Calculation of the 4D complex number tau.

It is about high time for a new post, now some time ago I proposed looking at those old classical equations like the heat and wave equation and compare that to the Schrödinger equation. But I spilled some food on my notes and threw it away, anyway everybody can look it up for themselves; what often is referred to as the Schrödinger equation looks much more like the heat equation and not like the classical wave equation…

Why this is I don’t know.

This post is a continuation from the 26 Feb post that I wrote after viewing a video from Gerard ‘t Hooft. At the end of the 26 Feb post I showed you the numerical values for the  logarithm of the 4D number tau. This tau in any higher dimensional number system (or a differential algebra in case you precious snowflake can only handle the complex plane and the quaternions) is always important to find.

Informally said, the number tau is the logarithm of the very first imaginary component that has a determinant of 1. For example on the complex plane we have only 1 imaginary component usually denoted as i. Complex numbers can also be written as 2 by 2 matrices and as such the matrix representation of i has a determinant of 1.
And it is a well known result that log i = i pi/2, implicit the physics professors use that every day of every year. Anytime they talk about a phase shift they always use this in the context of multiplication in the complex plane by some number from the unit circle in the complex plane.

In this post, for the very first time after being extremely hesitant in using dimensions that are not a prime number, we go to 4D real space. Remark that 4 is not a prime number because it has a prime factorization of 2 times 2.

Why is that making me hesitant?
That is simple to explain: If you can find the number i from the complex plane into my freshly crafted 4D complex number system, it could very well be this breaks down to only the complex plane. In that case you have made a fake generalization of the 2D complex numbers.

So I have always been very hesitant but I have overcome this hesitation a little bit in the last weeks because it is almost impossible using the complex plane only to calculate the number tau in the four dimensional complex space…

May be in a future post we can look a bit deeper in this danger; if also Cauchy-Riemann equations are satisfied in four real variables, that would bring a bit more courage to further study of the 4D complex number system.

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After the introduction blah blah words I can say the 4D tau looks very beautiful. That alone brings some piece of mind. I avoided all mathematical rigor, no ant fucking but just use numerical results and turn them into analytical stuff.

That is justified by the fact that Gerard is a physics professor and as we know from experience math rigor is not very high on the list or priorities over there…

That is forgiven of course because the human brain and putting mathematical rigor on the first place is the perfect way of making no progress at all. In other sciences math should be used as a tool coming from a toolbox of reliable math tools.

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This post is seven pictures long, all are 550 by 775 pixels in size except for the last one that I had to make a little bit longer because otherwise you could not see that cute baby tau in the 4D complex space.

Here we go:

Just take your time and look at this ultra cute number tau.

It is very very hard to stay inside the complex plane, of course the use of 4 by 4 matrices is also forbidden, and still find this result…

I am still hesitant about using dimensions that are not prime numbers, but this is a first result that is not bad.

End of this post.

What is the inverse Pythagoras theorem?

It is already late in the evening, actually it is past midnight so I will keep the text of this post short. It was a nice day today and this evening I brewed the 23-th batch of a beer known as ‘Spin half beer’. (I name it that way because it contains only half of the dark malts I use in the beer known as dark matter…;) so it has nothing to do with electrons).

This is a very basic post about some ‘inverse Pythagoras theorem’ as came flying by in some math video. I was rather surprised that I have not seen it before but there are so many theorems out there using that old fashioned Euclidian geometry that I might have forgetten all about it.

Within 10 minutes I had a good proof for the 2D version of this ‘inverse Pythagoras theorem’. You can find it in the first picture below.

One day later when I was riding a bit around I tried to find the higher dimensional analog of that easy to understand 2D statement or theorem. And as such it crossed my mind the important role a distance number d played in my proof for the general theorem of Pythagoras that acts on simplexes that are the higer dimensional analog of 2D triangles.

