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.
Source of this lovely picture: Electron Paramagnetic Resonance EPR
http://encyclopedia2.thefreedictionary.com/Electron+Paramagnetic+Resonance+EPR
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…
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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.
Technical details:
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.
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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…
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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.
Just over one week ago I posted reason number 48 as why electrons cannot be magnetic dipoles over on the other website, it is about the failure of IBM in crafting a new kind of fast memory. They failed because they treat electron spin like it is a vector while it makes much more sense that electron spin is one of two possible magnetic charges.
It took me relatively long to find where the stuff all went wrong, at first I spend over a week every evening trying to find some stuff on the preprint archive and although there are some explanations found over there, because the writers of those articles are professional physics people they do not understand electron spin.
Also they DO NOT WANT TO UNDERSTAND ELECTRON SPIN because if you view electron spin as a magnetic dipole you end up in a gigantic ocean of nonsense, for example in the science of chemistry very often the electron pair plays a major role in the binding of all kinds of molecules. But if electrons were magnetic dipoles there would be no reason at all to limit the number of electrons to two; you would get all kinds of weird constellations of triplet electrons or whatever you can make with dipole bar magnets…
But if electrons carry two different magnetic charges suddenly it makes a whole lot of sense that we only observe electron pairs; the magnetism is neutral in an electron pair while the repelling electrical charge ensures no larger configurations beyond the pair formation are found. With a magnetic dipole you just would not observe this kind of behaviour…
Now back to IBM’s racetrack memory: All the time I did not understand how the IBM research folks did write the electron spin domains on the racetrack memory; electrons behave very much like cats:
It is easy to chase a cat into a tree but very hard to convince the cat it should leave the tree and come down to earth again…
With electrons you have the same: the two magnetic charges on the electron have a slightly different energy level, when an electron falls from the highest energy level to the lower one we observe the famous 21 cm wavelength photon. It is a well known fact from astronomy that interstellar and intergalactic hydrogen atoms only very very seldom have their electron fall from the highest magnetic energy level to the lowest energy level. This is what I name the ‘combed up universe’; even in intergalactic space most electrons are in the highest energy state because there are plenty of photons flying around to keep them ‘combed up’ when it comes to energy levels…
Back in the year 2004 IBM patented so called racetrack memory; the goal was to leave the 2D structure we have in present day computer hardware and use nano wires to go 3D and as such exploit three dimensional architecture of future computer hardware. The racetrack memory is made from nano wires, those nano wires contain lots of magnetic domains but contrary to the magnetic domains you find in, for example, iron these domains contain only one spin state.
According to IBM researchers all spin states are in the direction of the nano wire (from that you can understand they think electron spin is a vector, the vector represents the magnetic bipolar nature of the electrons according to IBM researchers).
In the next picture you see a boatload of information; the red and blue colour represents of course the two magnetic spin states of the electron. As you see on inspection they can inject blue electrons from the left and red electrons from the right.
If the IBM researchers inject red or blue electrons they can shift the entire column of electrons in the nano wire, according to IBM fellow Stuart Parkin the borders between the magnetic domains get transported…
Of course back in the year 2004 IBM thought they had hit the jackpot because if you neatly follow the standard model of physics where electrons are always having two magnetic poles you will always have that such borders are North pole against North pole (or South against South pole) and as such these borders should be extremely fragile…
And IBM thought they could transport those fragile things at high speeds, if true they would earn not billions but trillions over the long run of a patent.
Yet in my theory of magnetism, if it is true there are two magnetic charges the borders between red and blue magnetic domains are the most strong structures into the nano wire anyway so it is logical they keep intact while the electron column is transported…
Here you see why it is important to keep an open mind on electrons spin because if you follow the standard model companies like IBM cannot make technical progress.
For myself speaking I did not understand how to write information to the nano wire; I was thinking they did it with electro-magnetic radiation because any photon with a wavelength below 21 cm could bring an electron from the lowest energy state to the highest energy state…
But how to go from high energy to low energy is like talking to a cat high in a tree…
And no matter how much articles I did read on the preprint archive, nowhere an answer was to be found…
In the next picture you see how IBM visualizes how a small red region from the nano wire turns into blue: IT IS THAT WRITING WIRE BELOW WITH RED ELECTRONS IN IT!!!!!
