The discussion revolves around the classification of quantities without units of measure, specifically focusing on whether such quantities can be considered scalars, vectors, or neither. The refractive index is frequently mentioned as an example, raising questions about its nature in isotropic versus non-isotropic media.
The conversation is ongoing with various interpretations being explored. Some participants suggest that the refractive index is a scalar in isotropic media, while others question this classification and consider the implications in non-isotropic contexts. There is no explicit consensus, but several productive lines of inquiry have been established.
Participants note that definitions may vary and that the classification of quantities could depend on the context or specific educational expectations. There is also mention of the potential for dimensionless quantities to be treated differently based on their application.
I am very curious to know how to resolve this problem in detail, as I have never seen this discussed in any book. I am a physics teacher and I am writing a book on vectors in which I wish to insert such a discussion.fresh_42 said:Why do you insist on this wording? It's important to understand what is meant by scalar, vector, quantity, unit and dimension. Among these, quantity is certainly the least rigorously defined term.
I apologize for the persistence and thank you for your attentionfresh_42 said:Quantities can be a scalar or a vector (C). And it doesn't matter whether they have a unit or not, only that they can be measured somehow. This makes them different from a quality.
De nada.Caio Graco said:I apologize for the persistence and thank you for your attention
I would consider this a poor question because it is not clear what is allowed, though maybe there is an interesting question hiding within it.Caio Graco said:So to close, in case you were to mark my initial question, you would mark the letter A. Is that it?
Quantities without unit of measure are:
A) Necessarily scalar
B) Necessarily vector
C) Can be scalar or vector
D) They are neither scalar nor vector
Interesting twist to this thread...Caio Graco said:I am a physics teacher and I am writing a book on vectors in which I wish to insert such a discussion.
See if any of these are useful:Caio Graco said:I am very curious to know how to resolve this problem in detail, as I have never seen this discussed in any book. I am a physics teacher and I am writing a book on vectors in which I wish to insert such a discussion.
Ok. Thanks.haruspex said:See if any of these are useful:
https://www.physicsforums.com/insights/frequently-made-errors-mechanics-forces/
https://www.physicsforums.com/insights/frequently-made-errors-pseudo-resultant-forces/
https://www.physicsforums.com/insights/frequently-made-errors-mechanics-moments/
https://www.physicsforums.com/insights/frequently-made-errors-mechanics-momentum-impacts/