Looking for a book on Quaternions

[Julano]

Hello everyone,

Lately, I have been reading and studying the Maxwell's https://es.wikipedia.org/w/index.php?title=A_Treatise_on_Electricity_and_Magnetism&action=edit&redlink=1 https://es.wikipedia.org/w/index.php?title=A_Treatise_on_Electricity_and_Magnetism&action=edit&redlink=1

Thanks for your help!

 

[micromass]

Wouldn't you prefer to study geometric algebra (aka Clifford algebra) instead, which is a very beautiful and comprehensive theory which contains the quaternions as a special case.

https://www.amazon.com/dp/0521715954/?tag=pfamazon01-20

 

[Julano]

Wouldn't you prefer to study geometric algebra (aka Clifford algebra) instead, which is a very beautiful and comprehensive theory which contains the quaternions as a special case.

https://www.amazon.com/dp/0521715954/?tag=pfamazon01-20

Surely I prefer it! haha
Well, for being honest, I had never heard about Geometric Algebra neither topics related with it (only quaternions). I am seeing, as you said, that is a more general theory.

Thanks for your recommendation!

 

[Aufbauwerk 2045]

Hello everyone,

Lately, I have been reading and studying the Maxwell's https://es.wikipedia.org/w/index.php?title=A_Treatise_on_Electricity_and_Magnetism&action=edit&redlink=1 https://es.wikipedia.org/w/index.php?title=A_Treatise_on_Electricity_and_Magnetism&action=edit&redlink=1

Thanks for your help!

Maxwell discusses quaternions, and said some of the ideas are useful. However, he also said that for purposes of calculation the Cartesian coordinates are more useful, and he intended to use only that system in his Treatise.

If you look at the history of how quaternions have been used in physics, there simply isn't much there. Dirac wrote at least one paper using quaternions (Applications of Quaternions to Lorenz Transformations), and after reading it I realized why people don't use quaternions. There was also The Theory of Relativity (Silberstein, 1914) which is fascinating, but this book does not encourage me to switch to quaternions, to say the least.

The fact is, if quaternions were so useful in physics and so much better than current methods, we would be using them. They are used somewhat in computer graphics because they can be convenient for rotations, but I think that's about it. The physicists of the 20th century who did not use quaternions were not stupid. Quaternions are a fringe subject because in general they are not useful.

Maxwell was great but he's not the last word. His theory of E&M consisted of 20 equations in 20 variables. Later Heaviside wrote his own Treatise and put E&M theory into a much simpler form. Heaviside did not use quaternions, which he condemned. He used vectors. Sometimes today we talk about the Maxwell-Heaviside equations.

 

[Julano]

Maxwell discusses quaternions, and said some of the ideas are useful. However, he also said that for purposes of calculation the Cartesian coordinates are more useful, and he intended to use only that system in his Treatise.

If you look at the history of how quaternions have been used in physics, there simply isn't much there. Dirac wrote at least one paper using quaternions (Applications of Quaternions to Lorenz Transformations), and after reading it I realized why people don't use quaternions. There was also The Theory of Relativity (Silberstein, 1914) which is fascinating, but this book does not encourage me to switch to quaternions, to say the least.

The fact is, if quaternions were so useful in physics and so much better than current methods, we would be using them. They are used somewhat in computer graphics because they can be convenient for rotations, but I think that's about it. The physicists of the 20th century who did not use quaternions were not stupid. Quaternions are a fringe subject because in general they are not useful.

Maxwell was great but he's not the last word. His theory of E&M consisted of 20 equations in 20 variables. Later Heaviside wrote his own Treatise and put E&M theory into a much simpler form. Heaviside did not use quaternions, which he condemned. He used vectors. Sometimes today we talk about the Maxwell-Heaviside equations.

Hello David,

One of the reasons why I wanted to read about quaternions it because of the concept of vector and its development at the end of XIX century. I think quaternions took a fundamental role in this development, but of course vector calculus, for example, is more useful.