Coming home it was easy to write out the details, but for me it was all so simple that does this stuff deserve the title ‘theorem’? Well make up your own mind about that, but if it is not a real complicated theorem it is still a nice and cute result…

This post is six pictures long (all 550×775 pixels beside the last one that needed a bit expansion because the math did not fit properly so that one is 600×775 pixels).

At times it might look difficult but this is only because it is in a general setting when it comes to the number of dimensions, the basic idea’s are all simple things like taking an inner product with a normalized normal vector.

Here are the six pictures:

That is a cute result but for me the normal vector is just as cute but only a bit harder to write out because that part deals with general setting where the dimension n is not fixed.

For the time being is this the end of this post. See you around my dear reader.

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Addendum added on 30 March 2018: In the previous post I forgot to place a link to the proof of the general theorem of Pythagoras as I crafted it once a long time ago.

Before this link I would like to show you once more how to prove the general theorem of Pythagoras for the 3D case using only the 2D theorem.

After all, that is the first basic step in my proof for the general theorem of Pythagoras…

Here are the two addendum pictures outlining how this basic step from the two dimensional plane to the 3D space goes:

Here is the link to the proof of the general theorem of Pythagoras:

The general theorem of Pythagoras (second and final post).

The general theorem of Pythagoras (second and final post).

Ok that was it, till updates.

A new page on magnetics covering this year 2018.

After a little bit of thinking I decided to open another page on magnetic, mostly the tiny fact that electrons carry magnetic charge and are not magnetic dipoles, covering stuff as it is found in the year 2018.
Of course I will not push that idea for an infinite amount of time but this is about year number four and I still like it to look into the details of all things wrong with the official version of electron spin.
Likely this year will be as the previous years; total 100% silence from all physics professors, you can view that kind of behavior as a combination of being stupid and coward at the same time. This is known as a super position of cowardice and stupidity…
Also this year I will never ever try to attempt to write an official publication on the subject of electron spin, I still estimate the likelihood of rejection above 90% and on top of that I do not like it to be judged by some coward dumb ass.
No, the year 2018 is just another year of strong separation between me and all those university people.
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After having said that, here is the link to the new page three:

http://kinkytshirts.nl/rootdirectory/just_some_math/monopole_magnetic_stuff03.htm

This year I posted four more reasons as why electrons cannot have magnetic dipole properties of their own, basically most stuff observed like the electron pair in chemical bonding is not based on two magnetic dipoles doing ‘mysterious stuff’ but the pair is a sole reflection of the fact the pair has opposite magnetic charges.

Here is a screen shot from where I am now:

A very short description of the content of the four new posted reasons:

Reason 53: It was observed that in the IBM attempts to craft so called magnetic racetrack memory, the domain walls could not be moved by magnetic fields in those nano structures. Very boldly I simply claimed that in all metals with magnetic domains, the domain walls contain (much) more electron pairs…
This was very bold but if you want to shoot my theory out of the sky, the professional professors have to prove that the magnetic properties of the unpaired electron are more or less the same as the electron pair while at the same time upholding the Gauss law for magnetism (no magnetic charges do exist).

Reason 54: The circular magnetic field around circular (copper) wires when they transport electrical current. In my view, dependent on the magnetic charge of the individual electrons they will spiral at the surface of the wire into two different kind of spirals.

Reason 55: If what the video says is true and this is how the electron spin valve works, that is one more contribution to the simple fact electrons carry magnetic charge. It all boils down to the idea that opposite charges attrack while like charges repel.
That is the way such spin valves work.

Reason 56: After watching a lot of so called ‘spin torque transfer’ video’s I was so completely fed up with these people who only do theoretical blah blah blah but never ever in their lives as perfumed princes touch things like a screwdriver, I decided to do a simple experiment that debunkes a lot of that theoretical ‘spin torque transfer’.

Here is picture number two of my very simple experiment that shows there is no spin torque tranfer observed in a time frame of about 25 hours:

It is not observed: The strongest magnets possible in this year against the weakest macroscopic magnet still in my possesion, no spin torque transfer observed…..

