Unit Quaternions and Electrodynamics

[@neerajkumarsingh]

Thanks, nicely explained the mathematical structure of Quaternions. B.T.W I live next to the stone bride where great man Sir. Hamilton once walked and got inspired.

[@JoseSilveira-newhandleforYT]

Very pleased that you made a talk in my country :-) A long time has passed since I've last been to UTAD.

[@TheMachian]

My pleasure. Would be great to see you next time :-)

[@JoseSilveira-newhandleforYT]

@@TheMachian Thanks! I'll see what I can do - it's not easy with all my constraints, but I would certainly like to hear you live :-)

[@mathoph26]

Alexander, you should check the astonishing work of Roger Boudet on the topic. Hé reformulated QED in semi classical field using quaternions. Semi classical means that the photon field is a wave, and not a creation operator. He uses current transition, analogous to current probability in QM, as a source of electromagnetic field. I was on this problem since month: it has been solved by him like 20 years ago. The notation is quite hard to follow, this is the bad point.

[@Burevestnik9M730]

Is this related to bootstrap physics and different spins particles interactions?

[@Burevestnik9M730]

It seems there is a link. From Wikipedia: "The finding of 1924 that in quantum mechanics the spin of an electron and other matter particles (known as spinors) can be described using quaternions furthered their interest; quaternions helped to understand how rotations of electrons by 360° can be discerned from those by 720° (the "Plate trick").[22][23] As of 2018, their use has not overtaken rotation groups.[a]"

[@walterbrownstone8017]

Wait what a particle is a screw now?

[@2tehnik]

Mr. Unzicker, have you considered making a video/presentation series covering some of these topics about QM and quaternions in more detail like you have for variable speed of light?

[@TheMachian]

Yes, but I feel I have still to work on the content.

[@2tehnik]

@@TheMachian on other content?

[@tinkeringtim7999]

​@@TheMachian I strongly suggest you research quaternions more extensively and from the original sources.
You are understanding quaternions based on a particular visualisation which is an extremely limited and obscuring lens. Fundamentally they are a ratio of line segments. You are reading about them from the lens of formalist mathematicians who smashed quaternions up with a hammer and hid the pieces.
I'm a maths geek with almost all original source materials and a degree in theoretical physics, let me know if you're interested in a chat.

[@RohitSharma-mi8gt]

nice way to think about electrodynamics.

[@NikolajKuntner]

Interesting, what other presentations where given at the Quaternions and Octonions conference? Its web page lists some names but not really the titles.

[@TheMachian]

You may want to contact the organizers. But as fdar as I know, there is no such thing like proceedings.

[@DalbyJoakim]

Questions raised in this talk seem to have been solved in the 4D Special Relativity field theory of John Williamson. Origin of the assumed rigididity of the flexible Either mentioned here is proposed by John Macken to be due to an exlosively increasing density of space state with space volume. Solutions to the resulting field equations are given in "44" by Thad Roberts. Unit quaternions are essential but not enough to describe all operations - a scalar field is needed also, and that requires octonions also, to describe special relativity.
The John Williamson theory can probably be expanded to non-rigid smaller John Macken space also, by breaking it up into a Finite Element Analysis of pseudo-rigidities each with their own offset from some unitary scale.

[@heavyduty8194]

Hi, what are your thoughts on Enrico Fermi? Does he belong to your category of great physicists.

[@alphalunamare]

Regarding the Mathematics, why not take a look at Clifford Algebra's ? A more modern term is that of "Geometric Algebra" It provides a more robust mathematical basis for the Physics of the large and small. It can very easily be seen as a natural home for Quaternions .

