What would a quantum measurement on Paul his IQ yield?

Magnetism

Today I came across one of those video’s where people try to explain how permanent magnets work. And originally I thought of a title like ‘Idiot of the day observed’ but soon I changed my mind because Paul Sutter does not do it on purpose; what he says is more or less the general accepted version of permanent magnetism…

In general there are two lines of reasoning when it comes to permanent magnets: One line of reasoning is that the magnetic domains get aligned, the other way is that the electron spin of all unpaired electrons align.

Paul Sutter goes for the second line of reasoning; the spin of all unpaired electrons align giving rise to a permanent magnet. Just like everything else in the video it is just wrong; in my view where the electrons carry magnetic charge, it is the placement of the unpaired electrons in the inner shells of for example an iron atom that makes the global permanent magnet emerge.

If it was just electrons having all their dipole magnetic moments point in the same direction, in that case with a strong magnet you could always change or invert the magnetic direction of a weak magnet. In practice this just does not happen; last spring I even made a simple experiment with this: I took my stack of the most strong magnets I have and placed them over 24 hours against the two most weak magnets I have. And, like expected, there was no change at all in the weak magnets indicating there is some kind of threshold at work. The threshold is of course that it is hard to remove the magnetically charged electrons from the inner shells of the iron atoms…

Here are two pictures of the simple experiment from 08 March 2018; the permanent but very weak magnets on the left were exposed to the stack of neodymium magnets for just over 24 hours and just nothing changed in the behavior of the weak magnets. If electron magnetic moment alignment were a significant factor in permanent magnetism, the stronger permanent magnets should alter the magnetic properties of the weak magnets. It just does not happen…

Weak at the left, strong at the right.
After 24+ hours of waiting zero change observed in the weak magnets.

A link to what I wrote one year back on this very simple experiment is:
08 March 2018: Reason 56: This experiment shows zero spin torque transfer. http://kinkytshirts.nl/rootdirectory/just_some_math/monopole_magnetic_stuff03.htm#08March2018

It is lovely to see so many of the wrong stuff bound together in just one short video: For example when Paul explains why electron pairs are magnetically neutral while the unpaired electrons are not. In my view if it is true that electrons are magnetic dipoles, they would be magnetically neutral. They are not and in my view this shows electrons are magnetic monopoles. How does Paul explain it? Very simple: The electron pair is magnetically neutral because one of the electrons has spin up while the other has spin down and that cancels each other out.

Here is the Youtube video of Paul Sutter, please don’t think that Paul is a dumb person or so. This is just the view of professional physics folks that have studied magnetism for centuries…

Link: https://www.youtube.com/watch?v=6uwjqy2HCgY

May be at last I am getting a little bit sarcastic: They have studied that for centuries… But if you let go that dumb and unproven Gauss law for magnetism, just try to think about our physical reality as electrons also carry magnetic charge beside their electric charge, a lot of things become better to understand. After all, why do we only observe electron pairs? Why never something else like an electron triplet?

Ok, let’s leave it with that. Till updates my dear reader.

On Schrödingers cat & an example known as the envelope problem.

Quantum mechanics

Today the Youtube channel SciShow had one more video out on quantum mechanics and as such the famous cat of the Schrödinger cat in a box problem comes along once more.

As usual we are told the cat can be in a super position of being alive and dead at the same time. I wonder why people think that this can be true, as far as I know history the Schrödinger guy came up with this example as an antidote as being everything into a super position…

I suppose you already know what the cat in the box setup is. The cat dies if just one radioactive atom decays yes or no. If you are outside of the box it makes sense to use a probalistic model of the situation, but does this mean that in reality inside the box the cat is dead and alive at the same time? After all the cat will be the very first to observe if radio active decay has happened because as soon as it does the state of the cat goes from alive to dead. So inside the box there is at least one observer present and as such all quantum states we are interested in (radio active decay yes or no) is constantly measured all of the time.

For myself speaking I use the fact that a cat cannot be in a super position of being alive and dead as an example that an individual atom cannot be in a state where radio active decay has passed yes or no.

That does not mean quantum particles cannot be in super positions, for example photons behave often like they took all possible paths to arrive somewhere. But as soon as there are all kinds of different energy levels involved this becomes more and more problematic. For example can a particle be in a super position of being a neutron and a proton? Can a particle be in a super position of being an electron and a positron? Can a particle be in a super position of being a hydrogen ion (a proton) and a plutonium atom?

