A doubt regarding vectors, scalars and their role in physics

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Discussion Overview

The discussion revolves around the classification of physical quantities as vectors or scalars, and the implications of this classification on operations performed with these quantities. It touches on foundational concepts in physics, including axioms and postulates in classical and relativistic mechanics.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the guarantee that all measured quantities in physics can be classified as either vectors or scalars and whether they will adhere to established operational rules.
  • Another participant suggests that there are no guarantees, yet the use of vectors and scalars has been effective in achieving results in physics.
  • A later reply emphasizes that the classification of mass in classical mechanics (e.g., combining masses) is more of an axiom that is tested experimentally, rather than a guaranteed truth.
  • It is noted that in relativistic mechanics, the simple addition of rest masses does not hold true, as illustrated by the example of a hydrogen atom's mass not equating to the sum of its constituent electron and proton masses.
  • Another participant introduces the concept that scalars and vectors can be viewed as zero- and first-order tensors, respectively, and mentions the necessity of higher-order tensors in physics and engineering.

Areas of Agreement / Disagreement

Participants express differing views on the guarantees surrounding the classification of physical quantities as vectors or scalars, with some asserting that there are no guarantees while others highlight the axiomatic nature of these classifications. The discussion remains unresolved regarding the foundational aspects of these classifications.

Contextual Notes

The discussion includes assumptions about the nature of physical quantities and their classifications, as well as the implications of these classifications in different physical contexts, such as classical and relativistic mechanics.

JackFyre
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TL;DR
A doubt regarding vectors, scalars and their role in physics
I have a doubt regarding the basic function of vectors and scalars in physics-

What is the guarantee that every quantity(measured) in physics can be classified as either a vector or a scalar, and that while performing operations on said quantities, they will obey the already established rules of vector/scalar operations?
 
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JackFyre said:
What is the guarantee that every quantity(measured) in physics can be classified as either a vector or a scalar, and that while performing operations on said quantities, they will obey the already established rules of vector/scalar operations?

zero... zero guarantees... It just seems to do quite alright considering what we've achieved by using them. What do you suggest as alternative?
 
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JackFyre said:
Summary:: A doubt regarding vectors, scalars and their role in physics

I have a doubt regarding the basic function of vectors and scalars in physics-

What is the guarantee that every quantity(measured) in physics can be classified as either a vector or a scalar, and that while performing operations on said quantities, they will obey the already established rules of vector/scalar operations?
Can you be more precise about your question?

It's generally implied in classical physics that if we have two particles of mass ##m_1## and ##m_2## and we put them together, then we have a system of mass ##m = m_1 + m_2##.

There's no guarantee that will be correct. It's more an axiom or postulate of classical mechanics that gets tested (along with all the other axioms, postulates or laws of motion) during an experiment.

And, in fact, in relativistic mechanics if ##m## above represents rest mass, then it's not true. For example, if ##m_e## is the mass of an electron and ##m_p## the mass of a proton, and ##m## is the mass of a hydrogen atom with one proton and one electron, then: ##m \ne m_p + m_e##.
 
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PeroK said:
Can you be more precise about your question?

It's generally implied in classical physics that if we have two particles of mass ##m_1## and ##m_2## and we put them together, then we have a system of mass ##m = m_1 + m_2##.

There's no guarantee that will be correct. It's more an axiom or postulate of classical mechanics that gets tested (along with all the other axioms, postulates or laws of motion) during an experiment.

And, in fact, in relativistic mechanics if ##m## above represents rest mass, then it's not true. For example, if ##m_e## is the mass of an electron and ##m_p## the mass of a proton, and ##m## is the mass of a hydrogen atom with one proton and one electron, then: ##m \ne m_p + m_e##.
That pretty much answers it, thanks!
 
Scalars and vectors are just zero- and first order tensors, respectively. In physics and engineering we also need to employ higher order tensors, such as the stress tensor.
 
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