[@hansvetter8653]

Some fundamentals of epistemology:
1) Nature is reality and therefore true and rational, but human thinking is just irrational and they invented the idea of "contradiction" in the frame of a calculus ...
2) It was Aristoteles who came up with his concept of calculus named syllogism. It's a frame of thinking founded on premisses, rules and derivations ... later expanded by Gottlob Frege to his calculus named "First Order Logic" ... (Prädikatenlogik)
3) Any calculus is only valid if premisses & rules are free of contradictions ... ! ...
4) Premisses cannot be proofen, but someone could come up with even more fundamental premisses ... and so on ... ending up into the regress ad infinitum ... defining scientific dogma ...
5) David Hume postulated his "fork": if and its exists, than it is real and true and free of contradiction ... e.g. the colors "black" & "white" ...
6) But terms like "slower" & "faster" cannot be valid at the SAME time for the same objects ... that would be a contradiction falsifying the thesis ...
Now ... lets apply this to Einstein's theory of "special relativity":
... lets do the same thought-"experiment" as the president of the Royal Astronomical, Dr. Herbert Dingel, has described in his book "Science at the Crossroads":
- imagine two identical precision clocks placed apart by a distance of lets say 100 m and the start moving toward each other ...
- surprisingly the first clock announced "Hey! You second clock! You are ticking SLOWER!" ...
- ... but the second clock responses: "False! I am ticking FASTER than you!" ...
THAT is a classical epistemological contradiction ... ! ... falsifying Einstein's theory of "special relativity" because the second clock can NEVER EVER tick SLOWER & FASTER at the SAME TIME !
Ernest Rutherford took Einstein's concept about speed depending "spacetime" as a (bad?) JOKE! ... and Werner Heisenberg mentioned once that these phanomens only seems to take place and ONLY for the so called "OBSERVER", which was invented by Albert Einstein in order to replace the "ether", which in turn got invented by physicists, because of the lack of an coordination zero-point in space for the universe ... and in general every experiment produces measurement results ... just not Einstein's thought-"experiments" ... so he should have named them "thought-games" ... ;-)
But still even the critical thinker Dr. Alexander Unzicker still trusts Einstein and Minkowski's (Einstein's math teacher!) invention of "spacetime". Since a century the majority of physicists are covering up this false spacetime scheme ignoring e.g. the GOM-Project relativity, listing more than 3,700 papers falsifying Einstein's theory of "special relativity". One good example is e.g. the paper from Dr. Louis Essen - source: od.lk/f/OV80NjcxMTI1NV9rMkJwZQ
,,, Dr. Louis Essen invented the first atomic clock (caesium) and his research effected the redefinition of the SI-unit 'second". So he is one of the most competent experts for measurements of time on the globe ... claiming that Einstein's idea of "time-dilation" is just an illsion!
Here the link to the GOM-Project relativity:
- www.ekkehard-friebe.de/95yearsrelativity.pdf
- www.kritik-relativitaetstheorie.de/Anhaenge/NPA_Paper_GOM_2013.pdf
... as Einstein himself declared ... "What you cannot explain, you have NOT understood yourself!" ... and Karl Popper rearticulated this important insight in an interview of the weekly magazin "Die Zeit" in the year 1971: "What you cannot simply say, you simply should'nt say ... so shut up and continue working ... until you can!" ... ;-)
But hey ... even Wolfgang Pauli critized Immanuel Kant in his 1919 paper about Einstein's concept of "relativity" heavily for his audacious postulation that "space" & "time" is stable & unchangeable ... Einstein skipped that and postulated himself that the speed of light is not only "constant" but even a "constant of nature" ... ;-)
In his annus mirabilis paper back in 1905 "Zur Elektrodynamik bewegter Körper" Einstein declares that simultanious events at different location in space are "impossible" just because of the transit-time of photons ... ignoring that events in moving frameworks still & always have a length of ZERO ... ! ... ;-)
Source: users.physik.fu-berlin.de/~kleinert/files/1905_17_891-921.pdf
Einstein even did not bother much about what his understanding of the term "time" is all about ... he simply declared that "time" is what clocks are displaying ... and he even did not bother about what exactly get slowed by speed ... "time" or "clock" ... ?!? ... and by inventing kind of a "speed of time" and taking into account that "speed" is the ratio of "distance" divided by "duration" everybody can see the tautology ... ! ... SO ... just keep your critical faculties safely if you hear articulations like ... "there MUST be a problem, because ..." ... (17:20 min:sec)
Even the simple math behind Einstein's theory of "special relativity" (based on the Pythagorean theorem) and specifically the paragraph §5 (Additionstheorem der Geschwindigkeiten - page 905) builds into the SRT mathematical contradictions, because either two objects starts symmetrically and end up at different locations in space or they have to start unsymmetrically in order to end up at the same location in space ... here is my little paper with exemplar calculations: www.slideshare.net/HansJVetter/falsification-of-einsteins-theory-of-special-relativity-250229728
...