Energy is at the heart of the quantum measurement problem: In order to measure a quantum particle some kind of interaction with the particle must be there. This interaction changes (or not) the state of the particle. It is a bit like this: Suppose I am sitting in my home country and I have to measure the length of some grassfield in Germany or Belgium but I can only use atom bombs for that. No matter how smart I craft my grass length measuring device, the giant explosions from the atom bomb will bring a great uncertainty in the outcome of the measurements… Here is the video:

The cat is also an observer…

Ok, now for the lesser known but rather interesting envelope exchange problem. In a nutshell it goes as next:

You can choose one of two closed invelopes and they contain money. The only thing you are told is that the amount in one of the envelopes is double that of the other envelope.

Now you play the game and you choose one of the envelopes, let’s say it contains 100€. You are asked by the quiz master if you want to keep those 100€ or that you want to change your choice and go for the other envelope.

You think about that for a few seconds and you figure out: If this envelope has 100€ and given the rules of the game, the other envelope contains 50€ or 200€ with equal probability of 50%. Suppose I want to swap to the other envelope, what is my expectation for the amount of money? That is simple, both 50€ and 200€ have 50% probability so the expectation of swapping becomes 0.5*50 + 0.5*200 = 125€. Therefore it makes sense to swap and choose the other envelope.

But hey, whatever envelope you choose at first and you find X money in it, isn’t it weird to swap that always? If you would have chosen the other envelope you would also swap…

This envelope swap problem or paradox has a relative simple solution: You assume equal 50% probabilities for having double or half the amount of money you found in the first envelope. But in that case the whole thing crashes because you are now calculating with three outcomes: the 100€ from the first envelope and two other amounts 50 and 200 Euro while there are only two enveloples. It is unwise to calculate the expectation values because the 50€ and 200€ exclude each other: if the outcome 50€ is observed all of the time the 200€ was non existant. And as such the expectation value makes no sense for an individual experiment.

Ok, let me end this post with a standard wiki around the two envelope thing: Two enveloples problem. https://en.wikipedia.org/wiki/Two_envelopes_problem

End of this post.

The logarithm of all 2D circular numbers (the split complex numbers).

Uncategorized

Yesterday I was editing the six pictures for this update and all of a sudden I realized I had made a dumb dumb mistake: The pictures count down from number 7 to number 2…

I had processed them in the wrong order; I had made seven background pictures but I filled in the math text in the wrong order.

All in all I decided to leave it this way; it might be a stupid mistake but it is not a critical mistake like making a critical math error or having wrong ideas about what is actually happening on the math level. It is just an editing error and also funny. So I leave it this way.

In this post we look at the so called split complex numbers, they are the cousin of the numbers from the complex plane. The only difference is that where in the complex plane the square of the imaginary unit equals minus one, for the split complex numbers this equals plus one.

Although this is a minor change, split complex numbers are not a field because it contains non-invertible numbers outside the number 0. All I do in this post is finding the eigenvalues and eigenvectors of all split complex numbers and via taking the log of the eigenvalues we calculate what the log of an arbitrary split complex number is.

In the speak of this website the split complex numbers are just the 2D circular numbers. Remeber in all dimensions numbers are complex or circular depending if the first imaginary unit equals -1 or +1. You can find many more ways of crafting a multiplication but the best math results are always found in the complex and circular version of the numbers in that particular dimension…













Ok, in this post I left all things out that talks about the 4D hybrid space that is a mixture of the 2D circular and complex numbers. But as you see on inspection of the above six pictures, the eigenvalues might be always real but they can be negative. As such always pay attention when you apply that function named the log…

That was it for this post, at this point in time I have no idea what the next post will be about. After all we had this long rout of over 20 posts on the 4D complex numbers and I left a whole lot of other stuff out in that period. Stuff like 3D Gauss integers or a general definition for integration that works in all dimensions. Till updates my dear reader.

And life? Life will go on.

Uncategorized

Originally I planned on showing you some numerical results from the circular 4D numbers while explaining there is also a number alpha in 4D. For me that would be a nice holiday away from all that 4D complex number stuff from the last months…

But the numerical applet did not work, it is still dead in the water:

http://calculator.vhex.net/calculator/linear-algebra/matrix-exponential-using-the-pade-approximation

Ok ok, I could have done those numerical showings also in rigid analysis but I guessed that calculating a 4D tau for circular numbers via analysis was too much. And I settled for a much more easy to understand thing:

The logarithmic function for every 2D circular number. In the field of professional math professors the 2D circular numbers are known as the split complex numbers.