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Ok, end of this post. Thanks for your attention.

I am innocent, I did not do it. I just found the numbers tau in the Schrödinger equation your honour…

Judge: But you were caught red handed placing the number tau in a Schrödinger equation while you do not qualify for being a member of the most bright and enlightened persons in our society: The PHYSISCS PROFESSORS.

Reinko: But Judge I can explain, it was that evil guy that Gerard ‘t Hooft who did it. I can prove that because it is on video.

Judge: Yes you already told that into the statements you made after arrest by the police. So we took the freedom and ask Mr. Gerard ‘t Hooft himself about the evil you have done with molesting the Schödinger equation. Mr. ‘t Hoofd said it had to be Hermitian and although I do not know what that means he said that by using anti-Hermitian matrices you, Reinko Venema, you are nothing more as some sadistic pedophile piece of shit.

Reinko: But judge, it is not Hermitian, that is only a trick. You see if you multiply it by the number 1 like 1 = – i squared you see it is not Hermitian.

Judge: Do you think we get complex analysis in law school? We don’t, we asked some experts and all agreed that Gerard is right and you are wrong and right now rewarded by your own evil deeds to 75 years in prison in a maximum security facility.

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After this somewhat strange introduction I repeat I was innocent. I was just looking at a video of a guy that is just like me old and boring.

And that guy, Gerard ‘t Hooft, was able to give me three nice punches in the face.
That is what this post is about; Three punches in the face as delivered by Gerard.

It is the very first time I observe professional physics professors using the number tau while claiming the stuff has to be Hermitian to make any sense.

I was devastated because in my little world of mathematics it had to be anti Hermitian so at a first glimpse it looks like a simple shootout between Gerard and me: Only one can be right…

Let me first show you the Youtube video where right at the start Gerard succeeds to bring my small sack of human brain tissue into an exited state and after that I am rewarded with finding the number tau into the famous Schrödinger equation.

Let me also temper the enthousiasm a little bit because at present date 26 Feb in the year 2018 I only know of one example where three quantum states are rotated into each other:
That is the transport of the color charges as it is found on the quarks inside the proton and neutron…

Here is the video, after that the nine pictures that make up the mathematical core of this new post:

Gerard ‘t Hooft – How Quantum Mechanics Modifies the Space-Time of a Black Hole (QM90)

Let me spare you a discussion on the entire video but only look at what you can find on the very introduction as shown above because all of the three punches at my face are already found there.

Here are the nine pictures for this new post:

For readers who have found themselves lost on what a Hermitian matrix is, here is a wiki:

Hermitian matrix
https://en.wikipedia.org/wiki/Hermitian_matrix

And for readers who have found themselves lost on finding an ‘analytic handle’ about how to calculate matrices like in picture 09, a good starter would be about the calculation of the 7D number tau:

An important calculation of the 7D number tau (circular version).

That’s it, till updates.

Oops; CERN did not find magnetic monopoles.

It has to be remarked that the physics folks are very persistant to keep on trying to find the so called Dirac monopole. How this has come to be is still a miracle to me. After all if the electron has one electric charge and for the rest it is a magnetic dipole, it would look naturally to look for a particle that is a magnetic monopole and an electric dipole at the same time…

But I have never heard about such an investigation, it is only the Dirac magnetic monople and that’s it.

Here is a quote from sciencenews dot org:

If even a single magnetic monopole were detected, the discovery would rejigger the foundations of physics. The equations governing electricity and magnetism are mirror images of one another, but there’s one major difference between the two phenomena. Protons and electrons carry positive and negative electric charges, respectively, but no known particle has a magnetic charge. A magnetic monopole would be the first, and if one were discovered, electricity and magnetism would finally be on equal footing.

