Undergrad Covariant Derivative: Limits on Making a Tensor?

Click For Summary
Covariant derivatives can only be applied to tensor quantities, not to arbitrary components or non-invariant quantities. The process of taking a covariant derivative does not transform non-invariant components into invariant tensors. There are inherent limitations on what can be classified as a tensor, emphasizing the necessity of starting with a proper tensorial structure. The discussion highlights the importance of understanding the foundational principles of tensor calculus. Overall, the ability to derive invariant tensors is restricted to valid tensor inputs.
dsaun777
Messages
296
Reaction score
39
Can you take any non invariant quantity like components and take the covariant derivative of them and arrive at an invariant tensor quantity? Or are there limits on what you can make a tensor?
 
Physics news on Phys.org
dsaun777 said:
Can you take any non invariant quantity like components and take the covariant derivative of them and arrive at an invariant tensor quantity?

You can't take covariant derivatives of components. Covariant derivatives operate on tensors.
 
PeterDonis said:
You can't take covariant derivatives of components. Covariant derivatives operate on tensors.
Sorry my brain is not working long day...
 

Thread 'EPR revisited'

In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...
View full post »

Similar threads

High School Prove that metric tensor is covariant constant
  • · Replies 11 ·
Replies
11
Views
1K
Undergrad Commutation between covariant derivative and metric
  • · Replies 16 ·
Replies
16
Views
4K
Graduate Proof of covariant derivative of spinor
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Ricci Tensor: Covariant Derivative & Its Significance
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Dirac comment on covariant derivatives
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Covariant divergence of vector; physical meaning with contracted Tuv
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad What is a Covariant Relation? GR Problem Solution Explained
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Physical Difference Between Co- and Contravariant Vectors
  • · Replies 6 ·
Replies
6
Views
1K
Undergrad Can We Explain the Cosmological Constant as a Tensorial Concept?
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Decomposing Rank-2 Tensors in Dirac's "General Theory of Relativity
  • · Replies 5 ·
Replies
5
Views
2K