational force here on earth.
I have decided to leave the pictures in the previous update unchanged because if a fault of forgetting a factor of 1/2 leads to a rejection by so called professional physics professors, that only shows these people are garbage to begin with.
Here is the correction that I will not show in the previous post:
Lately I viewed a video of some folks who did throw a bureau chair into a medical MRI machine of 3 or 6 Tesla stationary magnetic field. The magnetic field of the MRI machine pulled at the chair with a force of about 1000 kg (ok that would be 10 thousand Newton).
Just imagine what a magnetic field with a gradient of 10 million Tesla would do…
And on top of that, in the original Stern-Gerlach experiment it were not loose unpaired electrons that did get accelerated but silver ions that are many thousands times more massive as our poor unpaired electron that makes the entire silver ion moving…
So instead of 10 million Tesla / meter, 10 billion Tesla per meter should be more reasonable in order to explain the results of the Stern-Gerlach experiment from the year 1922. (That is if you base your theories on the assumption that elementary particles like electrons cannot be magnetic monopoles.)
End of this correction, please take your time in order to understand the content of the previous post because that is much more important! Till updates.
This post is based on a video from Dr. Brant Carlson who is talking about a spin half particle in a magnetic field. I have selected this video because Mr. Carlson is rather good at explaining the stuff so although I hefty disagree with most of his conclusions this post should not be viewed as some kind of character attack on Mr. Carlson.
Let me first give you the video, you can watch it now or later.
Spin 1/2 in a B field:
This post is just about two details;
1) Is electron spin conserved yes or no?
2) The lack of insight Mr. Carlson shows while discussing the Stern-Gerlach experiment.
Let’s start with 1) Is electron spin conserved?
If you read some wiki’s about the Stern-Gerlach experiment you often come across the repeated measurements of electron spin. There are of course infinitely many ways to measure electron spin if it were a vector but the professionals only do it in three directions known as x, y and z.
It is important to never forget all those measurements are done during the application of a vertical magnetic field, the vertical magnetic field is there all the time and within that boundary condition they derive the properties of the spin operators that measure spin into the x and y axis directions.
When you read about the Stern-Gerlach experiment it is often stated that if you measure spin in the vertical direction, half of the electrons go up and the other half go down.
If after that you make a measurement into the x or y direction of the up electrons, once more the beam of electrons will split 50/50.
If after that you make a new z-axis direction measurement, once more it will split into 50% up and 50% down states of the electron.
To put it simple: There can not be conservation of electron spin if a second measurement rams half of the electrons into another spin state… Anyway this is what the official generally accepted knowledge strongly suggests: if changing the applied magnetic field pushes electrons out of their previous state it looks like there is no conservation of electron spin.
From the beginning of the video in the next picture you see the so called Pauli matrices and the two Pauli matrices for the x and y direction have interesting eigenvectors:
These eigenvectors suggest a super position of the two eigenvectors into the z-axis direction and very important:
If you square the probability amplitudes you always get 50%.
This is a theoretical result, I have never found any experimental proof validating these theoretical considerations. Here is the picture that is a screen shot from the beginning of the video:
So if Sz is already measured, suppose it is plus h bar over 2, if after that Sx is measured and it is minus h bar over 2, is spin conserved?
I would say no, but I think the electron has one of two possible magnetic charges and with charge it does not matter in what kind of direction you measure it.
The professional physics professors think that electron spin in the z-axis direction is independent of any direction perpendicular to the z-axis direction. So they will argue that it is irrelevant what the outcome of Sx is because the spin in the z-axis direction will be conserved because it is angular momentum…
As I see it, repeated measurement of electron spin in orthogonal directions should always give the same result. But there are serious problems with an experiment like that:
1) It should be done inside a cage of Faraday because em-radiation reacts with the electrons, 2) It should be done in a vacuum because the electron beam should not interfere with the electrons in the air molecules.
If done properly, in my view you should always measure the same spin for the electron.
