# The last theorem of Fermat does not hold for the 3D so called Gaussian integers.

On the one hand it is a pity I have to remove the previous post from the top position. Never ever I would have thought that the Voyager probes would be a big help in my quest of proving that electrons are magnetic dipoles. On the other hand this post is about Gaussian intergers for the 3D complex and circular numbers and it is with a bit of pride that I can say we have a bunch of beautiful results because the last theorem of Fermat does not hold in these spaces.

The last theorem of Fermat is a kind of negative result, it says that it is impossible for three integers x, y and z that x^n + y^n = z^n, this for integer values of n greater than 2 of course. (For n = 2 I think most readers know it is possible because those are the Pythagoras triples.)

Anyway I succeeded into writing the number 3 as the sum of two Gaussian 3D integers that are also divisors of zero. So this pair of integers, in this post I name them A and T because they are related to the famous 3D numbers alpha and tau, are divisors of zero so as such AT = 0. As such as a denial of the Fermat theorem, an important result as posted here is that A^n + T^n = 3^n. So on the 3D complex & circular numbers this result is possible while if you use only the 2D complex plane and the real line this is not possible…
But there are plenty of spaces where the Fermat conjecture or the last theorem does not hold. A very easy to understand space is the ring of integers modulo 15. In this ring there are numbers that do not have a multiplicative inverse, say 3 and 5. And if inside this ring you multiply 3 and 5 you get 15 and 15 = 0 in this ring… Hence inside this ring we have that 8^n = 3^n + 5^n (mod 15) also contradicting the Fermat stuff.

I did some internet searches like ‘Fermat last theorem and divisors of zero’ but weirdly enough nothing popped up. That was weird because I view the depth of the math results related to this divisor of zero as the depth of a bird bath. It is not a deep result or so, just a few centimeters deep. But sometimes just a few centimeters can bring a human mind into another world. For example a long time ago when I still was as green as grass back in the year 1986 I came across the next excercise: Calulate the rest of 103 raised to 103 and divided by 13. I was puzzled, after all 103^103 is a giant number so how can you find the rest after dividing it by 13? But if you give that cute problem a second thought, after all that is also bird bath deep because you can solve it with your human brain…

This post is 11 pictures long, all of the standard size of 550×775 pixels. Because I could not find anything useful about the last Fermat theorem combined with divisors of zero I included a small addendum so all in all this post is 12 pictures long.

After so much Gaussian integer stuff, there is only one addendum about the integers modulo 30. In that ring you can also find some contradictions to the standard way of presenting the last theorem of Fermat.

Ok, if you are still fresh after all that modulo 30 stuff, for reasons of trying to paint an overall picture let me show you a relatively good video on the Kummer stuff. Interesting in this video is that Kummer used the words `Ideal numbers´ and at present stuff like that is known as an ideal. For myself speaking I never use the word ´ideal´ for me these are ´multiplicative attractors´ because if a number of such an ideal multiplies a number outside that ideal, the result is always inside that ideal. Here is a relatively good video:

And now you are at the end of this post. Till updates.

# Voyager probe says: Solar electrons accelerated to 670 times the initial speed…

In the first place I wish you all a happy new year & let’s hope for some improvement this year when it comes to the new corona virus.

It seems that the Voyager probes, who are now in interstellar space, have done a remarkable discovery when it comes to electron speeds coming from the sun. This was found when observing electron bursts that originate from solar bursts, first the electrons are detected while the plasma shock wave itself only arrived weeks later. This is a happy finding because it now is very hard to deny electrons get accelerated by magnetic fields because they are all magnetic monopoles. Of course 100% of the university people will deny that electrons are magnetic monopoles, this is a clear case of the law of conservation of retardness…;)
Anyway let me post a few quotes, the first quotes come from space.com. Here is a link: https://www.space.com/nasa-voyager-electron-bursts-interstellar-space. My comment is in a bold font.

The Voyager mission has detected a new type of “electron burst,” which will provide insights into the mechanisms of flaring stars, a new study reports.

“The idea that shock waves accelerate particles is not new,” corresponding author Don Gurnett, professor emeritus in physics and astronomy at the University of Iowa,
said in a statement.