I think I'm not going to discover gunpowder reading Maxwell, but for me it is extremely interesting how classical physicist as Ampere, Maxwell, Biot, Weber disscused the topics of electric and magnetic field. For example, Maxwell talked so much frecuently on his works about Potential Vector A, and sometimes he gives it a physical meaning, something that is not common nowadays.

On the other hand I respect Heaviside so much and i really like his lectures. As you said, he simplify Maxwell theory and even expanded it. He was an autodidactic scientist sometimes mistrated by the scientific community and he is the father of E&M classical theory, circuit theory, operational calculus and even vector calculus. In my opinion he is one of the physicist who more contributed to physics and mathematics at the XIX century.

The physicists of the 20th century who did not use quaternions were not stupid.

It wasn't my intention and i didn't say anything similar.

The fact is, if quaternions were so useful in physics and so much better than current methods, we would be using them.

Well, i don't agree with this assertion. The fundamental example of why i think this is not true it's the fight between the corpuscular theory and the wave theory of light. Took centuries to wave theory to be accepted, even when it described experiments better, because Newton was an authority in the scientific community and he didn't like wave theory, rightfully. Finally it was accepted, but god damn. What i tried to say is I do not believe in the collective wisdom of individual ignorance.

Thank you so much for your answer, good day to you

 

[Aufbauwerk 2045]

Hello David,

One of the reasons why I wanted to read about quaternions it because of the concept of vector and its development at the end of XIX century. I think quaternions took a fundamental role in this development, but of course vector calculus, for example, is more useful.

I think I'm not going to discover gunpowder reading Maxwell, but for me it is extremely interesting how classical physicist as Ampere, Maxwell, Biot, Weber disscused the topics of electric and magnetic field. For example, Maxwell talked so much frecuently on his works about Potential Vector A, and sometimes he gives it a physical meaning, something that is not common nowadays.

On the other hand I respect Heaviside so much and i really like his lectures. As you said, he simplify Maxwell theory and even expanded it. He was an autodidactic scientist sometimes mistrated by the scientific community and he is the father of E&M classical theory, circuit theory, operational calculus and even vector calculus. In my opinion he is one of the physicist who more contributed to physics and mathematics at the XIX century.It wasn't my intention and i didn't say anything similar.Well, i don't agree with this assertion. The fundamental example of why i think this is not true it's the fight between the corpuscular theory and the wave theory of light. Took centuries to wave theory to be accepted, even when it described experiments better, because Newton was an authority in the scientific community and he didn't like wave theory, rightfully. Finally it was accepted, but god damn. What i tried to say is I do not believe in the collective wisdom of individual ignorance.

Thank you so much for your answer, good day to you

Thanks for your reply. I wasn't aiming remarks at you but actually taking the opportunity to express my frustration, because I spent way too much time on quaternions, and I wanted to warn people about their strange appeal. I found quaternions dangerously fascinating. Now that I think about it, maybe I will look into them again. Then again, maybe not. Sorry if I caused any offense. Even though I sometimes do cause offense, it is never my intention.

:)

 

[Aufbauwerk 2045]

P.S. I don't quite follow your point about light as particle vs light as wave, compared to whether quaternions are useful. I think if a mathematical technique proves itself to be useful, people tend to use it. For example, some people do not like Feynman diagrams. Schwinger did not allow them to be used in his class. He said they are a technique people use when they don't understand the subject. But people use them regardless of what Feynman or Schwinger says about it, because they are useful. There has never been such a movement of people to quaternions. Could there be in the future? I suppose time will tell. Maybe we will hear from some people on this forum who swear by quaternions. Then I may need to change my opinion.

 

[Dr Transport]

one of my late professors swore by quaternions in physics, he was convinced that General Relativity was way more predictive although highly non-linear. the whole subject is interesting.

 

[Ssnow]

From a comprehensive historical introduction it investigates the geometry of quaternion and octonion algebras:

https://www.amazon.com/dp/1568811349/?tag=pfamazon01-20

Ssnow