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Question about General Relativity equations

Question about General Relativity equations - Physics Forum

Question about General Relativity equations - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.


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  #1  
Old 08-31-2004, 09:11 AM
Jacques Pelletier
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Default Question about General Relativity equations



Hi!

I would like to know if the General Relativity equations, normally
expressed with tensors, can be expressed in more familiar terms, i.e. with
gradient, curl, etc. I'm only an engineer and I have no knowledge oftensor
calculus.

Thanks in advance!

--
JP

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  #2  
Old 08-31-2004, 01:40 PM
N:dlzc D:aol T:com \(dlzc\)
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Default Question about General Relativity equations

Dear Jacques Pelletier:

"Jacques Pelletier" <jpelletier@ieee.org> wrote in message
newsan.2004.08.31.09.11.13.403036@ieee.org...

Can the Navier Stokes equation be presented in anything except a tensor,
when solving for flow in a flume? Tensors are familiar to engineers, even
civil engineers. Look again.

Gradient and curl are operators. Tensors (in this context) are simply an
array of differential equations.

David A. Smith


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  #3  
Old 08-31-2004, 02:33 PM
tadchem
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Default Question about General Relativity equations

Jacques Pelletier <[Only registered users see links. ]> wrote in message news:<[Only registered users see links. ]>...

Of course.

Four-tensors simply provide a shorthand way of expressing the same
equations that could be expressed, in space-time of a lower
dimensionality, using more equations.

The d'Alembertian operator, for example, is simply a second-order
derivative involving 16 elements with indices i,j = 1,...4. It can be
replaced by 16 second order derivatives, each with 2 independent
variables selected from the list x,y,z,t.

The d'Alembertian does in four dimensions what the Laplacian does in
three.

BTW, what kind of engineering do you do that has not exposed you to
stress tensors during your education?


Tom Davidson
Richmond, VA
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  #4  
Old 08-31-2004, 09:40 PM
Jacques Pelletier
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Default Question about General Relativity equations

On Tue, 31 Aug 2004 07:33:52 -0700, tadchem wrote:


Electrical engineering. I was certainly exposed to stress during my
education, but obviously not the same kind of stress that you're talking.

Joke aside, we didn't use tensor at all in the baccalaureate level
(electrical engineering). I studied at Polytechnical school in Montreal
(Canada). I would consider it normal since it's applied science.
I don't know if tensors are used in other universities at the
same level.

I don't even know about the d'Alembertian operator. I will check my
encyclopedia of physics tonight. Physics is such a vast field and I'm just
an amateur.


--
JP

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  #5  
Old 08-31-2004, 09:56 PM
Jacques Pelletier
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Default Question about General Relativity equations

On Tue, 31 Aug 2004 06:40:32 -0700, N:dlzc D:aol T:com (dlzc) wrote:


I expect that the answer is probably no (I don't know).

Tensors are familiar to engineers, even
I should have precised that I'm an electrical engineer and an amateur
physicist. In my education, we didn't need tensors for our courses.
I will check this out and buy a good book of tensor calculus.
Would you have any suggestions for this?


--
JP

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  #6  
Old 09-01-2004, 01:45 AM
N:dlzc D:aol T:com \(dlzc\)
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Default Question about General Relativity equations

Dear Jacques Pelletier:

"Jacques Pelletier" <jpelletier@ieee.org> wrote in message
newsan.2004.08.31.21.56.31.103081@ieee.org...

I will give thanks to Eric Grise who said, on 2004aug21, in
sci.physics.relativity, in a thread titled "The meaning of Einstein's
equation"
<QUOTE>
My tipping point for understanding those odd constructs was 1) Linear
Algebra [im doing this way too early in my education, hehe], and 2)
Carroll's book on GR.

MTW left too much out. MTW makes sense *after* I grok tensors, and
look back at it. Other tensor geometry books made no sense, mostly
because I saw them before Linear Algebra!

Carroll's book is 'an introduction to general relativity spacetime and
geometry'. I just can't reccomend that thing enough, considering it
was the first book that made tensors make sense for me

Keep this in mind as you work...

1-forms, vectors, and scalars are all tensors. They all follow the
same rules, they can all be broken into component form. The tensor is
just a generalization up from 1forms/vectors. Carroll's book goes into
the nitty-gritty early..
<END QUOTE>

It may be a bumpy ride for you, but you will have handled worse...

David A. Smith


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