Definition of Second-Order Tensor by Jim Adrian

  • Context: Undergrad 
  • Thread starter Thread starter jamesadrian
  • Start date Start date
  • Tags Tags
    Tensor
Click For Summary

Discussion Overview

The discussion centers on the definition of a second-order tensor, exploring its formal definition and the distinctions between various terms related to tensors. Participants express a desire for clarity on the mathematical and physical implications of the term, while avoiding application-based explanations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Jim Adrian seeks a formal definition of a second-order tensor, emphasizing the need for clarity without application examples.
  • Some participants suggest summarizing the understanding of "tensor" and "tensor product" to clarify the question.
  • There is a discussion about the terminology, with some preferring "rank" over "order" when describing tensors.
  • A participant proposes defining a tensor as a multi-linear map, requiring a vector space and its dual, indicating that a rank 2 tensor can be defined in various ways.
  • Another participant points out that a matrix is only one representation of a tensor, not equivalent to the tensor itself.
  • Jim Adrian references Einstein's Equation to illustrate the complexity of tensor definitions and their applications in physics.
  • There is a suggestion that the definition of a tensor should be chosen based on its relevance to understanding specific equations, such as Einstein's Equation.

Areas of Agreement / Disagreement

Participants express differing views on the terminology and definitions of tensors, with no consensus on a singular definition or understanding of the term "second-order tensor." The discussion remains unresolved regarding the most appropriate definition and its implications.

Contextual Notes

Some participants note the ambiguity in the term "second-order tensor" and the potential confusion surrounding the distinction between rank and order. The discussion highlights the need for clarity in definitions and the varying interpretations of tensor concepts.

  • #31
jamesadrian said:
Transformation rules must be explicitly stated in a formal definition of a second rand tensor or any tensor.

Who came up with this meaning of "formal definition"? Are you incapable of deducing the transformation rules from the rank of the tensor and which indexes are upper and which are lower?
 
Physics news on Phys.org
  • #32
PeterDonis said:
You mean you are unable to fill in the dots from what has already been said? Posts #5 and #7 in particular?

That is correct.

Jim Adrian
 
  • #33
jamesadrian said:
That is correct.

Then this thread's level cannot be "A", since you do not have that level of background knowledge. Changing it to "I".
 
  • #34
jamesadrian said:
That is correct.

Do you understand what vector spaces and their duals are? Do you understand how vectors and dual vectors (or covectors or 1-forms--nomenclature varies among different sources) transform under transformations of the coordinates?
 
  • #35
PeterDonis said:
Then this thread's level cannot be "A", since you do not have that level of background knowledge. Changing it to "I".

You didn't ask Why.

Jim Adrian
 
  • #36
jamesadrian said:
You didn't ask Why.

Why what?

If you mean I didn't ask why you can't fill in the dots, I don't care why. The mere fact that you can't means you don't have "A" level background knowledge in the topic of this thread.
 
  • #37
If anybody here has an answer to my question, they can write to jim@futurebeacon.com

Jim Adrian
 
  • Sad
Likes   Reactions: weirdoguy
  • #38
jamesadrian said:
If anybody here has an answer to my question, they can write to jim@futurebeacon.com

If you would answer the questions I asked in you post #34, we would be able to gauge your level of background knowledge. I don't know how you expect anyone to be able to give you an answer you can understand without that information. If you had had an "A" level of background knowledge the answers already given in this thread would have been more than enough.

If you are unwilling or unable to provide that information, we'll just close this thread.
 
  • Like
Likes   Reactions: pervect and vanhees71
  • #39
We have given tons of answers already!
 

Similar threads

Undergrad How to derive irreducible representations/tensors?
  • · Replies 22 ·
Replies
22
Views
4K
Undergrad The Order and Valence of Tensors
  • · Replies 6 ·
Replies
6
Views
5K
Graduate MTW Gravitation: Exercise 5.1 | Beginner GR Stress-Energy Tensor Symmetry
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad Invariance of a tensor of order 2
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Deriving tensor transformation laws
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Transformation of second rank tensor
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Explore Coordinate Dependent Statements in Orodruin's Insight
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Understanding the Stress-Energy Tensor in Special Relativity
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Pressure term in the energy stress tensor
  • · Replies 9 ·
Replies
9
Views
3K
Graduate Find SEM Tensor from Lagrangian of Temporal Variable
  • · Replies 7 ·
Replies
7
Views
1K