“Physicists believe these electrons in the interstellar medium are reflected off of a strengthened magnetic field at the edge of the shock wave, and subsequently accelerated by the motion of the shock wave,” the University of Iowa said in the same release. “The reflected electrons then spiral along interstellar magnetic field lines, gaining speed as the distance between them and the shock increases.”

Comment: The above is retarded nonsense that shows university people think that electrons cannot be accelerated by magnetic fields and as such you get all that blah blah blah about shockwaves that can accelerate particles. If memory serves these are Alvén waves, but it is straight in your face: 670 times as fast and that is far out of the realm any Alvén wave can do.

Since it is a joyful day, why not include some fictional pictures representing what likely is one of the Voyager probes in space:

From a website under the name extremetech.com I found the next cute quote. A CME is a solar coronal mass ejection while the ISM is the inter stellar medium:

Each time one of these big CMEs reaches the ISM, the researchers have noted an electron burst in advance — the shockwave itself didn’t arrive until 13 to 30 days after the high-energy cosmic ray electrons. It’s counterintuitive to see this signal showing up ahead of the shockwave, but the team says this is all thanks to the properties of magnetic field lines in the ionized gas of the ISM, which are apparently almost perfectly straight. Large CMEs punch through the heliopause and interact with these field lines, causing some of the electrons inside to accelerate along the magnetic straightaways. They can reach relativistic speeds, about 670 times faster than the shockwave that originally delivered them to the edge of the solar system. That’s why Voyager 1 and 2 see the electron burst before the CME shockwave.
Scientists have never seen electrons accelerated ahead of a shockwave like this. It’s an entirely new mechanism and one that could help us better understand the ISM.

Comment: Just another example of how retarded all those explanations are. It has nothing to do with the ISM but only with electrons getting accelerated by magnetic fields because electrons are magnetic monopoles. It serves as another example of a law from the social sciences namely the conservation of retardness inside academic organizations.

Link from the quote:

Ok, that was it for this update. Once again a happy new year and thanks for your attention.

05 Jan 2021: Correction & addendum: May be I should have included a link to the ‘scientific article’ the whole stuff was based on. Here is a link to that: https://iopscience.iop.org/article/10.3847/1538-3881/abc337

Anyway you have to pay if you want to read that article so I won’t do that.

Yet in my line of thinking where electrons are always magnetic monopoles, they come in two different kinds like the south pole and north pole magnetically charged electrons. Also they are never in a mixed state of ‘spin up’ and ‘spin down’. Just like in the hydrogen atom the proton and electron never get confused what particle carries the electric charge…

But hey, let’s ask the professional physics community once more to bring forward some experimental proof that the electron is actually a magnetic dipole… Of course they do not have such experimental proof or at least some kind of validation, so they will keep on talking weird stuff when it comes to electron spin.

End of the Correction & addendum thing.

# Another tiny victory for electrons being magnetic monopoles? Solar corona temperature ‘explained’.

Since the official version of the electron is that it is a magnetic dipole, as such it cannot be accelerated by magnetic fields. But often people do not understand why but if I explain it via atomic hydrogen all of a sudden everybody thinks ‘hey that is logical’.
Explanation via atomic hydrogen:
Atomic hydrogen is made from one proton and one electron and as such it cannot be accelerated by electrical fields.
End of the explanation.

Ok ok the electric field can be so strong that the hydrogen atoms get ripped apart but as long as that is not the case it can’t be accelerated by any electric field. Now if electrons are truly magnetic dipoles, if that were true they cannot be accelerated by magnetic fields.

Tiny problem: Every idiot looking at those beautiful video’s from the sun can see with their own eyes that the plasma gets accelerated by magnetic fields… And there are more problems; the surface temperature of the sun is far below that of the solar atmosphere or the solar corona.

In the last five years I have given plenty of explanations of how those solar loops and stuff likely work. It is very likely that below all those sun spots the plasma is actually rotating, spitting out the electrons that are getting much more accelerated compared to the protons and as such we have a giant dynamo made from rotating plasma.
Well nobody talks about that because university people only talk about the stuff you find in expensive journals like Nature or Science. And of course I am not going to waste my money on journals that are too expensive anyway & read only by overpaid perfumed princes from the universities…

But let’s go to the video stuff from Anton Petrov. He talks about Eugene Parker and Mr. Parker is the guy who’s name is used in the Parker solar probe. Already in the 1970-ties Eugene explained how the solar corona could be so hot compared to the surface of the sun. According to Anton he explained it via mini flares coming from the surface heathing the atmosphere of the sun. With such an explanation Eugene Parker avoided being a pariah by stating that this is only possible if electrons and protons are not magnetic dipoles but are all magnetic monopoles and as such carry magnetic charge. My estimate is that both Eugene and Anton do not have any fucking clue as why the plasma gets accelerated, if you keep on hanging to that retarded Gauss law for magnetism it is very hard to explain stuff like that.
Anyway, here is the video and the title is:
We Finally Know Why Sun’s Corona Is So Extremely Hot
I would add: No you don’t, observation is not explanation.