Source:

Magnets with a single pole are still giving physicists the slip
https://www.sciencenews.org/article/magnetic-monopoles-single-pole-physics

Comment on the quote: Because in my view I consider the electrons having one electrical charge and one of two magnetic charges, I think we have a nice equal footing of electricity and magnetism… (End of the comment.)

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Back to CERN and stuff. Last month it came out that the MoEDAL experiment has failed in the sense that no magnetic monopoles were observed. Here is a small screenshot from the preprint archive stuff:

Comment: No idea what these people are talking about when they talk about 68.5 times the electric charge… Are they talking about electric charge or magnetic charge?
(End of comment)

Source of the content of the picture above:

detector in 2.11 fb−1 of 13 TeV proton-proton collisions at the LHC.

https://arxiv.org/pdf/1712.09849.pdf

After a bit of searching I found back this beautiful video, coming from CERN, explaining how to find magnetic monopoles. It is clear they never ever studied the electron.

Yeah yeah my dear average CERN related human; what exactly is a magnetic monopole?

Does it have electric charge too and why should that be?

In my view where the electrons carry both electric and magnetic charge, a magnetic monopole with zero electric charge just does not exist.

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Ok, let me bring this post to an end by observing that at CERN they were not capable in the year 2017 of detecting the magnetic monopole as it should exist following the lines of thinking like Paul Dirac once did.

So that is a good thing because after thinking about four years about magnetism it would be horrible for me to find that at CERN they had a major discovery about magnetic monopoles…

Sorry CERN folks, your failure to find magnetic monopoles your way does not prove that electrons are indeed carrying magnetic charge. It just makes it a little bit more plausible that they do…

So my dear CERN folks, thanks for publishing your failure because for me it is another tiny quantum move into the direction of accepting the electron as it is.

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End of this post.

More on the Majorana equation.

Yesterday I finally looked into the so called Majorana equation and it is easy to find where the Dutch universities have gone wrong. At the technical universities in Delft and Eindhoven they use electrons together with a hole that supposedly has a positive electrical charge so that the overall combination of electron and hole is electrically neutral.

And it is very easy to explain: If I am in the right and electrons also carry magnetic charge, the above constellation of an electron and a hole is not magnetically neutral like, for example, the Cooper pairs of electrons in super conductivity.

They want unpaired electrons because the Cooper pairs live there in the nano wire where the super conductivity is so they do not consider an electron pair together with two holes because that is both magnetic and electrically neutral…

No, I do not think that in Delft they found the elusive Majorana fermion. But time will tell because if this way of quantum computing will keep on failing or never get anywhere, I can use that as a future reason of why electrons cannot be magnetic dipoles.

Here is a wiki about the Majorana equation, already at equation number 2 I am lost in the woods because the mass m suddenly goes to the other term in the equation.

Majorana equation
https://en.wikipedia.org/wiki/Majorana_equation

And here is a short video from Youtube where the technical university of Eindhoven explains how they will try to prove the existence of the Majorana fermion as a quasi particle. The video is from 23 August 2017, that is only four and a half months ago.

From the wiki we have this information, what the differential operator with the ‘Feynman slash’ does is actually not important at all. The nice thing here is to understand what they try of find here:
A particle (or a collection of particles, the quasi particles) where all charge is compensated. Apperently the mass related to charge comes in with opposite charge and indeed if you can find solutions to such a wave equation you might hope to find it one day.

Yet in Delft and Eindhoven they hang on to the opinion that electrons are magnetic dipoles and as such they never had a need to put the ‘anti part’ of the magnetic dipole into the problem…

That was more or less what I had to say about the Majorana equation.
Of course I also wish you a happy new year! Till updates.

Prediction for 2018 and beyond: The Delft quantum computer attempts will fail.

Already for a few years the folks at the university of Delft are trying to make a quantum computer. They even teamed up with Microsoft and as memory serves the Dutch government is investing about 100 million € over the course of 10 years.