So far the pondering if electron spin is conserved, one thing is clear: the last word is not spoken on that detail.
Detail 2 is about the staggering lack of insight Mr. Carlson shows upon that very important experiment: the Stern-Gerlach experiment. The weird thing in this experiment is the fact that half of the unpaired electrons go into the direction of the stronger part of the inhomogeneous magnetic field while the other half goes into the direction of the weaker part.
When I first learned about the SG experiment I was completely puzzled by the fact the electron went into the direction of the weaker part of the magnetic field.
Here is a picture of the Stern-Gerlach experiment, one of the faults that so many physics people expose is that it are ‘silver atoms’. But it is silver vapour and that is over 2000 degrees Celsius. Also silver is a diamagnetic material; at present day we know that if a metal has no unpaired electrons it is diamagnetic and as such repels magnetic fields very weakly… (Cute detail: the electron pairs in a diamagnetic material start to spin in such a way that the outside magnetic field is partly offset, but it does not fade away and as such the spinning electron pair is the smallest scale super conductivity possible. Even at room temperature…)
By the way, silver has 47 protons so there should be one unpaired electron in a neutral silver atom.
One of the problems with electrons being a magnetic dipole is that the electron pair is also a magnetic dipole but there are huge differences between the behaviour of diamagnetic materials (containing only electron pairs) and para & ferro magnetic materials that have unpaired electrons.
Since in the original Stern-Gerlach experiment the beam of silver ions was split in 2 we can conclude that it is likely that only one unpaired electron was responsible for this to happen. To understand the result a bit; the nucleus of a silver atom or ion is about 108 thus 47 protons and 61 neutrons. Different isotopes might have another number of neutrons but anyway: the protons is about 1800+ times as heavy as the electron so one unpaired electron moves the mass of a silver nucleus that is about 108 times 1800 or about 200 thousand times the mass of the electron.
Now why should electrons move to the weaker part of the applied magnetic field?
You always hear explanations like the Larmor frequency that makes the electrons that are anti aligned with the applied magnetic field that prevent them from alignment with the magnetic field.
I think that these Larmor frequencies are much more like a tiny ball on an elastic string, just like electrons can vibrate under the application of an electric field.
If true, in my view only electrons that are part of an atom/molecule or ion will produce this so called Larmor frequency while if you put a magnetic field on a plasma nothing will happen…
Here is a nice picture of some stuff with spin 5/2, that means there are five unpaired electrons. By the way, did you notice that the official professional professors just add up the electron spin like it is a charge and not a vector?
But the official theory says electron spin should be viewed as a tiny vector…
Anyway, in the picture you see that as the applied magnetic field increases one by one the electrons start vibrating. In my view this suggests that at a particular strength of the B field the electron comes loose and vibrates a short time as a tiny ball on an elastic string.
The main problem is still not solved: Why do the electrons in the Stern-Gerlach experiment go into the direction of the weaker parts of the inhomogeneous magnetic field???
Why do these magnetic dipoles not turn in order to get attracted by the stronger parts of the magnetic field?
In my view this is because the electron is not a magnetic dipole but a particle that carries a north or a south magnetic charge.
How does Dr. Brant Carlson explain this very strange behaviour of the unpaired electron?
From the video of Dr. Carlson we observe that for inhomogeneous magnetic fields the classical way of calculating the force on a (macroscopic) magnet is given by:
This is easy to understand: The mu is the dipole moment of lets say a bar magnet, B is the applied external magnetic field. If I remember it correctly you should take the inner product against the gradient of B but let not put salt on all snails.
With the above mechanism Dr. Brant wants to explain as why just one electron can pull an entire silver ion from it’s original trajectory. But an electron is very very tiny, it is about 10 to the minus 15 in size. Let us give Dr. Brant the benefit of doubt and suppose the dipole distance in the electron is 10 times the size of the electron or 10 to the power minus 14.
This tiny distance gives rise to almost no difference in magnetic field strength yet the lonely unpaired electron moves the silver ion that is about 200 thousand time as heavy as the electron is.