[@Burevestnik9M730]

If you were to imagine that Ed Whiten was in the audience asking a question, what would that question be?

[@TheMachian]

I have no idea what's going on in his head. Certainly not much physics-related things.

[@seedsole]

For the 'unsolved' mathematical problems mentioned at around 28:00, how about the eccentric but interesting work of Dennis Morris? See his book "Non-commutative differentiation and the commutator"

[@TheMachian]

Thanks for the hint.

[@simonstrandgaard5503]

Excellent talk. However audio quality is terrible.

[@g1a18]

Thank you 😊 professor

[@TheMachian]

Welcome! I am Dr.

[@g1a18]

@@TheMachian oh sorry thank you doctor

[@BarriosGroupie]

@@g1a18 His doctorate is in neuroscience and not physics

[@Dyslexic-Artist-Theory-on-Time]

Three plus one, the Inverse Square Law, we have three dimensions interior of a sphere with its two dimensional surface. The two dimensional surface can form a geometrical bases for positive and negative charge. Could we have a geometrical process that forms your 'Quaternions and Octonions' and the potential for ever more abstract mathematics?

[@TheMachian]

I don't know (yet? see 2nd question :-)) how to give a physical meaning to octonions. I am still struggling with the intricacies of the non-commutative quaternions.

[@FunkyDexter]

​@@TheMachian Octonions (a split-complex subalgebra of them, which gets rid on non associativity) are useful as the algebraic representation of the 3-sphere, when you consider handedness as a fundamental feature of the topological space instead of as a convention. I highly suggest you check out Joy Christian's work.

[@justinmurre5193]

Let’s think square of a quaternion as a ”metric element” in 4D, real part referring to radial displacement and 3 imaginary elements to relative position in 3D shell. So far so good, or is this already erong somehow?
If you calculate the real part of the square, there you got Lorentz invariant distance when you leave (timelike) radial component as it is and divide all imaginary terms by c.
That is a great indicator to my mind. Please tell me if the reasoning is wrong here.

[@TheMachian]

Rather than considering the 4-D quaternions, I am more intrigued by the unit quaternions as a model for spacetime. But this is still a guess.

[@richardgreen7225]

@@TheMachian - I think "4D space-time" is a classical distraction (It goes back to 1800s.)
- We need 6+3 observables to describe the classical EM and gravity fields at each point in an "laboratory" frame which is requires 3+3+3 spatial observables (position, velocity, and rotation) for its description. Thus the frame is 9+1 and the fields are also 9+1. Is that a coincidence?
- The parameter space has 20 variables (including local time and retarded time).
- In addition to the classical spatial dimensions, there appears to be one or more compact dimensions producing effects at the nuclear level.

[@FunkyDexter]

You ought to check out Joy Christian's work.

[@TheMachian]

Know his work, also referenced in my book "The Mathematical Reality". Very intriguing.

[@nunomaroco583]

Very interesting....