So that is what the next post will be about: Finding log(z) for all invertible split complex numbers.

I only wrote one previous post on the 2D circular aka split complex numbers and that dates back to Nov 24 of the year 2016:

The second hybrid: a 4D mix of the complex and the circular plane.

Ha ha, now I can laugh about it but back in the time it was some hefty pain. Anyway to make a long story short: In that old post from 2016 I calculated the log for just one split complex number namely the first imaginary unit j.

Let me show you my favorite part of that old post from 2016:

So the next update will only contain 2×2 size matrices while I skip the detail that the log lives mainly in the hybrid number system from the old post.

Till updates.

Part 20: On the structure of non-invertible 4D complex numbers.

4D complex numbers

In general it is rather hard to find non-invertible 4D complex numbers because the determinant is non-negative everywhere. Just try it yourself, write down just one 4D complex number that is non-zero and not invertible.

That is not an easy task, after some time you will find some but do you have all?

But if you understand the concept of the eigenvalues that every 4D complex number Z has, it is easy to understand that if a 4D complex number is non-invertible at least one of the eigenvalues must be zero.

In previous posts we already unearthed the four eigenvalue functions that return the four eigenvalues each 4D complex number has.

In this post we will try to find where these eigenvalue functions are zero.

Since eigenvalue functions come in pairs whenever possible in the case of 4D complex numbers we only have two pairs of those eigenvalue functions.

Let’s stop the talking and just post the twelve pictures that make up part number 20 into the basics of the four dimensional complex numbers.

 

 

 

 

 

 

 

 

 

 

 

 

Ok, that was it for part 20 in the series that covers the basics of 4D complex numbers.

See you around my dear reader.

A teaser question: Can you prove this inequality?

4D complex numbers

Recently I am working on part 20 to the basics of the 4D complex numbers. Ok ok if you need 20 parts to explain ‘the basics’ how basic is it you can ask yourself.

You can argue long and short on this: are fresh Cauchy integral formula’s really ‘basic stuff’? I don’t know how a democratic vote among professional math professors would fall down.

Anyway, an important property of the determinant of 4D complex numbers is the fact that the determinant is always non-negavite. At least it is zero and at those points in space we have found a non-invertible number.

In part 20 on the basics to 4D complex numbers we will look when the eigenvalues of 4D complex numbers vanish; at those points the stuff is non-invertible & that is what we will be hunting on part 20.

In the next picture you see a difficult to understand inequality & the teaser question is:
Can you prove this inequality via math methods that do not use 4D complex number theory at all?

If so, you should definitely pop up a second pint of perfect beer on a late Friday evening.

Ok, that was it. Till updates in part 20 where we try to find all non-invertible 4D complex numbers in a not too difficult way.

The inverse theorem of Pythagoras (part 2).

Pythagoras stuff

Somewhere last year I just looked some nice video from the Mathologer about the theorem of Pythagoras. And since I myself have found a proof for the general theorem of Pythagoras in higher dimensions, I was puzzled about what the so called ‘inverse theorem of Pythagoras’ actually was.

Could I do that too in my general proof? And the answer was yes, but when I wrote that old proof of the general theorem of Pythagoras it was just a technical blip not worthwhile mentioning because it was a simple consequence of how those normal vectors work.

Anyway to make a long story short, a few days back I likely had nothing better to do and for some reason I did an internet search for ‘the inverse theorem of Pythagoras’. All I wanted to do is read a bit more about that from other people.

To my surprise my own writing popped up as search result number 3, that was weird because I wanted to read stuff written by other people… Here is a screenshot of the answers as given by the Google search machine:

Ok ok, not bad at search result number 3.

Now why bring this up? Well originally I forgot to post to the video that started my thinking in the first place. It is from the Mathologer and here at 16.00 minutes into his video is where my mind started to drift off:

The video from the Mathologer is here (title Visualizing Pythagoras: ultimate proofs and crazy contortions):

It is a very good video, my compliments.

After so much advertisements for the Mathologer, just a tiny advertisement for what I wrote on the subject of the inverse theorem of Pythagoras on March 20 in the year 2018:

What is the inverse Pythagoras theorem?

Ok, that was it. Till updates.

Part 19: Four integrals defining the 4D complex number tau.

4D complex numbers, Exponential circle, Exponential curves

It is a bit late but a happy new year anyway! In this post we will do a classic from the complex plane: calculation of the log of the first imaginary unit.

On the complex plane this is log i and on the complex 4D space this is log l .