Observing solar plasma acceleration by magnetic fields is not an explanation if your belief system is the standard model of physics in general and the Gauss law for magnetism in particular.

Anyway, Anton rightly remarkes that those mini solar loops & flares are only observed on a tiny part of the sun this does not prove the overall temperature of the solar corona…

He is right with that, Let me end this post with two pictures and after that we will split and say goodbye until the next year 2021.

And the last picture, it is not a mini-loop but one of those giant loops:

Ok, that was it for the last post of the year.
See you in the next year.

# The total differential for the complex plane & the 3D and 4D complex numbers.

I am rather satisfied with the approach of doing the same stuff on the diverse complex spaces. In this case the 2D complex plane and the 3D & 4D complex number systems. By doing it this way it is right in your face: a lot of stuff from the complex plane can easily be copied to higher dimensional complex numbers. Without doubt if you would ask a professional math professor about 3D or higher dimensional complex numbers likely you get a giant batagalization process to swallow; 3D complex numbers are so far fetched and/or exotic that it falls outside the realm of standard mathematics. “Otherwise we would have used them since centuries and we don’t”. Or words of similar phrasing that dimishes any possible importance.

But I have done the directional derivative, the factorization of the Laplacian with Wirtinger derivatives and now we are going to do the total differential precisely as you should expect from an expansion of the century old complex plane. There is nothing exotic or ‘weird’ about it, the only thing that is weird are the professional math professors. But I have given up upon those people years ago, so why talk about them?

In the day to day practice it is a common convention to use so called straight d‘s to denote differentiation if you have only one variable. Like in a real valued function f(x) on the real line, you can write df/dx for the derivative of such a function. If there are more then one variable the convention is to use those curly d’s to denote it is partial differentiation with respect to a particular variable. So for example on the complex plane the complex variable z = x + iy and as such df/dz is the accepted notation while for differentiation with respect to x and y you are supposed to write it with the curly d notation. This practice is only there when it comes to differentiation, the opposite thing is integration and there only straight d‘s are used. If in the complex plane you are integrating with respect to the real component x you are supposed to use the dx notation and not the curly stuff.
Well I thought I had all of the notation stuff perfectly figured out, oh oh how ultrasmart I was… Am I writing down the stuff for the 4D complex numbers and I came across the odd expression of dd. I hope it does not confuse you, in the 4D complex number system I always write the four dimensional numbers as Z = a + bl + cl^2 + dl^3 (the fourth power of the imaginary unit l must be -1, that is l^4 = -1, because that defines the behavior of the 4D complex numbers) so inside Z there is a real variable denoted as d. I hope this lifts the possible confusion when you read dd

More on the common convention: In the post on the factorization of the Laplacian with Wirtinger derivatives I said nothing about it. But in case you never heard about the Wirtinger stuff and looked it up in some wiki’s or whatever what, Wirtinger derivatives are often denoted with the curly d‘s so why is that? That is because Wirtinger derivatives are often used in the study of multi-variable complex analysis. And once more that is just standard common convention: only if there is one variable you can use a straight d. If there are more variable you are supposed to write it with the curly version…

At last I want to remark that the post on the factorization of the Laplacian got a bit long: in the end I needed 15 pictures to publish the text and I worried a bit that it was just too long for the attention span of the average human. In the present years there is just so much stuff to follow, for most people it is a strange thing to concentrate on a piece of math for let’s say three hours. But learning new math is not an easy thing: in your brain all kind of new connections need to be formed and beside a few hours of time that also needs sleep to consolidate those new formed connections. Learning math is not a thing of just spending half an hour, often you need days or weeks or even longer.

This post is seven pictures long, have fun reading it and if you get to tired and need a bit of sleep please notice that is only natural: the newly formed connetions in your brain need a good night sleep.

