On Feb 20, 10:37 pm, Koobee Wublee wrote:
On Feb 20, 11:50 am, JanPB wrote:

On Feb 19, 10:15 pm, Koobee Wublee wrote:
Kinetic energy is observer dependent, and so is the momentum. This is
also true for the observed mass. Thus, the energy-momentum tensor
must be observer dependent as well.

No - the correct statement would be "thus, the energy-momentum tensor
_components_ must be observer dependent as well".

Given a matrix with its elements being observer dependent, the matrix
must be observer dependent as well.

The matrix - yes, obviously. But not the tensor each matrix represents
in this case.

Again, it's like vectors: a vector is not an n-tuple of numbers. If I
say "let the vector v be given as (1,2)", I'm not saying anything -
it's just a pair of numbers. Without specifying a basis, (1,2) does
not specify a unique vector:

- is it 1 unit in the x-direction and 2 units in the y-direction?
- is it the opposite?
- is it 1 unit Northeast and 2 units Southeast?
- is it 1 radian clockwise from the direction West and 2 units counted
along that direction?
- etc. etc.?

OTOH if I say "let v be (1,2) in polar coordinatese" then I'm
specifying a vector. This vector - which is a 1 x 2 matrix - has
different matrix elements in the Cartesian frame:
(cos(2), sin(2)).

Two different matrices:

(1,2)

and:

(cos(2), sin(2))

yet one vector represented by both.

Same with tensors.

--
Jan Bielawski