Quaternions or Vectors: Which is the Better Choice for Electromagnetism?

[Gerenuk]

I read that people prefer vectors over quaternions (e.g. for electromagnetism), since one can do the same operations more transparent. Is it really a matter of preference? What's advantages of one or the other?

 

[nanobug]

I read that people prefer vectors over quaternions (e.g. for electromagnetism), since one can do the same operations more transparent. Is it really a matter of preference? What's advantages of one or the other?

Actually, differential forms together with vectors appears to be the currently preferred "flavor".

 

[tacman]

The choice between quaternions and vectors for electromagnetism is not necessarily a matter of preference, but rather depends on the specific application and the needs of the user. Both quaternions and vectors have their own advantages and disadvantages.

Vectors are a commonly used mathematical tool in electromagnetism because they are easy to understand and manipulate. They have three components (x, y, and z) which correspond to the three-dimensional space in which electromagnetic phenomena occur. Vectors are also useful for representing physical quantities such as electric and magnetic fields, and they can be added and subtracted to obtain the net field at a particular point. In addition, vectors are well-suited for graphical representations, making it easier to visualize electromagnetic phenomena.

On the other hand, quaternions have four components (x, y, z, and w) and are less commonly used in electromagnetism. However, quaternions have the advantage of being able to represent rotations in three dimensions, which makes them useful for describing the orientation of objects in space. This can be particularly useful in applications such as robotics or aerospace engineering. Quaternions also have the ability to represent complex numbers, which can be useful in certain electromagnetic calculations.

In terms of operations, vectors are more straightforward and transparent compared to quaternions. This is because vectors follow the basic rules of vector algebra, such as addition, subtraction, and dot and cross products. On the other hand, quaternion operations can be more complex and require a deeper understanding of their properties.

In conclusion, the choice between quaternions and vectors for electromagnetism depends on the specific needs and applications of the user. Vectors are more commonly used and easier to understand, while quaternions have unique properties that make them useful in certain scenarios. It is important for individuals to assess their specific needs and choose the mathematical tool that best suits their application.