Because this number is so important I have given it a separate name a long long time ago: These are the numbers tau in the diverse dimensions. In the complex plane it has no special name and it simply is i times pi/2.

On the real line it is pretty standard to define the log functions as the integral of the inverse 1/x. After all the derivative of log x on the real line is 1/x and as such you simply define the log to be the integral of the derivative…

On the complex plane you can do the same but depending of how your path goes around zero you can get different answers. Also in the complex plane (and other higher dimensional number systems) the log is ‘multi valued’. That is a reflection of the fact we can find exponential periodic functions also known as the exponential circles and curves.

The integrals in this part number 19 on the basics of 4D complex numbers are very hard to crack. I know of no way to find primitives and to crack them that way. May be that is possible, may be it is not, I just do not know. But because I developed the method of matrix diagonals for finding expressions for the value of those difficult looking integrals, more or less in an implicit manner we give the right valuations to those four integrals.

With the word ‘implicit’ I simply mean we skip the whole thing of caculating the number tau via matrix diagonalization. We only calculate what those integrals actually are in terms of a half circle with coordinates cos t and sin t.

This post is 8 pictures long in the usual size of 550 by 775 pixels (I had to enlarge the latest picture a little bit). I hope it is not loaded with typo’s any more and you have a more or less clean mathematical experience:

End of this post.

At year’s end: What is the most nice magnetic result of this year?

Magnetism

There is more than one candidate; the possible explanation of those solar loops via the rotating plasma under it is indeed very very nice.

But it is very hard to find experimental evidence for that, how to check that on the sun where there is one of those solar loops, the solar plasma underneath it is rotating?

So my choice for this year most beautiful insight is how those magnetic domains in materials like iron actually work. If my thinking on electrons as magnetic monopoles is correct, you could view those magnetic domains as surplusses of either north-pole electrons or south-pole charged electrons.

This should be much more easy to verify experimentally. After all there is still plenty of magnetic tape around and the best way of checking if magnetic domains are suplusses of one of the two magnetic charges is much more handy if you have a flat surface like magnetic tape.

Furthermore at present day it should be possible to measure very small magnetic charges. After all in most computers there still are spinning hard disks that use magnetism as the basic information storage.

Anyway to make a long story short: If in a flat material like magnetic tape you can go around a magnetic domain with a tiny compass, all of the time the tiny compass should point towards that magnetic domain with the same side of the compass needle.

So it should always point with the north-pole of the compass needle or the south-pole of the compass needle. Remark that according to standard physics theory going around a magnetic domain should always give different readings with a tiny compass needle…

Also in that line of thinking, the domain walls shoud have surplusses of electron pairs that all are spinning around to compensate or neutralize the magnetic forces they feel. An important clue to that lies in the fact you cannot really move or transport domain walls in a wire as the engeneers of IBM tried with making their nano wire racetrack memory.

This year we heard more or less nothing from IBM with progress into the concept of nano wire racetrack memory. Yeah yeah, the price of not understanding electron spin is huge, if we could have fast computer memory that uses very little energy that would be great…

This year I also gave up on my fantasies of trying to make an official publication in some physics yournal. I don’t think such a publication will ever pass the peer review that those scientific yournals use. Those peer review people just want the electron is a magnetic dipole and that’s it. So I did not try that this year nor will I try next year.

Not that I am aginst peer review. Suppose there would be zero peer review and think for example medical scientific publications. They would be filled with all kind of weird benefits that homeopathy therapy has, or the healing of your chakra’s with mineral chrystals… Of course we cannot have that. As such there must always be the so called peer review…

Ok, the word count counter says 500+ words written so I have to stop writing.

Here is the link to what I self more or less consider as the best improving insight on my behalf on the behavior of all things magnetic. It is from 7 July this year:

07 July 2018: Reason 64: Bloch and Neel walls explained.
http://kinkytshirts.nl/rootdirectory/just_some_math/monopole_magnetic_stuff03.htm#07July2018

Ok, that was it. Happy new year.

Just a short video on the Fourier stuff.

Exponential circle, Uncategorized

This is the shortest post ever written on this website.

I found one of those video’s where the Fourier series is explained as the summation of a bunch of circles. Likely when you visit a website like this one, you already know how to craft a Fourier series of some real valued function on a finite domain.

You can enjoy a perfect visualization of that in the video below:

Only one small screen shot from the video:

Oh oh, the word count counter says 80+ words. Let me stop typing silly words because that would destroy my goal of the ‘shortest post ever’. Till updates.