Here we go with the seven pictures:

Yes, that’s it for this post. Sleep well and think well & see you in the next post. (And oh oh oh a professional math professor for the first time in his or her life they calculate the square Z^2 of a four dimensional complex number; how many hours of sleep they need to recover from that expericence?)
See ya in the next post.

# Majorana particles gone? How significant is this?

It is no secret that over the years I have made a few rather bald predictions when it comes to magnetism. I think each and every electron is in fact a magnetic monopole and not a ‘tiny magnet’ like the professional professors think. As such I have predicted that all nuclear fusion reactors based on the magnetic confinement design will never work because if you turn such a machine on it will accelerate the electrons to crazy speeds creating tons of instability and turbulence in the plasma. And if I say ‘hey where is your experimental proof that electrons are actually magnetic dipoles’ of course nothing happens. You must never forget that all these physics professors are extremetly important persons and they will never mingle with inferior shit like people who are unemployed for almost 20 years now… No no no, we are not going to react on some crazy stuff like electrons are not magnetic dipoles. If we start doing that, the next day a homeless person will come along saying if we heal the electrons from their trauma’s you get better beer. No no no, incompetent people aren’t unemployed for no reason at all. We will neglect weirdo’s like that, after all we are the physics professors and we are on the edge of becoming masters of the universe once we have our quantum computers up and running!
I also predicted a few years back that the approach of the Delft university combined with Microsoft will not work because the Majorana particles they are based upon do not exist. It is very simple: a Majorana particle is it’s own anti particle, physics professors thought that if you combine an electron with a hole (the absense of an electron) you have a structure that is it’s own anti particle. But if you combine an electron with a hole, what mechanism is there to ensure the hole and the electron also carry opposite magnetic charges? Just like the electron and the positron carry opposite electric charges the same should go for the magnetic charges after my lazy unemployed insights.

A couple of days back when reading the news on Google news I made an internet search for ‘quantum computing’ and to my surprise there was an article from last May in the local newpaper De Volkskrant stating there was ‘bad luck’ for the heroes at Delft university. Oopsy toopsy, the Delft heroes had to withdraw an article published in Nature where the existance of Majorana particles was claimed. The fact that Nature published this bullshit in the first place is also interesting, likely the peer review mechanism works perfectly for getting the best of science into that outlet of articles. Today I checked what the publication fees are for Nature, it is only 5000€ or so (I more or less expected it to be at least 10000€) so today I learned something too… Those fees are of course a fundamental root cause as you will never find my name Reinko Venema in such overpaid shit publications. Why should I lay out 5000€ for something that will never ever pass the peer review hurdle? Since I am not an overpaid person, most of the time I try to spend my money wise.

I am sorry that the news article is in Dutch, but here is a link:
Tegenslag voor Nederlandse pionier van de quantumcomputer.

Anyway I consider this a very small success, of course the main success I am hunting for is that plasma instability in fusion reactors is caused by the acceleration of the applied magnetic fields and as such we cannot halt climate change with fusion reactors. But we have to do with overpaid university shitholes, so the waiting will be long. The combination of being overpaid while at the same time you are to stupid to ‘do the math’ often does not give a good outcome. As an example for that, look at the last financial crises that started in 2008: all those overpaid bankers and the troubles they created.

We close this post with a few pictures. The copyright of the content goes to Sam Rentmeester who likely made the photo from that extremely important Delft based physics professor:

Ok, that was it for this post. The next post is about math and we will dive into the total differential for 2D, 3D and 4D comples numbers.

# Factorization of the Laplacian (for 2D, 3D and 4D complex numbers).

Originally I wanted to make an oversight of all ways the so called Dirac quantization condition is represented. That is why in the beginning of this post below you can find some stuff on the Dirac equation and the four solutions that come with that equation. Anyway, Paul Dirac once managed to factorize the Laplacian operator, that was needed because the Laplacian is part of the Schrödinger equation that gives the desired wave functions in quantum mechanics. Well I had done that too once upon a time in a long long past and I remembered that the outcome was highly surprising. As a matter of fact I consider this one of the deeper secrets of the higher dimensional complex numbers. Now I use a so called Wirtinger derivative; for example on the space of 3D complex numbers you take the partial derivatives into the x, y and z direction and from those three partial derivatives you make the derivative. And once you have that, if you feed it a function you simply get the derivative of such a function.