Picture source:
Now we have two clashing versions on electron spin:
The standard model version where electrons are magnetic dipoles says: The red writing wire cannot change the red domain in the nano wire because all red electron spins point into the same direction. And if you add more bar magnets perfectly aligned that only makes the red state stronger. Versus:
If electrons carry one of two magnetic charges and we use the principle that like charges repel, the red electrons on the writing wire repel the red electrons in the nano wire into the blue neighbouring blue domains. At the same time blue electrons will flow to the red region.
So if my view on electron spin is true, in that case the simple act of writing information to such nano wires destroys the information in the surrounding magnetic domains.
And that my dear reader is something that the professional physics people still do not want to acknowledge until this present day of 03 August 2017.
By the way, next winter it is about the fourth or even the fifth year I am explaining as why electrons cannot be magnetic dipoles. Those people, the so called ‘professionals’ will keep on hanging to their silly beliefs around electron spin for a much longer time.
Another misleading title, but it is fun to write it down so why not?
In this post (8 pictures long) we have two parts:
Part 1: The relation between the modulo row’s and the modular arithmetic groups Z/jZ.
Part 2: A proposal (or schematic outline) of an important part of the algorithm that brings you from one stratum to the other.
I think this is my last post on this subject of modulo row’s.
Lately websites using RSA encryption methods (that is why we look at large prime numbers made of two factors N = p*q) have gone from a 1048 bit long key to 2096 binary digits long keys. The idea is that it makes life just so much more safe; but the important part of the algorithm for transport over the strata is remarkable resilient towards such moves…
Furthermore, doubling the length of the encryption keys (squaring the size so to say) will in general also increase the size of the Jente basin as found just before the largest prime factor q.
I do not claim to know a lot about encryption, but as far as I know there is zero point zero use of idea’s like the Jente basin. People use a lot of so called ‘trial division’ but even that is not a real division but mostly just taking N modulo something.
For example; want to know if the number 73 is a factor of N?
They simply calculate N mod 73 and if the outcome is 0 they say that 73 is a factor of N, otherwise it is not. The use of idea’s like a Jente basin so you can scrap a lot of trial numbers in the region you are in is, as far as I know, not used.
To be honest, I also do not know how they factor large hundreds of decimal digits long numbers anyway; so it might very well be they use similar idea’s. But if that were the case why is everybody else only talking about taking a huge number of trial divisions without any strategy behind that?
The numbering of the pictures is a continuation of the previous post.
Here are the 8 pictures, have fun reading it.
At this point in time the so called quantum computers are going from the lab to the field, anyway a lot of people claim this. But since after my humble opinion electrons have one electric charge and one of two possible magnetic charges, it will be a long long time before we have a working quantum computer based on electron spin.
Just like IBM with their racetrack technology for 3D memory; the idea is ok but at IBM too they think electron spin a like a vector and not like a charge. And voila; year in year out you never hear from it again…
Ok, for the time being this is what I had to say. See you in the next post.
Ok ok, I admit instantly that the title of this post is way over the top but for once I allow myself a catchy title that has only limited resemblance to what this post is about. In this post, if I write the word computer I always mean a classical computer so not a quantum version of it.
In the previous post there is a video in from the ‘Infinite Series’ that serves as an introduction to the Shor algorithm; if this algorithm could be implemented into a quantum computer that would likely break internet security for a short while. Beside the fact that large prime numbers are used in standard classical encryption, it can also be done with elliptic curves.
This post is about the principle of Jente, with a bit of luck you can find factors of large numbers using the principle of Jente. Counter intuitively the largest (prime) factor will be the easiest to find.
Now how did Jente find the principle of Jente?
Back in the time, end 1997 or begin 1998, we lived in a house without a garden and since I still smoked a lot of tobacco I always had a window open in my working room. Since this work room was next to the entry of the house, very often when the door to my room opened papers would fly from my desk because of wind going through the room.
There was this cute baby crawling around and one day she brought me back a piece of paper that had flown off my desk. And on that piece of paper was a little cute formula that read
m_{j+1} = m_j – d_j. So that is how this got the name the principle of Jente.
Lately Jente turned 21 years of age, she now lives temporary in Australia, and I decided to write this old stuff down as a kind of present for her. The principle of Jente is extremely easy to understand, but as far as I know mathematical reality this principle has not been exhausted very much by the entire math community over centuries of time.
