Unit Quaternions and Electrodynamics

Talk given at the conference "New Trends in Quaternions and Octonions" in Vila Real, 2021 by Alexander Unzicker.

[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.

[mathoph]

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.

[JoseSilveira-newhandleforYT]

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

[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 .

[BurevestnikM]

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

[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.

[RohitSharma-migt]

nice way to think about electrodynamics.

[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"

[tehnik]

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?

[NikolajKuntner]

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

[simonstrandgaard]

Excellent talk. However audio quality is terrible.

[hansvetter]

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 <something> and its <opposite> 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" ... ;-)
, ,, 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:
... 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 ... ! ... ;-)
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)
...

[heavyduty]

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

[BurevestnikM]

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

[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?

[FunkyDexter]

You ought to check out Joy Christian's work.

[justinmurre]

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.

[schizoidman]

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 YouTube. 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.

[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:

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.

[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.