Now such a Wirtinger derivative also has a conjugate and the surprising result is that if you multiply such a Wirtinger derivative against it’s conjugate you always get either the Laplacian or in the case of the 3D complex numbers you get the Laplacian multiplied by the famous number alpha.

That is a surprising result because if you multiply an ordinary 3D number X against it’s conjugate you get the equation of a sphere and a cone like thing. But if you do it with parital differential operators you can always rewrite it into pure Laplacians so there the cones and spheres are the same things…

In the past I only had it done on the space of 3D numbers so I checked it for the 4D complex numbers and in about 10 minutes of time I found out it also works on the space of 4D complex numbers. So I started writing this post and since I wanted to build it slowly up from 2D to 4D complex numbers it grew longer than expected. All in all this post is 15 pictures long and given the fact that people at present day do not have those long timespan of attention anymore, may be it is too long. I too have this fault, if you hang out on the preprint archive there is just so much material that often after only five minutes of reading you already go to another article. If the article is lucky, at best it gets saved to my hard disk and if the article has more luck in some future date I will read it again. For example in the year 2015 I saved an article that gave an oversight about the Dirac quantization condition and only now in 2020 I looked at it again…

The structure of this post is utterly simple: On every complex space (2D, 3D and 4D) I just give three examples. The examples are named example 1, 2 and not surprising I hope, example 3. These example are the same, only the underlying space of complex numbers varies. In each example number 1 I define the Wirtinger derivative, in example 2 I take the conjugate while in the third example on each space I multiply these two operators and rewrite the stuff into Laplacians. The reason this post is 15 pictures long lies in the fact that the more dimensions you have in your complex numbers the longer the calculations get. So it goes from rather short in the complex plane (the 2D complex numbers) to rather lengthy in the space of 4D complex numbers.

At last I would like to remark that those four simultanious solutions to the Dirac equation it once more shouts at your face: electrons carry magnetic charge and they are ot magnetic dipoles! All that stuff like the Pauli matrices where Dirac did build his stuff upon is sheer difficult nonsense: the interaction of electron spin with a magnetic field does not go that way. The only reason people in the 21-th century think it has some merits is because it is so complicated and people just loose oversight and do not see that it is bogus shit from the beginning till the end. Just like the math professors that neatly keep themselves stupid by not willing to talk about 3D complex numbers. Well we live in a free world and there are no laws against being stupid I just guess.

Enough of the blah blah blah, below are the 15 pictures. And in case you have never ever heard about a thing known as the Wirtinger derivative, try to understand it and may be come back in five or ten years so you can learn a bit more…
As usual all pictures are 550×775 pixels in size.

Oh oh the human mind and learning new things. If a human brain learns new things like Cauchy-Riemann equations or the above factoriztion of the Laplacian, a lot of chages happen in the brain tissue. And it makes you tired and you need to sleep…
And when you wake up, a lot of people look at their phone and may be it says: Wanna see those new pictures of Miley Cyrus showing her titties? And all your new learned things turn into insignificance because in the morning what is more important compared to Miley her titties?

Ok my dear reader, you are at the end of this post. See you in the next post.

# Three video’s to kill the time.

Orginally I wanted to include some video in the previous post that serves as a teaser post for the impending factorization of the Laplacian for 2D, 3D and 4D complex numbers. But it was already late at night and only adding one video made the post look like it is just as chaotic as I always am…;)

So let’s get started with video number 1: Goodbye Determinism, Hello Heisenberg Uncertainty Principle from Irvin Ash. This Irvin guy is one of those professional Youtubbers that apearently can make money by throwing out a lot of video’s. In his case it is often physics and in my view he only repeats what he has read or seen in other video’s. There is not much original thinking in but hey Irvin can make a buck and it keeps him busy.

But in one of the video’s he is making such a strange mistake, it is so stupid that it is unbelievable. It is like stating that 1 + 1 = 3 or like 1 – (-1) = 0. Some mistakes or faults are so trivial that no matter what your own brain instantly recognizes something is going wrong. In this case Irvin explains the double slit experiment and his explanation for the first place where interference disappears is that they are out of phase by one wavelength… I wonder how you can make such a mistake without your own brain instantly jumping in with ‘that is not right’.