[@zyxzevn]

Do you know that you can have Electromagnetism without Magnetism?
It will remove the need for the mathematics transformations, like quaternions.
You only need to compensate for the time-delay between moving objects,
and add a small energy-conserving correction.
Electromagnetism without Magnetism explained:
If you have a static charge, the electrical force (FE) between charge q and chrage Q is:
FE = C*q*Q/(R*R) - Coulomb's equation
If both charges are moving with speed V in parallel, the force changes.
That is because there is a delay before the change arrives at the other charge.
You can see in electronics that this change moves with the speed of light.
I assume that the charges have moved distance d during the time T that the electric force arrives.
d= V*T
T = sqrt(R*R +d*d) / c
sqrt = square root.
Note that the R and d form a triangle.
So we have a dynamic electric force (FEd):
FEd= C*q*Q/ ( (R*R+d*d) )
FEd is a bit smaller than FE, because the electrical field needs to cross more distance
while the objects are moving.
The difference ( FH ) between the static force (FE) and the dynamic force (FEd) is ...
FH = FE - FEd
FH = C*q*Q* X
X = 1/(R*R) - 1/(R*R + d*d)
X = d*d / (d*d*R*R + R*R)
FOR slow speeds..
for very small d we have:
X= d*d / ( R*R )
T = R/c
so: d = V*R/c
so: FH = FE - FEd = C*q*Q * V*V/(c*c * R*R)
FH= CH *q*Q* V*V/(R*R), where CH= C/(c*c)
This FH looks very much like the magnetic force.
And sure, in an electrical neutral system, this is the magnetic force.
FOR all speeds...
Via WolframAlpha I get:
Full equations:
www.wolframalpha.com/input/?i=d%3D+v*t%2C+t%3D+sqrt%28+r*r%2Bd*d%29%2Fc%2C+H%3D+1%2F%28r*r%29+-+1%2F%28r*r%2Bd*d%29%2C+solve%28H%2Cd%2Ct%29
Result (simplified):
H= C*q*Q* V*V/(c*c*R*R)
Yes, I double checked. It is the same,
while the d and T get a Lorentz transformation.
Just as if there was relativity.
CORRECTION for energy:
While you can not see it in the mathematicss, I omitted the direction of the force.
As the objects move, one might think of a field moving like a wave on the sea.
This would mean that the electrical force might come slightly from behind the objects.
This will cause energy-gain or energy-loss, and is physically not possible.
So the force is always in the direction where the object should be, assuming no change of speed.
MY CONCUSION:
There is no need for magnetism.
Nor is there any need for relativity, at this point.

[@kantanlabs3859]

Indeed this well known classical example made many of us perplex for a while !
However such a removal of the magnetic field is only simple when you consider charges moving in a single direction relative to other static charges (then transformations between galilean frames). If you want to cancel the magnetic field in more complex situations (for rotations for instance or many charges moving in different directions), there is no simple transformation that allows you to cancel the magnetic field. Said othervise a general cancellation of the magnetic field involves non galilean transformations. In such cases coriolis forces arises everywhere and calculation are much simpler in a galilean frame of reference whith a magnetic field rather than in a complexely distorted spacetime without it !
However this does not answer the fundamental question about the nature of these fields !

[@zyxzevn]

@@kantanlabs3859 Thanks for feedback. It is all indeed much more complicated.
Though, I never seen it mentioned as a classic example.
I was working on a simulator, when I noticed that it is important to include the delay of the fields. And when I calculated them, I noticed that the magnetic field was unnecessary via the above principle.
With magnetic fields from many particles, it seems to fail, but an electrical system is also quickly in equilibrium. The charges often move too quickly for us to measure. It would be a good falsification experiment to check if these electrons do indeed move. And with that we know whether the magnetic field really exists.
On quantum scales the magnetic fields are more mysterious too. Within an atom an electron does not create radiation via its circular movement. While outside the atom it does.
My theory is that the electrons are "captured" in some way, via their own "quantum resonances".

