ATAR Notes: Forum

Uni Stuff => Science => Faculties => Physics => Topic started by: /0 on May 17, 2011, 09:16:36 pm

Title: Wtf are tensors
Post by: /0 on May 17, 2011, 09:16:36 pm: From the lecture notes:

Write the following operations in terms of vectors and matrices:
$a_\mu b^\mu$ , $a_\mu b^v$ , $a_\mu^v b^\mu$ , $a_\mu^v b_k^\mu$ , $a_\mu^v b_v^k$

Can someone show me how to interpret these... thanks
Title: Re: Wtf are tensors
Post by: TrueTears on May 17, 2011, 09:32:43 pm: lol, sorry but this just totally reminds me of tensor tenergy table tennis rubbers LOL, one of the best rubbers around nowadays, probably the physics behind them makes em so pr0pr0pr0
Title: Re: Wtf are tensors
Post by: /0 on May 17, 2011, 09:48:31 pm: Quote from: TrueTears on May 17, 2011, 09:32:43 pm
lol, sorry but this just totally reminds me of tensor tenergy table tennis rubbers LOL, one of the best rubbers around nowadays, probably the physics behind them makes em so pr0pr0pr0

LOL xD
As exams get nearer i get tensor and tensor everyday
Title: Re: Wtf are tensors
Post by: TrueTears on May 17, 2011, 10:52:41 pm: Quote from: /0 on May 17, 2011, 09:48:31 pm
Quote from: TrueTears on May 17, 2011, 09:32:43 pm
lol, sorry but this just totally reminds me of tensor tenergy table tennis rubbers LOL, one of the best rubbers around nowadays, probably the physics behind them makes em so pr0pr0pr0

LOL xD
As exams get nearer i get tensor and tensor everyday
LOL same here, gl on ur exams btw :D ull own them like always
Title: Re: Wtf are tensors
Post by: jimmy999 on May 18, 2011, 07:58:30 pm: Go to here http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/documents/Tensors_TM2002211716.pdf

Lovely little read about them. I can't wait to learn them next semester :)
Title: Re: Wtf are tensors
Post by: mark_alec on May 18, 2011, 09:47:17 pm: I'll assume in all cases that the indices go over the values 0,1,2,3 (Lorentz indices, for relativistic things).

When you have the same index, one upstairs, one downstairs, the lingo is that you "contract" the objects, which is a fancy way of saying do something like a Minkowski inner product.

For example:
$a_\mu b^\mu = a_0 b_0-(a_1 b_1+a_2 b_2+a_3 b_3)$ , a scalar. The second one has two different indices, so you don't contract them together. The object it represents will be like the outer product of the two 4-vectors (rather than the inner product if they have the same index).

You can think of indices as generalisations of scalars, vectors, matrices - the rank corresponds to the dimensions (0, 1 and 2 respectively).
Title: Re: Wtf are tensors
Post by: Mao on June 02, 2011, 04:51:45 am: Quote from: mark_alec on May 18, 2011, 09:47:17 pm
For example:
$a_\mu b^\mu = a_0 b_0-(a_1 b_1+a_2 b_2+a_3 b_3)$ , a scalar.
That's only for Minkowski space using the signature (+,-,-,-) right?

That is one application of the Einstein notation for tensors (or Einstein summation notation). Tensors are just matrices with higher orders (i.e. 3rd order tensor requires two index to pin-point an element, etc. Vectors are 1st order tensors, matrices are 2nd order tensors.) For the Einstein notation, if an index appears twice in one term, it represents a sum over the degrees of freedom (dimensions) of the tensor, e.g.

$a_\mu b^\mu = \sum_{\mu=1}^{n} a_\mu b_\mu$ where n is the degree of freedom

Not quite sure how to interpret the latter few of your expressions, what is the order of a and b? (matrices? 3rd order tensors?)
Title: Re: Wtf are tensors
Post by: QuantumJG on June 22, 2011, 10:40:55 pm: Tensors are just awesome things to use. Especially in relativity if you want to measure the current density in a loop moving at a relativistic speed, etc.