Only recently I dived into that Delft stuff and the spokeswoman from Microsoft was even talking about a Nobel prize for Leo Kouwenhoven because he seemed to have discovered so called Majorana fermions.

And I just felt sooooo proud that my fellow Dutch guy Leo who is sooooo ultrasmart would have a chance of winning such a prestigious prize like the Nobel prize. I will never get a Nobel prize for my stupid finding of the magnetic monopoles, come on that is not important because I am not a university person and Leo is a full blown physics professor.

After having said that it is nice to observe that the Delft team is trying to craft quantum computer with qubits made from Majorana fermions. So what are Majorana fermions because they have never been found since a guy named Ettore Majorana speculated about stuff like that in 1937? Well these are fermions that are their own anti particle.

It is well known that when you have a particle with a particular charge, the anti particle must have the opposite charge. Now our Leo Kouwenhoven genius from the Delft university is putting an electron into entanglement with an electron hole and as such it has no electrical charge if the electron hole has a positive electrical charge.

Furthermore since an electron entangled with a hole is only like half a fermion they cannot exist on their own so our genius folks from Delft figured out that two of those quasi particles would form a Majorana fermion.

Here is a Youtube video of about one hour long where our super hero Leo explains it all:

Majorana Fermions: Particle Physics on a Chip- Leo Kowenhoven – May 28 2015

Anyway, to make a long story short:

The Majorana particles as found by the heroic members of the Dutch university of Delft have a tiny problem: the electrons carry also magnetic charge beside the electrical charge. So a quasi particle made up of an electron and an electron hole cannot have the Majorana property of being it’s own anti particle…

So my estimation is rather simple: As long as the Delft hero’s keep on ignoring that electrons carry also magnetic charge, they will not succeed. On the contrary they will fail and very likely they will keep on failing because they are university people.

Too much money and too much titles & prestige, why should they change and get a more realistic view on quantum computing?

Before we split, here is a wiki on Majorana fermions. For me it is new that when a fermion is it’s own anti particle the wave function is real valued and not complex valued. As a take away you can also conclude that the Delft hero’s also got the wave function of the electron and electron hole completely wrong. Just like all those people in the science of chemistry who cannot model even the hydrogen molecule properly. So the chemistry people say ‘We need quantum computers’ and Leo Kouwenhoven says ‘I have great ideas in topological quantum computing!’

In my view these people are all crazy, but here is the wiki stuff on Majorana fermions:

Majorana fermions
https://en.wikipedia.org/wiki/Majorana_fermion

Till the next post.

Electron spin as explained by the Scientific American.

In a nice article there are three people explaining, for example, electron spin. The reason to post this here is because they are in climbing order of stupidity and explainer number three gives a total retarded explanation.

Recall once more that the name electron spin is one hundred percent misleading because of what we know of the size of the electron it should certainly be rotating much faster than the speed of light even if all electrical charge was concentrated on the equator of the electron.

I hope that by now my dear reader you know that I think electrons carry beside electrical charge also magnetic charge and as such they come in two flavours:
1) Electrons with a negative electrical charge and a north magnetic charge and;
2) Electrons with a negative electrical charge and a south magnetic charge.

Because particles with mass cannot mover faster than the speed of light, all explanations based on the electron spinning are wrong by definition. Therefore it is often said that electrons (and also protons and neutrons) have so called intrinsic spin so the rotation problem can be avoided.

It has to be remarked once more that this is about the fourth year I am writing about electrons having magnetic charge and that as such they are the long sought magnetic monopoles, but until now I have zero reactions from only one of those professional physics professors… That abundantly shows how dumb they actually are and that there is little use in trying to write a real publication because it is still totally impossible to pass the so called ‘peer review barrier’. I mean; read the quotes I will post from these three people as found in the Scientific American and suppose they would be the ones that do the peer review of my article. What would happen?
Very simple: It will be rejected.

