Hijack from Is there anything left to discover in electromagnetism? Are there any mysteries regarding electromagnetism?

[neuerwind]

3 minutes ago, studiot said:

Here is an extract from Artzy : Geometry an Algebraic Approach, if you want more to see how quaternions have been brought into the fold of modern algebra.

Now I see: you don't understand me. But that's OK.

[studiot]

Just now, neuerwind said:

Now I see: you don't understand me. But that's OK.

No I don't understand why you apparantly don't wish to learn more about the subject of quaternions.

[beecee]

49 minutes ago, neuerwind said:

Well, I shall abide by the rules and keep dead silence

Speculate all you want, just make sure you are able to back your claims up and that they are in the appropriate section.

[Strange]

1 hour ago, neuerwind said:

Unfortunately, I'm lacking proper mathematical background to discuss all pros and cons of tensors vs. quaternions.

So you don't know what you retaking about and yet you still make these claims?

You can' even explain why you believe that vectors can only represent  two dimensions

1 hour ago, neuerwind said:

My point: if you'd like to obtain new results, you should use the new maths. And quaternions are not exactly 'new' to this field, as Maxwell tried to employ them, too.

So you think you need to use new maths to get new results (there is no reason that should be true) but then you want to go back to the old maths. That is not logical (in the correct meaning of the word).

1 hour ago, neuerwind said:

I would rather not bring it to the public.

Reported.

Edited August 27, 2018 by Strange

[Markus Hanke]

4 hours ago, neuerwind said:

No, they are. Vector algebra stipulates that we analyze rotary motion by projecting it on flat surfaces. On the contranry, the quaternion is a perfect mathematical representation of a rotating body per se.

A couple of points:

• Vector algebra stipulates no such thing
• The curl and divergence operators are differential operators; they are not part of vector algebra, but rather vector calculus
• You are trying to contrast vector algebra with quaternions, but quaternions and their inner product are an early type of vector algebra
• To avoid any of these types of issues, I have presented the differential forms formalism, which supersedes both quaternions and vector calculus, since it is both covariant and more general than either of these. 
• Differential forms are in fact antisymmetric tensors, so there is a strong link between exterior calculus, and tensor calculus
• The curl (being a differential operator) does not actually represent any rotating bodies, but infinitesimal rotations of a vector field about some point. 
• You can indeed use quaternions to represent rotations (such objects are called versors), but this method is not any more or less advantageous than more common methods such as rotations matrices. In fact, I’d say an argument can be made that quaternions are more cumbersome, and less transparent, in terms of computational effort.

Edited August 27, 2018 by Markus Hanke

[neuerwind]

12 minutes ago, Markus Hanke said:

this method is not any more or less advantageous than more common methods

This can only be proven after a thorough study. As far as I understand, no one even tried.

[Markus Hanke]

Just now, neuerwind said:

This can only be proven after a thorough study. As far as I understand, no one even tried.

Using quaternions for rotations - as well as comparing that method to other methods - is pretty basic material, and has hence been well studied and understood. You’d be discussing this stuff on an undergrad level of a math degree. There’s even a Wiki page on it:

https://en.m.wikipedia.org/wiki/Quaternions_and_spatial_rotation

[neuerwind]

6 minutes ago, Markus Hanke said:

Using quaternions for rotations - as well as comparing that method to other methods - is pretty basic material, and has hence been well studied and understood. You’d be discussing this stuff on an undergrad level of a math degree. There’s even a Wiki page on it:

https://en.m.wikipedia.org/wiki/Quaternions_and_spatial_rotation

I'm talking about application of quaternion to Maxwell's electrodynamics. You're derailing the thread.

Do you realize that this "pretty basic material" has never been studied? There is no such thing as "fully quaternion-based electrodynamics".

Edited August 27, 2018 by neuerwind

[swansont]

4 hours ago, neuerwind said:

I would rather not bring it to the public.

!

Moderator Note

Kind of awkward, this being a discussion site and all.

 

 

4 hours ago, neuerwind said:

 Well, I shall abide by the rules and keep dead silence

!

Moderator Note

To paraphrase Tom Lehrer, I feel that if a person has decided not to communicate, the very least they can do is to shut up.

 

As the hijacker of the discussion refuses to elaborate, this is going to the trash rather than speculations.

 

[Strange]

31 minutes ago, neuerwind said:

I'm talking about application of quaternion to Maxwell's electrodynamics. You're derailing the thread.

Do you realize that this "pretty basic material" has never been studied? There is no such thing as "fully quaternion-based electrodynamics".

Says the guy who admits he doesn’t know what quaternions are or how to use them. 

[Markus Hanke]

16 minutes ago, neuerwind said:

I'm talking about application of quaternion to Maxwell's electrodynamics. You're derailing the thread.

Do you realize that this "pretty basic material" has never been studied? There is no such thing as "fully quaternion-based electrodynamics".

I spoke about rotations in the post you quoted me on, as did you yourself in the post I quoted you on. You then said that this has never been studied, which is evidently wrong.
As for electrodynamics, of course this can be formulated using quaternions - even Maxwell himself did this. You need to realise that there is nothing special at all about the quaternion formulation - using quaternions just means you are using different language to describe the same physics. Here’s a sample text of how electrodynamics are done using quaternions:

https://www.scribd.com/document/91253848/quaternionic-electrodynamics

As a matter of fact, quaternions are a very common tool in mathematical physics, and are used extensively in all different areas. To prove that point, here’s a further 1382 (!) references to texts and papers employing the quaternion formalism in one form or another:

https://arxiv.org/pdf/math-ph/0510059.pdf

Are you still so sure that they have never been studied (and not just in electrodynamics)?