[@kantanlabs3859]

@@zyxzevn Indeed electric and magnetic near-fields are not well introduced in academic books. The only exception is found in Melcher book and work. A recent Veritassium video highlighted the poor understanding most engineers and academics have on the way energy is transferred in quasi-static near-field situations. The Poynting vector (the local energy flux) is often introduced as a real quantity but in fact it is not locally defined, only the balance of the energy flux over a closed surface has a physical meaning. Many different definitions of the local flux lead to the same result (I wrote an article on this subject a few years ago).
Don't get me wrong, there is no problem with Maxwell equations that are essentially of empirical origin, but a misunderstanding of their meaning in the low frequency domain where solutions splits into two different non-relativistic quasi-static domains.
My point is that this presently nearly discarted electric-magnetic separation has deep conceptual implications. I recently wrote a didactic kindle book on this subject. Infortunately its in french but you may catch the general ideas through the many illustrations provided. If you are interested in pushing forward your investigations in this area, just look for "Les concepts sans les Maths - l'Electromagnétisme" on Google search. You may later contact me using Researchgate for instance. Regards !

[@clmasse]

Electrodynamics without explicitly taking about the magnetic field is not electrodynamics without magnetism. Talking about light is talking about the magnetic field, since otherwise it couldn't propagate.

[@kantanlabs3859]

@@clmasse Well technically this argument is not the best one as in this case the magnetic-field can be easily removed from the picture: its amplitude is E/c and its direction is perpendicular to E. Beside your idea that the two fields are necessarily involved probaly rely on the idea that energy alternates in quadrature inbetween electric and magnetic forms. This is also wrong as the two fields are in phase 🙂

[@phyarth8082]

Lewis Carol most famous Euclidian geometry teacher in Victorian England and criticism of new appearing mathematics non-Euclidian geometry and of course (complex numbers and quaternions)of Alice in wonderland tea-party T-party aka pun on Time, party. Lewis was unhappy with Hamilton absolute time concept rotation around T-party table without reasons but that is reason I think Irish was genius he created absolute time concept. Entropy arrow of time always is straight line erosions of French Riviera is beautiful and that entropy of time, wave erosion of coastline or biological clock from past to future, but Hamilton with quaternions created absolute time concept.
Lack in physics of absolute time and energy concepts, we have time and energy units (which is arbitrary units created by humans) but deeper understanding how time and energy is created by fundamental laws of mathematics most fundamental level is very vague concepts.

[@richardgreen7225]

Energy and time are bookkeeping artifacts. They are derived from other "real" observables. Treating such metrics as part of nature creates confusion.

[@daemonnice]

Full disclosure; I am not a mathematician, but rather, a natural philosopher. Mathematics is an abstraction of reality according to mathematician Alfred North Whitehead, and this is something that I feel we have lost sight of. Mathematics can also be a great liar convincing us for over a millennia of a geocentric cosmology due to its predictive success. Well, that is after a few ad hoc adjustments. Nonetheless, the math was genius and had significant success, but in the end, described a false reality. This is why math is a tool of science and not science as believed by many today and is why we shouldn't confuse the ability to map 3D reality through time as reality itself. Treating Time as a dimension may be mathematically convenient and a useful tool, but, in reality, it isn't anything like the dimensions of physical space. This 4D mapping of space-time is analogous to a movie film, and similarly, a good means of making observations of 3D processes over time.
Because I am not a mathematician, I truly appreciated the animation. Watching the lines move I instantly thought of the solar system where I see many layers of magnetic fields beginning with the interplanetary magnetic field, within which are a plethora of magnetic fields from magnetospheres of planets to magnetic flux loops all interacting and flexing due to the current of the heliocentric current sheet within the solar wind. Could quaternions be used to explain what I believe is the electromagnetic nature of orbital mechanics?

[@clmasse]

Questions about mathematics are not the good questions. As soon as a space is endowed with a quadratic form, a Clifford algebra can be built on it with all the necessary structures, and quaternions are but one of them. Space with any dimension and signature can be constructed, there is all too many mathematics to describe comparatively few physical phenomena.