I also made a nice cube from the above screen shot:

And finally the video itself:

The second video is from Sabine Hossenfelder. Unlike Irvin Sabine has a lot of original thinking to share and as such she is a far cry from a talking book like Irvin Ash. In her video she explains how medical magnetic resonance devices work. Back in the time when I figered out that it is just not logical on all kinds of levels that electrons and other spin half particles are magnetic dipoles, for me it was important to find alternative explanations for things like MRI devices. In physics it is well known that accelerating electrons and protons give off electro-magnetic radiation, if there is zero acceleration no radiation is emmited. So the explanation as given in the video cannot be right, it is about magnetic moments that start spinning round and ‘therefore’ give off radiation. Problem with this is: there is no real acceleration so what explains the emitted radiation?

If protons and electrons carry magnetic charge, that is they are magnetic monopoles, all of a sudden there is room for acceleration and as such you can observe those resonance frequencies. Compare it to a music intrument: if you have a guitar with zero tension on the wires, it will never produce any sound let alone some cute music. In MRI scans there is also a static magnetic field, only when the protons and electrons are magnetic monopoles this ‘brings the tension’ needed for the resonance to work in the first place. Sorry Sabine, your version of physical reality has a lot of holes in it because it is based on the Gauss law for magetism and that law says that no magnetic monopoles exist…

In case you never dived into the niceties of MRI scanners, please see the video. And don’t forget to be a bit critical: if protons are really magnetic dipoles, then what the fuck is that static magnetic field doing? But if protons (and electrons) carry magnetic charge all of a sudden things become logical. Not that I expect during my lifetime only one of the professional physics professors to say that I am in the right, but there is no use in getting emotional. All I do is repeating the nonsense that goes on as accepted common knowledge while it is retarded: If a proton has two magnetic poles then why do you need the static magnetic field?

The third video is about how Paul Dirac succeeded into factorizing the Laplacian differential operator. It is far different from how I managed to do that; I used so called Wirtinger derivatives and multiply those against their conjugate and voila: there is your factorization. No, Paul Dirac used 4×4 matrices that anti-commute and as such he was able to get rid of a nasty square root. Phyics people go totally bonkers on that calculation, I do not. Not that I do not like it, but Paul made the mistake of basing his matrices on the Pauli matrices for electron spin. And the Pauli matrices can’t be correct because it is based on the flawed idea that electrons are magnetic dipoles.

There is a funny anecdote going round about Paul Dirac. It says: There is no God and Dirac is his prophet. But serious: If electrons were magnetic dipoles you instantly run into dozens of weird problems. Like permanent magnets, of they are explained by the spins of the electrons aligning themselves and just as if you have a bunch of tiny magnets they will form a large permanent one. But in chemistry and electron pair with the same spin is known as an anti-binding electron pair. How can in permanent magnets the alignment of electrons enforce each other while in chemistry that causes a non-binding electron pair? Once more: I only use logic. It is logical that electrons, protons and neutrons carry net magnetic charge and as such are always magnetic monopoles.

Enough of the blah blah blah, here is the last video of this post:

At last a ‘cube picture’ for the Dirac thing:

Ok, that was all I had to day. Thanks for your attention and don’t forget to turn enough math professors into bio-diesel. Everybody knows that bio-diesel made from math professors is the finest quality there is on this entire earth… So good luck with the hunt for math professors…;)

# Teaser for the next post on Wirtinger derivatives.

Man oh man, the previous post was from 12 Nov so time flies like crazy. Originally I wanted to write a post on a thing you can look up for yourself: the Dirac quantization condition. I have an old pdf about that and it says that it was related to the exponential circle on the complex plane. Although the pdf is from the preprint archive, it is badly written and contains a ton of typo’s and on top of it: the way the Dirac quantization is formulated is nowhere to be found back on the entire internet. In the exponent of the exponential circle there is iqg where q represents an elementary electric charge and g is the magnetic monopole charge according to Paul Dirac. Needless to say I was freaked out by this because I know a lot about exponential curves but all in all the pdf is written & composed so badly I decided not to use it.

After all when I say that electrons carry magnetic charge and do not have bipolar magnetic spin, the majority of professional physics professors will consider this a very good joke. And if I come along with a pdf with plenty of typo’s the professional professors will view that as a validation that I am the one who has cognitive problems and of course they are the fundamental wisecracks when it comes to understandig electron spin. Our Pauli and Dirac matrices are superior math, in the timespan of a hundred years nothing has come close to it they will say.