What is missing in this post is a way to converge fast with high speed to one of the factors of one of those huge composite numbers the software engineers use for internet security. My gut feeling says that it should not be that hard but until now I have never found it. It might very well be that inside things like Diophante equations somewhere the solution to this problem of fast finding the largest prime factor is solved without the person who has done that being aware of it…
I tried to keep this post as short as possible so I scrapped a whole lot of stuff but it is still 15 pictures long (picture size as usual 550 x 775 pixels). A feature that I like very much is that I am using so called Harry Potter beans in order to explain as why the Jente principle works. I feel a bit proud on that because it is so simple you could explain that to elementary pupils in their highest years.
For myself speaking I also like this approach to finding prime factors because it is so different from all other ways, yet it has that underlying undeniable thing in it named the Jente principle. The most important detail in this post is the table with the diagonals in it.
If you understand that table and, for example, you can find another algorithm for quantum computers that solves that problem, you have found an alternative to the Shor algorithm…
Have fun reading it, take your time because it is not meant to be grasped in five minutes or so.
I hope you understand the fundamental problem still open after almost two decades:
You start with some number j, calculate m_j = N mod j and d_j = N div j.
Having these, the Jente principle guarantees you can find (j + k) mod N for all k > 0.
But, how oh how, do you converge towards a solution of
m_{j+k} = 0 mod (j+k) ?????
__________
The Shor algorithm: In the world of quantum computing we have the theoretical side where people just write down all kinds of elaborate scheme’s like the Shor algorithm and just as easy they throw in a lot of Hadamard gates that supposedly will bring a giant bunch of quantum bits into super position.
On the other hand you have people that actually try to build quantum computers.
As far as I know stuff, there is no way of bringing a lot of qbits into a nice super position or, for that matter, entangle them into a good initialization state in order to run your quantum software.
Ok, that was it. Don’f forget to pop open a few beers. Don’t believe all that nonsense that doctors are telling you like drinking less = good.
As far as I know reality, all people in my social environment that drink far too little beer always get killed in extremely violent events… 😉
A few months back suddenly there was a new video channel about math and it goes under the cute name Infinite Series. About two months back the channel posted a way to destroy internet security if you could only find that factorization of two giant prime numbers.
Most of present internet security hangs around the difficulty of observing a giant number N of, let’s say, one hundred digits and our incapability to factorize large numbers like that into their prime factor numbers.
Of course, since the Infinity Channel is USA based, it is completely impossible that fresh math will come from that space. Here is the video and indeed only ancient math is around:
The idea’s as expressed in the video are very interesting, but is just does not use the Jente principle that ensures you can find weakness in the integers surrounding the prime numbers that make up the factorization of the stuff you want to encrypt.
In the next two pictures you see that a prime number is extremely weak in avoiding detection using the Jente principle if you are close enough to that prime number.
And if a prime number is detected, in principle you could break down the security of the communication channel.
Let’s leave it with that, after all talking about a basin around a prime number that shouts out ‘the prime number is here’ is one hundred percent outlandish to those overpaid USA math professors…
End of this teaser post, I hope I have some more next week so see you around!
This post has many goals, for example in the previous post I talked about a ‘very rudimentary Fourier transform’. In this post it is a bit less rudimentary, a bit more satisfying definition is given but still I did not research all kinds of stuff like the existence of an inverse & lot’s more basic stuff.
For myself speaking I consider this ‘new Fourier transform’ more as some exotic bird that, if capable to fly a few meters, will only draw applause from specialists in Fourier analysis.
So for myself speaking I am far more happy we need a more advanced number tau and the mathematical miracles you can do with it in three dimensions.
Therefore I included two examples of exponential curves that go through the plus and minus of all three basis vectors in 3D space, after all this is one of my most remarkable math results…
In this post I also show you how to use the calculus of ‘opposite points, in three dimensions it works like a bullet train but the higher the dimensions become the harder it is to frame it in simple but efficient calculus ways like using opposite points on exponential circles.
Another thing to remark is that an exponential circle is always a circle; it is flat in the 2D sense and has a fixed radius to some center. When this is not the case I always use the words exponential curve…
This post is nine pictures long, I truly hope you learn a bit from it.
You really do not need to grasp each and every detail, but it is not unwise to understand that what I name the numbers tau are higher dimensional versions of the number i from the complex plane.
Ok, here we go:
In these nine pictures I forget to remark you can also craft a new Cauchy formula for the representation of analytic functions. For myself speaking this was far more important compared to a new way of Fourier transform.
You still need that more advanced version of tau…
Can´t get enough of this stuff?
Ten more pictures dating back to 2014 at the next link:
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).
