Rotation and Boost of Tensor Components: Meaning?

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SUMMARY

The discussion centers on the transformation of tensor components under rotations and boosts in different coordinate systems. It is established that while vectors are commonly described as being rotated or boosted, the same terminology does not intuitively apply to general tensors of higher rank. The conversation highlights that tensors, particularly those of rank greater than one, lack a singular direction, complicating the notion of their transformation in the same manner as vectors. The concept of Lorentz invariance is emphasized in the context of physical rotations and boosts.

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  • Understanding of tensor mathematics and notation
  • Familiarity with Lorentz transformations in special relativity
  • Knowledge of vector and tensor components
  • Basic principles of coordinate transformations
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  • Explore the implications of tensor rank on physical interpretations
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Physicists, mathematicians, and students studying relativity, particularly those interested in the behavior of tensors under coordinate transformations.

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If two coordinate systems are related by a rotation or a boost, does it make sense to say the tensors components are rotated or boosted with respect to their components in the original coordinates? For vectors, I think it is standard to say that, but what about general tensors?
 
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A tensor could be also a vector.One call it a one tensor.A rotation is only a mathematical construction.Of course, a boost is also a rotation but with a physical meaning involved .Here you make a rotation in a Lorentz invariant manner.So the (relativistic)physics holds under this specific transformation.In this case you rotate you Frame Of Reference by an angle theta .
 
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troglodyte said:
A tensor could be also a vector
I know that
troglodyte said:
One call it a one tensor.A rotation is only a mathematical construction.Of course, a boost is also a rotation but with a physical meaning involved .Here you make a rotation in a Lorentz invariant manner.So the (relativistic)physics holds under this specific transformation.In this case you rotate you Frame Of Reference by an angle theta .
I also know that

Your didn't answer my question at all.
 
kent davidge said:
For vectors, I think it is standard to say that

I'm not sure it is. It's standard to say that vectors are rotated or boosted, but I'm not sure it's standard to say that vector components are.

kent davidge said:
what about general tensors?

Tensors of higher rank than 1 do not have a single "direction", so speaking of them as rotated or boosted by a coordinate transformation would not seem to make as much intuitive sense as the corresponding statement for a vector, which does have a single direction.
 
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kent davidge said:
Your didn't answer my question at all.
Sorry,than i have misinterpreted your question a bit.
 
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