May be the professional physics professors believe this, but I don’t.
The electron is just too small to give a significant change in the path of the silver ion…
At 28 minutes and 55 seconds in the video I completely loose the line of reasoning as done by Dr. Carlson; we only see some blah blah blah with exponential circles from the complex plane while the main problem that the tiny electron makes a significant change in the path of the silver ion is completely skipped.
Here is scientific disaster in a small screenshot:
Also in this point in time in the video Dr. Brant Carlson mentions the spins into the x and y directions; he claims that the spin relaxation into those directions is so short lived that it does not have any influence…
According to how I view the magnetic stuff as being a charge on the electron, it does not matter if the electron goes through a homogeneous magnetic field or some erratic inhomogeneous magnetic field. If the electron carries a south magnetic charge it will always be attracted to the north pole of the applied magnetic field.
So that is answer 1 to the four questions our brave Dr. Carlson is asking us at the end of this video:
Yeah yeah, check your understanding…
In the next part of this post we are going to use the formula for the force on a magnetic dipole in a non-uniform magnetic field as given by Dr. Brant Carlson above. In order to keep stuff as simple as possible I will multiply the magnetic moment of the electron against the gradient of the magnetic field while demanding the electrons are accelerated with a speed of 1 meter per second every second.
The conclusion is relatively staggering: The gradient of the applied magnetic field must be about five million Tesla in order to get only 10% of the gravitational force on the electron.
It becomes even more staggering if you remark that in the original Stern-Gerlach experiment the moved silver ions are about 200 thousand times as heavy as one unpaired electron. So the applied magnetic field should be also about 200 thousand times as big giving something that likely is not living inside this universe.
1) I used an electron size of 10 to the power -15 meter and
2) I used a dipole magnetic field around the electron that is 10 times as long so 10 to the power -14 meter.
If you do that, the outcome is a staggering gradient of 5 million Tesla per meter so one thing is very very clear: The acceleration as observed in the original Stern-Gerlach experiment from the year 1922 cannot explained by using an unpaired electron having a bipolar magnetic field…
The whole calculation is just two pictures long:
The conclusion is majestic:
If we want the electron to have only an acceleration of one tenth of the earth gravity field while using electron dimensions 10 to the minus 15 and the magnetic field of the electron about 10 times as bit, in that case you need the extreme gradient of five million Tesla per meter…
I was very amazed by this result I found three days back, but I checked and checked my calculations, did I do something wrong or so? Yet I cannot find any fault, furthermore we have to take into account that the professional physics people like Dr. Brant Carlson and thousands and thousands of this colleagues never ever show a calculation like this.
Five million Tesla is so far off the scale, here on earth the strong magnetic field as for example used in MRI scanning in hospitals are about 3 to at most 6 Tesla. We can safely conclude that the acceleration of electrons by magnetic fields in not caused by the supposed electron dipole moment.
For myself speaking I am glad I finally did this easy calculation and I have to thank Dr. Brant Carlson for making this video as shown above because that detail made me irritated enough to finally make the calculation. I am always a bit hesitant when it comes to physical calculation because they are not my first nature, math is often much more simple to me while with physics you also have to keep an eye if your SI units fit properly and so on.
The word count of this post is now over 2200 words, most of the time I try to limit the word count of a post to about 500 words so this is a very long post relative to that.
Lets call it the end and till updates my dear reader.
The last week I have been working on one of those many video’s out there about spin half particles. To be precise it is a video from a guy named Brant Carlson and at the end this guy comes up once more with a way of calculating the force on a dipole magnet in a non-uniform magnetic field.
I had seen stuff like that before but never tried to make the actual calculation, but yesterday I made it finally and the result was just so bizarre that I just checked and checked over where I made some stupid error.
But I cannot find any error in my easy to understand calculations, so what did I do?
Dipole magnets can have a net force on them in a non-uniform magnetic field because the force on the north pole can differ from that on the south pole.