Let’s get started, here is the title and link to the small article in the Scientific American:

What exactly is the ‘spin’ of subatomic particles such as electrons and protons? Does it have any physical significance, analogous to the spin of a planet?
https://www.scientificamerican.com/article/what-exactly-is-the-spin/

The first quote is from Morton Tavel, quote:

“Unfortunately, the analogy breaks down, and we have come to realize that it is misleading to conjure up an image of the electron as a small spinning object. Instead we have learned simply to accept the observed fact that the electron is deflected by magnetic fields. If one insists on the image of a spinning object, then real paradoxes arise; unlike a tossed softball, for instance, the spin of an electron never changes, and it has only two possible orientations. In addition, the very notion that electrons and protons are solid ‘objects’ that can ‘rotate’ in space is itself difficult to sustain, given what we know about the rules of quantum mechanics. The term ‘spin,’ however, still remains.”

Comment: From the macroscopic world we do not observe much ‘deflection’ of, let’s say, bar magnets in the presence of other magnets and magnetic fields. If electrons really were magnetic dipoles, because electrons are so small all magnetic forces would cancel out and we would never observe deflection.
And if Morton Tavel would have done some calculations or estimations, it is extremely hard for electrons to get deflected by non-constant magnetic fields. On the contrary, you need magnetic fields with a gradient of millions of Tesla’s per meter in order to accelerate the electron with only one meter per second squared…
No idea is smarthead Morton Tavel will ever read these words I write about him, but in reason number 50 I did such an estimation. Here is the link:

14 Oct 2017: Reason 50: A calculation on electron acceleration by a magnetic field.
http://kinkytshirts.nl/rootdirectory/just_some_math/monopole_magnetic_stuff02.htm#14Oct2017

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Let’s proceed with the second physics professional, his name is Kurt T. Bachmann and here is the quote from the wisdom he has to share:

“Starting in the 1920s, Otto Stern and Walther Gerlach of the University of Hamburg in Germany conducted a series of important atomic beam experiments. Knowing that all moving charges produce magnetic fields, they proposed to measure the magnetic fields produced by the electrons orbiting nuclei in atoms. Much to their surprise, however, the two physicists found that electrons themselves act as if they are spinning very rapidly, producing tiny magnetic fields independent of those from their orbital motions. Soon the terminology ‘spin’ was used to describe this apparent rotation of subatomic particles.

“Spin is a bizarre physical quantity. It is analogous to the spin of a planet in that it gives a particle angular momentum and a tiny magnetic field called a magnetic moment.

Comment: It is important to know that the original SG experiment was done with evaporated silver ions, this beam of silver ions was split in two parts by just a few unpaired electrons. If the professionals would do the calculations they would find this cannot be explained by inhomogeneous magnetic fields. The fact that no one says this makes clear they have never done the calculations needed…
That is the same as a carpenter that refuses to use the handsaw when needed or simply states: I do not need a screw driver, I just talk to these screws until the matter is resolved. Normally the carpenter would get fired but all those physics professors are glued to their seats living in ‘academic freedom’.

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The third person is truly 100% crazy, the term ‘intrinsic spin’ for the electron was used in order to avoid the problems with the spinning of an electron. And what does this weirdo named Victor J. Stenger make from this? Quoting this idiot:

“Spin is the total angular momentum, or intrinsic angular momentum, of a body. The spins of elementary particles are analogous to the spins of macroscopic bodies. In fact, the spin of a planet is the sum of the spins and the orbital angular momenta of all its elementary particles. So are the spins of other composite objects such as atoms, atomic nuclei and protons (which are made of quarks).

“In classical physics, angular momentum is a continuous variable. In quantum mechanics, angular momenta are discrete, quantized in units of Planck’s constant divided by 4 pi. Niels Bohr proposed that angular momentum is quantized in 1913 and used this to explain the line spectrum of hydrogen.

Comment: This is so utterly stupid it is hard to comment upon. By talking about intrinsic angular momentum he only shows that he thinks the electron is spinning. So he is a nutjob for sure.

