Rotation and Boost of Tensor Components: Meaning?

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Discussion Overview

The discussion centers on the interpretation of how tensor components are affected by rotations and boosts in different coordinate systems. Participants explore whether it is appropriate to describe the transformation of tensor components in the same way as vector components, considering both mathematical and physical implications.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants propose that it is standard to say that vectors are rotated or boosted, but they question whether this terminology applies to general tensors.
  • One participant suggests that a tensor can be a vector (a one-tensor) and that rotations and boosts have specific physical meanings, particularly in a Lorentz invariant context.
  • Another participant argues that while vectors have a clear direction making the terms "rotated" or "boosted" intuitive, higher-rank tensors lack a single direction, complicating the application of these terms.
  • There is a recognition of misinterpretation in responses, indicating a lack of clarity in addressing the original question.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of using the terms "rotated" or "boosted" for tensor components, with no consensus reached on the matter.

Contextual Notes

The discussion highlights the complexity of defining transformations for tensors of higher rank and the potential ambiguity in terminology when comparing them to vectors.

kent davidge
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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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