Developing a relativity module

[Abhishek K Das]

I was checking the physics module and saw there is nothing on relativistic mechanics as of now .
Is anyone working on that ? I would like to contribute in that or otherwise start implementing it .

[Joachim Durchholz]

What would be your idea of a module that fully implements RT?
This can be much more than your current project - it's good to have
lofty goals, they help determining the direction of the first baby steps.

[F. B.]

On Wednesday, May 14, 2014 8:41:35 AM UTC+2, Abhishek K Das wrote:

I was checking the physics module and saw there is nothing on relativistic mechanics as of now .
Is anyone working on that ? I would like to contribute in that or otherwise start implementing it .

Are you interested in special relativity or in general relativity? And especially, what abstraction depth are you planning to reach?

For special relativity, Lorentz transformations could be implemented as matrices acting on vectors. Lie algebra elements could be represented as matrices and then exponentiated. Similar work for spinor representations. But in that case you would still working in a fixed basis of the Minkowski space, while it would preferable to have a base-independent formulation in a CAS.

As for general relativity, there is the sympy.diffgeom module which could help. Here an example of the Schwarzschild solution from the GSoC 2012: http://krastanov.files.wordpress.com/2012/07/schwarzschild.pdf

In any case, I am currently trying to refactor sympy.tensor.tensor in order to allow operator formalism on tensors with abstract index notation. I will still take some times (probably months), but as soon as it is finished, it will be much easier to reason about relativity and quantum field theory.

The abstract index notation means that indices are not the component number, but rather contain information on which representation of which Lie algebra that component transforms.

[Abhishek K Das]

I am interested in special relativity .
Okay , the thing is I am currently an undergraduate in electrical engineering . I had a basic course on special relativity .
I don't know about Minkowski space and stuff . I was thinking of starting with simple stuff in relativity. You are saying that
as soon as tensor thing is done , you can easily implement relativity .

I basically need some project ideas to work on . It can be anything existing or anything new . Can you provide me with
some ideas to work upon .

[F. B.]

On Wednesday, May 14, 2014 10:07:12 AM UTC+2, Abhishek K Das wrote:

I am interested in special relativity .
Okay , the thing is I am currently an undergraduate in electrical engineering . I had a basic course on special relativity .
I don't know about Minkowski space and stuff . I was thinking of starting with simple stuff in relativity.

The point is, the deeper your knowledge is, the more elegant is the way you can represent it on a CAS.
 

You are saying that as soon as tensor thing is done , you can easily implement relativity .

Yes, because abstract tensors implicitly contain the transformation laws of relativity theory (and other symmetries), and allow to write formulae in a frame-independent way. Actually, most of modern physics uses tensors. But it will take some time before tensors are ready for use.
 

I basically need some project ideas to work on . It can be anything existing or anything new . Can you provide me with
some ideas to work upon .

A very simple idea: Lorentz transformations by 4 x 4 matrices.
https://en.wikipedia.org/wiki/Lorentz_transformation

[Abhishek K Das]

How much have you implemented ? May be I can also help . I will study the theory that is required .

[F. B.]

On Wednesday, May 14, 2014 10:55:47 AM UTC+2, Abhishek K Das wrote:

How much have you implemented ? May be I can also help . I will study the theory that is required .

Concerning relativity itself, I haven't implemented anything.

If you are willing to go on, may I suggest you a simple approach, that is, create two objects:

• FourVector
• LorentzTransformation
• observable quantities.
  

FourVector is the 4-tuple (x, y, z, t), while LorentzTransformation can be a boost or a rotation or both. Observable quantities extract measurable information from the FourVector, like length, momentum, etc...

Just learn how position and momentum generalize to FourVector in special relativity (maybe call those objects FourPosition, FourMomentum), then represent the transformations through matrices, and finally create methods in FourPosition and FourMomentum to extract physically measurable quantities.

I don't suggest you to use tensors because I am currently refactoring sympy.tensor.tensor.