So I just said: I want the acceleration of the electron to be 1 so only 1/10 of the gravitation force. I used an electron size of 10 to the power -15 and a size of the dipole magnetic field around the electron 10 times as big so 10 to the power -14.
The answer is staggering: For an acceleration of one extra meter per second you need a gradient in the applied magnetic field of about 5 million Tesla per meter. This is totally crazy, as a comparison most MRI machines in hospitals use a magnetic field of 3 to at most 6 Tesla.
Furthermore in the original Stern-Gerlach experiment it were silver ions that were accelerated and a silver atom or ion is about 200 thousand times as heavy as one electron. So in order to get the same acceleration you need a magnetic gradient of about one trillion Tesla per meter…
All in all it looks like a have another perfect reason as why electrons cannot be magnetic dipoles. So that is a good thing.
In the meantime I want to make another advertisement for the next video of about one hour long that is a good oversight upon this very important experiment from the year 1922.
The Stern-Gerlach experiment is so important because I have found out that almost one year later the professional physics professors still do not have a clue about what is happening in that experiment.
And from the beginning the understanding of the outcome of this experiment was a disaster. The Stern & Gerlach folks even thought they discovered spatial quantization…
And Stern later became the first assistant to Einstein, yet Einstein never understood the outcome of the experiment either because if an electron carries both an electric and a magnetic charge this has great influence on understanding light and other em-radiation.
If in the morning you look into a mirror to see your pretty face, all light gets mirrored by the free electrons in the metal that makes up the mirror. But if electrons have two magnetic poles, the magnetic parts of the em-radiation cannot react with the electron and no photon would get mirrored…
Anyway, here is the good but long oversight video once more:
Ok, lets leave it with that for the time being. I think that in a few days time the next relatively long post will be ready. So see you around!
In the beginning of this month I wrote in just 20 minutes of time a new reason as why electrons cannot be magnetic dipoles. I just came across a few news articles on a few of those websites popularizing science, it was about the amazing strength of the Jupiter aurora’s as discovered by the Juno spacecraft.
Only later I found out that writing stuff in just 20 minutes of time is asking for trouble, I completely skipped the fact that the Jupiter aurora’s are partly caused by other things than the aurora’s on earth. The explanation done by the official scientists is that on earth the vertical magnetic field is accompanied by an electric field and that this electrical field is what accelerates the electrons down to earth.
Here is a link with a short description of the stuff involved:
Interesting quote from the beginning of the Nature article:
The most intense auroral emissions from Earth’s polar regions, called discrete for their sharply defined spatial configurations, are generated by a process involving coherent acceleration of electrons by slowly evolving, powerful electric fields directed along the magnetic field lines that connect Earth’s space environment to its polar regions.
Comment: This is something I definitely need to study much more because electrons only get accelerated by electrical fields if the earth would be positive. But if my little theory of electrons accelerated by magnetic fields is true, in that case over the life of the solar system the sun would have ejected more electrons than protons and all planets with a magnetosphere would have taken in more electrons than protons.
Hence the sun should be positively charged and the earth should be negatively charged.
And indeed, the earth has a negative charge. It goes under the bizarre name of fair weather potential. Here is the link:
So the last word is definitely not spoken on that detail; we also must take into account that for professional physics professors they can only think of electron acceleration as done by electrical fields. Just look into any standard course in plasma physics and you always only see that Lorentz force thing. And of course this is directly related to the fact that the pppp (pppp = professional plasma physics professors) consider the electron a magnet dipole, there is no experimental proof for that but over there anything goes as long as the Maxwell equations are followed…
Here is a picture of a bit of solar plasma; the plasma is made up of spin half particles and guess what? They always follow the magnetic field lines so if you ask a pppp as why these particles do this they likely will say that there is an electric field parallel to the magnetic field lines…
And life, life will go on.
May be my next reason as why electrons cannot be magnetic dipoles is once more the temperature of the solar corona. That is another unsolved problem for about 75 years now and indeed it is very strange to observe that the surface of the sun is like 7000 degrees Celsius while the solar atmosphere (the corona) goes from like one million to four million degrees Celsius.