Here is a screen shot of what freaked me out:

Furthermore I was surprised that the so called professional physics professors have studied stuff like ‘dyons’. So not only a Dirac magnetic monopole (without an electric charge but only a magnetic charge), a dyon is a theoretical particle that has both electric and magnetic charge. But hey Reinko, isn’t that what you think of the electron? There are two kinds of electrons, all electrons have the same electric charge but the magnetic charge comes in two variants.
There are so many problems with the idea that electrons are magnetic dipoles, but the profs if you give them a fat salary will talk nonsense like they are a banker in the year 2007.

So I decided to skip the whole Dirac quantization stuff and instead focus a bit on factorizing the Laplacian differential operator. I the past I have written about that a little bit, so why not throw in a Google search because after all I am so superior that without doubt my results will be found on page 1 of such a Google search! In reality it was all ‘Dirac this’ and ‘Dirac that’ when it comes to factorization of the Laplacian on page 1 of the Google search. So I understood the physics professors have a serious blockade in their brains because this Dirac factorization is only based on some weird matrices that anti-commute. These are the Pauli and Dirac matrices and it is cute math but has zero relation to physical reality like the electron pairs that keep your body together.

No more of the Dirac nonsense! I sat down and wrote the factorization of the Laplacian for 4D complex numbers on a sheet of paper. Let me skip all this nonsense of Dirac and those professional physics professors and bring some clarity into the factorization of the Laplacian.
It took at most 10 minutes of time, it is just one sheet of paper with the factorization. I hope this is readable:

So that is what I have been doing since 12 April, since the last post on this website. I have worked my way through the 2D complex plane, the 3D complex numbers and finally I will write down what did cost me only 10 minutes of time a few weeks ago…

In a few days the post wil be ready, may be this week. If not next week & in the meantime you are invited to think about eletrons and why it is not possible that they are magnetic dipoles.

See you in the next post.

# The directional derivative (for 3D & 4D complex numbers).

A couple of days ago all of a sudden while riding my bicycle I calculated what the so called directional derivative is for 3D & 4D complex numbers. And it is a cute calculation but I decided not to write a post about it. After all rather likely I had done stuff like that many years ago.

Anyway a day later I came across a few Youtube video’s about the directional derivative and all those two guys came up with was an inner product of the gradient and a vector. Ok ok that is not wrong or so, but that is only the case for scalar valued functions on say 3D space. A scalar field as physics people would say it. The first video was from the Kahn academy and the guy from 3Blue1Brown has been working over there lately. It is amazing that just one guy can lift such a channel up in a significant manner. The second video was from some professional math professor who went on talking a full 2.5 hour about the directional derivative of just a scalar field. I could not stand it; how can you talk so long about something that is so easy to explain? Now I do not blame that math professor, may be he was working in the USA and had to teach first year math students. Now in the USA fresh students are horrible at math because in the USA the education before the universities is relatively retarded.

Furthermore I tried to remember when I should have done the directional derivative. I could not remember it and in order to get rid of my annoyance I decided to write a small post about it. Within two hours I was finished resulting in four pictures of the usual 550×775 pixel size. So when I work hard I can produce say 3 to 4 pictures in two hours of time. I did not know that because most of the time I do not work that fast or hard. After all this is supposed to be a hobby so most of my writing is done in a relaxed way without any hurry. I have to say that may be I should have taken a bit more time at the end where the so called Cauchy-Riemann equations come into play. I only gave the example for the identiy function and after that jumped to the case of a general function. May be for the majority of professional math professors that is way to fast, but hey just the simple 3D complex numbers are ‘way to fast’ for those turtles in the last two centuries…

Anyway, here is the short post of only 4 pictures:

Should I have made the explanation longer? After all so often during the last years I have explained that the usual derivative f'(X) is found by differentiating into the direction of the real numbers. At some point in time I have the right to stop explaining that 1 + 1 = 2.

Also I found a better video from the Kahn academy that starts with a formal definition of the directional derivative:

At last let me remark that this stuff easily works for vector valued functions because in the above limit you only have to subtract two vectors and that is always allowed in any vector space. And only if you hang in a suitable multiplication like the complex multiplication of 3D or 4D real space you can tweak it like in the form of picture number 4 above.

