I Is the premise of the Michelson–Morley argument still valid?

[PeterDonis]

the effect they have is to create a new model with different postulates in a new geometry

Yes, a new model. But there's no actual physical device you can build that will make an actual new geometry according to such a transformation. And the different geometry in the model has nothing whatever to do with the actual geometry of the actual world. So it's irrelevant for the discussion we are having here, which is about analyzing data from the actual world.

employing this powerful mathematical tool is something that can be made use to help various physical problems for example to removing singularities

You can't remove an actual, physical singularity in the actual world (supposing one were to exist) by changing your mathematical model. You are very confused.

i actually even have a very particular use case where i need to do such a transformation due to a practical scenario

Personal research is off limits for PF discussion; that is not what PF is for.

 

[jedishrfu]

Closing thread as the questions posed by the OP have been exhaustively answered and there's nothing more that can be said except thank you for participating here.

Jedi