The picture above came from the next video:
ScienceCasts: The Mystery of Coronal Heating
And it makes me wonder; there are so much video’s out there where solar plasma is ejected out and it gets accelerated before your eyes but still the pppp keep on hanging to their stuff like only electrical fields can do this…
Often when I am out I try to do a bit of math while riding my noble iron horse known as that old bicycle. The disadvantage of doing math on your bike is that one the one hand you cannot go very towards complicated stuff where you need pencil and paper but on the other hand you can get deep by getting some good idea’s.
And only when you get home and you have access to pencil & paper you can check if the stuff can be written out and see how your idea’s survive in the battle for attention from your brain.
After the previous post about magnetism I was only thinking ‘Why not do some pure 3D complex number stuff again’? But the math well is a bit dry lately when it comes to 3D complex numbers. May be this has a bit to do with the total and utter silence from the so called ‘professional math people’ who excel in staying silent…
But a few times it crossed my mind to do that mind boggling factorization of the Laplacian once more; if I would make a top 10 or top 25 list of the most strange results found this factorization of the Laplacian would end very high.
Yet when I check my own website, all that has to be said was already said about one year ago; on 05 August 2016 I posted the next seven pictures long post upon the factorization of the Laplacian using so called Wirtinger derivatives.
So there was little use in writing that stuff out again when there is, as usual, never ever any signal from the ‘professionals’ who rather likely are busy spending their too large salaries on stuff they think is important…
In another development I came across the latest video from the Mathologer, it is very interesting because he claims that the famous Euler identity is not from Euler at all.
But Mr. Mathologer comes up with what is one of the famous Euler stuff, anyway a long long time ago it was one of the details that made Euler famous was finding what the sum of squared reciprocals was: 1/1^2 + 1/2^2 + 1/3^2 + ….
Over 25 years back I did the same calculations as the Mathologer invites you to so let me share the video with you. At first it looks a bit difficult but all you need to do is think about how to write out those infinite products as sums and after that you apply the age old trick of equalling the left and right side of the equation.
May be in a future post we will be diving a bit deeper into this because Mr. Mathologer has nice news upon who found what but he skips all that stuff like how to write the entire functions from the complex plane as (infinite) products.
Furthermore he does not explain as why the given infinite product would be valid anyway…
Ok, may be in a next post I will be diving a bit deeper in all those kinds of infinite products.
Or may be it will be something completely different, anyway till updates.
Update from 22 August 2017:
By sheer accident while I was only watching a video about why there is such a break between higher math and higher physics, I came across some weird stuff from a guy named Edward Witten.
And the talk was about so called Seiberg-Witten monopoles, so my interest was aroused because I cannot allow plagiarism of course.
Anyway it turns out that Mr. Witten and his Seiberg pal talk about massless monopoles without laughing. The concept of a massless monopole is so idiot that normal people with just a tiny bit of self respect would never talk about that.
Anyway to make some long story short, Mr. Witten is also Mr. String Theory. You know that kind of theory that is impossible to validate in physical experiments so it is the opposite of what I do because if electrons carry magnetic charge it could be found in more and more experiments…
But the Witten guy wrote about Dirac operators and once more my interest was aroused and I looked it up: Dirac operators are differential operators D and if you square them you get the Laplacian…..
Basically when you try to find operators D that square to the Laplacian it is more like ‘operator problem looking for a fitting math space’ while in my above factorization of the Laplacian it is a math space (3D complex and circular numbers) that want a factorization.
In the wiki you also observe in example number 4 that Clifford algebras are named a possible candidates, that is true but a few remarks are at their place.
That is the content of the next two small pictures:
Ok, this wasn’t how I more or less planned the next update but when idiots come along talking about massless monopoles beside having deep fun I also have the right to expose the names of the idiots in question…
Let’s leave it with that, till updates my dear reader.