[@koenraad4618]

Quaternions, bi-quaternions, octonions. Siberstein's theory of special relativity in terms of quaternions is wrong. He made a math error, which resulted into a 'lorentz transform' rotation in eight space in stead of four space, so it is tricky business. In terms of bi-quaternions it is much easier to express the four maxwell field equations in one bi-quaterion equation. A big disadvantage of using this type of mathematics (quaternions etc): it becomes impossible (or very hard) to express the fact that the Coulomb field propagation velocity is much higher than 'c', which became evident during the last decade after a variety of experiments about measuring the speed of the Coulomb near field (Coulomb force). This is the reason I reject all 'bi-quaterion' theories of CED and SR: the resulting theories in terms of (bi)quaternions are unphysical, and in disagreement with experimental facts. Quaternion math is certainly interesting, but it is not necessarily useful for physics.

[@schizoidman9459]

I am very interested in the videos of this channel, but mainly for its contents. I have a PhD in Computer Science, English is not my native language either, and I did many presentations in conferences myself. However, I have to tell that some extra effort should be made by the author to enhance his English as well as his presentation skills. To say "coniugate" instead of "conjugate", or "excistential" instead "existential" is quite annoying, specially here on UA-cam. Using very known "false friends", such as "realize" instead of "perform", etc., terribly devalue these videos as well. Also the presentations lack fluidity. It is a pity that they lose a lot of their potential because of such basic mistakes that are normally quite easy to correct. Just recording your presentation and watching it would enormously contribute to a better delivery. I'm sorry for this comment, but I have to say that it's pretty bad and something should be done about it.

[@TheMachian]

I am ok with this criticism, I'll think about.

[@atol71]

zwei gleiche Hälften einer Münze sind keine Münze

[@richardgreen7225]

see also: "How the complex quaternions give each of the Lorentz representations of the standard model"
ua-cam.com/video/d3y72uw7M5Q/v-deo.html

[@TheMachian]

This is nice math, but unfortunately the lady does believe the standard model. There is no way that a fundamental approach to physics can reproduce this mess.

[@richardgreen7225]

@@TheMachian - ????
Why would Furey bother if she did not have some belief in the validity of the Standard Model.
- Furey reproduces the patterns of the first generation of the standard model in quaternion algebra patterns. She then goes on to reproduce the patterns of the second and third generations in octonion algebra patterns. This indicates some deeper structures. The patterns indicate some topology.
- However, she does not attempt to predict mass ratios (in this series of papers). IMO: Physics needs a better theory of inertia.

[@TheMachian]

As I said, mathematicians take the standard model for granted, but if you look of the evidence provided by high energy physics since 1930, most of these particles turn out to be bs concepts, forcefully interpreted into noisy data. See my book "The Higgs Fake" or Andrew Pickering's "constructing quarks". Thus, even if I appreciate such math activities in general, they do not advance fundamental understanding in this case.

[@richardgreen7225]

@@TheMachian - Okay. I see where you are coming from now. (I have read your books). I also find the particle physics "evidence" suspect. Even accepting the standard model, categorizing a "particle" in the second and third generations as "fundamental" even though they all decay quite rapidly seems like a contradiction in terms. Those behaviors look like excited states, not fundamental objects.

[@clmasse]

@@TheMachian The standard model describes the observed particles. A fundamental theory that doesn't reproduce the standard model (like string theory?) is _von vornherein_ false.

[@surendranmk5306]

All the lines you draw here are straight lines! That is classical mechanics. In general relativistic mechanics there is no straight lines. All the lines one can draw ought to be part of elliptic circles. In an expanding or contracting universe axis of time also curved like space. There is some mistakes in the very basics of physics. Some approximations leads over the truth. 3+1 dimensional continuum is limited and not applicable with infinite space!

[@andreasproteus1465]

Masked face. I stop watching.

[@giacomozucco8619]

Prof Unzicker had no facial diaper though.