That was all I had for you today, this is post number 166 already so I am wondering if this website is may be becoming too big? If people find something, can they find what they are searching for or do they get lost in the woods? So see you in another post, take care of yourself & till the next post.

# What is one-way light speed? + A plasma lamp in a magnetic field.

Lately the Veritasium guy from the Youtube channel with that name came out with a video that made me think. It seems that the only way light speed has been measured experimentally is by using a mirror and as such you always measure a so called ‘two-way light speed’ average. It is possible that in this universe light has some preferred direction and in that derection it goes faster compared to say the opposite way.

You might wonder as why that is but that is the old problem Mr. Einstein faced & solved: It is very hard to get two clocks synchronized when they are apart. Vertitasium explains that if light has a preferred direction, in that case it all gets even harder and rather complicated.

Anyway to make a long story short, he also claims there has never been such a ‘one-way’ experiment. That made me think about it and I think that I have found a solution that does not depend on the nasty synchronization problem. All you need is two atomic clocks that are always a fixed distance apart. It gets more complicated compared to where there is perfect sync but if the universe has a preferred direction for light to go in, from the data you collect you should be able to find it.

First let me show you via a screen shot from the video what the usual way is to experimentally measure the speed of light:

In the next six pictures I try to explain that using two atomic clocks on two satellites can pull the trick off. Both satellites have a laser or for that matter any em radiation would do like normal radio waves. And on both satellites there is perfect registration of the local time of the times a laser signal was put out or received. Both satellites should be in the same strength of the local gravity field so that their atomic clocks run at equal speeds. Every day both satellites send out one laser pulse on a fixed time and on a daily basis these send & receiving times are recorded.

We proceed with a video from the Brainiac channel. On Youtube there are more than one Brainac channels, I mean the guy with the big magnets. And with big I really mean big, the most heavy ones are a staggering 13 kg. A couple of years ago I wondered if I should buy a plasma lamp in order to study how my own set of small neodymium magnets should influence the plasma. These lamps cost only 20€ so that was not the problem. But I have already plenty of lamps so I decided not to do it. After all the photo’s from how an old television set reacts on the neodymium magnets should be enough.

Anyway that is what I thought: Given the fact the audience is composed of scientists, simply communicating the facts should be enough. And applying a bit of logic simply says electrons are not magnetic dipoles but in order to explain the behavior on an old television set is far better explained by electrons being magnetic monopoles. Of course now we are five or six years further down the timeline all I observed is that university people are still very good at just one thing: being important. And no no no, of course we do not talk about that. Electrons magnetic monopoles? Great minds from physics, also people who were very important, said it ain’t so. So no no no, we are important and those crazy people from outside science should shut up and pay the taxes we need for being so important.

Yet now a few years later the video from the Brainiac guy shows that the plasma in the plasma lamp does not react at all as you might expect from a bunch of magnetic monopoles. On the contrary: If he applies one of those 13 kg neodymium magnets, the plasma lamp stops working. So I am glad I never bought one of those lamps because that would make me doubt my own insights that were derived from the electron cannons in the old television set… But the Brainiac guy has much more electronic equipment and he soon found out that the plasma in a plasma lamp is steered by and alternating electric current. So the plasma shakes hin und her with a high frequency and it is not streaming in one direction or so…

Furthermore he explains perfectly why the lamp stops working: the applied magnetic field from the 13 kg magnet stops the transformator in the plasma lamp from working properly. And that explains why the lamp stops working… By the way, if electrons were really magnetic dipoles, the 13 kg magnet would never hinder the functioning of a transformator because a magnetic dipole the size of an electron is by definition neutral for external magnetic fields.

Well here is the perfect video if you want to understand a bit of nature and in case you are one of those fake scientist only occupied with the importance of self, why not walk to a mirror so you can look at yourself?

This post is getting far to long for the attention span people have in the present media environment. But I want to show you also a part that the Brainiac guy does not understand: the next screen shot from his video shows only electrons that are repelled by the giant magnet he uses. If he would have used an other direction you could have seen also the electrons that are attracted by the magnet. All of this stuff nicely confirming year in year out that it is impossible for electrons to be magnetic dipoles…

Ok, end of this far too long post. See you in the next post & thanks for having a long enough attention span for reading these very words.