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Schroedingers-Hat / jsphys

Libraries for physics simulation on javascript canvas
GNU Affero General Public License v3.0
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Test and prove the code. #23

Open Schroedingers-Hat opened 13 years ago

Schroedingers-Hat commented 13 years ago

Now that we have teleport it's a good time to design some experiments to test the simulator. Doing some analytic work on the code to check it for correctness, and try to calculate some error bounds is a good idea, too.

Schroedingers-Hat commented 13 years ago

We know that boost is not commutative, but I'm not sure on the exact effects Exercise: multiply together a boost in the directions left up right down. Compare the resultant matrix to a 3D rotation. Compare it to the result we get in our simulation (which includes a rotation). This is similar to the way you can roll by combining pitch and yaw. This has a lot to do with the way curved space can rotate things.

Schroedingers-Hat commented 13 years ago

Sometimes things start to red-shift when they are not yet behind you. Check at which angle and velocity the factor of gamma beats the factor of (1+v/c)

Schroedingers-Hat commented 13 years ago

@capnrefsmmat We really need to do some quantitative tests to determine if things are working right. Fixing things when we added c/changed A[0] to A[3] told me that the maths is actually remarkably robust in giving nearly-qualitatively-correct answers, as such we need to find some hard numerical predictions we can test things against. I'm a bit too close to the maths and as a result I will tend to be more easily convinced that I'm correct. Perhaps you could trawl some journals for relativistic optics results to test (do you have electronic journal access of some kind atm?)? The sphere thing is unfortunately out for 2D as the object has to have a circular profile when facing the camera, and all a 2D camera can see is lines.

capnrefsmmat commented 13 years ago

I do have electronic journal access, yes. Can you be more specific on the kinds of experiments you'd like to see?

Schroedingers-Hat commented 13 years ago

Any prediction about relativistic optics we can test in 2D? Apparent shape of a horizontal line at y=blah when you're moving at v=whatever predictions of colors apparent shape of circles in the plane of motion (I think I found one on that already, will see if I can get anything useful on it) Maybe some basic stuff for change of frame, just use lorentz contraction formulae and check against the size of our snake.

capnrefsmmat commented 13 years ago

This might be useful:

http://cartan.e-moka.net/content/download/253/1499/file/Forma%20apparente%20di%20oggetti%20di%20grande%20dimensione%20in%20movimento.pdf

I can probably get you any of the references if you need them. This is something to start with, at least.