 

Ok, end of this post without pictures but with three idiots as found in the Scientific American. Now some people might think I better be a little bit more diplomatic but from 1992 until 2012 I was very very diplomatic about higher dimensional number and thought that if you give people time enough that in the end they will do the right thing.

Two decades of diplomacy are gone, now I know that when confronted with idiots you better explain why they are idiots…

See you in the next post my dear reader.

On reason number 51 and 52 as why electrons cannot be magnetic dipoles.

This week I posted reason number 51 and 52 on the other website in the magnetic pages , page 1 contains 41 reasons and is from 2015 & 2016. Page 2 is covering what I wrote this year on the subject.

Very often when professional physics professors start explaining electron spin they do blah blah blah like the earth is spinning around it’s axis and also spinning around the sun. This is a retarded explanation because the strength of the magnetic stuff related to the electron cannot be explained by the electron spinning around it’s axis.

Now I was watching a few video’s from Microsoft where they explain the subject of topological quantum bits. The Dutch based university of Delft is also participating in that project of making topological quantum bits and the researchers from Delft are thinking they have found a quasi particle named the Majorana particle. This Majorana particle seems to be it’s own anti-particle and according to Leo Kouwenhoven such a quasi particle is comprised of a hole and an electron…

The fact they claim this stuff is it’s own anti particle struck me as odd, it is well known that if a particle meets it’s anti particle the result is a violent annihilation of both particles and it is very very hard to imagine that if two holes and two electrons meet there will be violence…

Anyway this made me think of what actually happens when in those high energy particle physics experiments like in CERN we observe the creation of an electron and a positron. The positron is the anti particle of the electron.

And even in such an elementary thing it makes no sense the electron is a magnetic dipole. It might look logical that if one particle has spin up the other created particle must have spin down.
But if we assume there is spinning around an axis, both the electron and the positron must rotate into the same direction, this is a direct violation of the principle of conservation of angular momentum.

So if electron spin is spinning around some axis and we want to preserve the total amount of angular momentum, they should be spinning in opposite directions but that would create two equal magnetic spins and that is also nonsense.

But if you assume that electrons and positrons carry beside electric charge also magnetic charge, all of a sudden the creation of the electron-positron pair becomes much more logical:
If the freshly created electron has north pole magnetic charge, the positron will have south pole magnetic charge…

That makes sense while the professional physics standard explanation does not make sense. Here is a link to the stuff involved in reason number 51:

17 Dec 2017: Reason 51: Spin properties of the positron.
http://kinkytshirts.nl/rootdirectory/just_some_math/monopole_magnetic_stuff02.htm#17Dec2017

Reason number 52 covers the fact that the Juno probe around Jupiter has observed that in the aurora’s on Jupiter the electrons also seem to be coming from the atmosphere of Jupiter. That would not be a problem if there were some electrical fields to move the electrons, tiny problem is those electrical fields seem to be missing often.

So all those so called professional physics professors have it straight in their face: how do those electrons get accelerated. I think it is the magnetic fields from Jupiter that do this, just like on the sun and so but before our precious ppp’s will arrive at the same conclusion we will be many centuries later… (Or not?)

In the next picture you can see how this was told in the news as you can find it on Youtube channels like Scishow (often more show than science but anyway they serve some part of the public).

Oh oh Catlin Hofmeister, they are not pulled up but expelled by the magnetic field of Jupiter… Reason number 52:

19 Dec 2017: Reason 52: Jupiter aurora’s without the electrical field acceleration.
http://kinkytshirts.nl/rootdirectory/just_some_math/monopole_magnetic_stuff02.htm#19Dec2017

Ok let’s say goodbye for the moment, till updates in the next post!

An important calculation of the 7D number tau (circular version).

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:

Matrix logarithm calculator
http://calculator.vhex.net/calculator/linear-algebra/matrix-logarithm

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.

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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.