The Vagueness of Inertial Reference Frames and the Classical Intuition Towards the EEP?

[The victorious truther]

I've been, as of late, debating with rather fringe or crackpot physicists on ResearchGate and in the process of such an exchange i've found myself forced to be rather particular about my terminology. It was a debate regarding Special Relativity and the person in question made the obvious mistake of assuming that such a theory couldn't be extended to accelerating reference frames. I came to clarify to him that in Special Relativity you could only deal with reference frames that accelerate as a result of dynamical influences or forces as General Relativity would come into the case for accelerated motions without forces. In hindsight, it is relatively true this is the case in so much as General Relativity accounts for everything that Special Relativity could account for as well as much more. However, I came to later realize in some respect that, in a similar manner to Classical mechanics, a fictitious forces would arise in any non-inertial reference frame I extend Special Relativity to so therefore it should equally as much handle it as well.

Then it occurred to me; the definition of an inertial reference frame or the general intuition many have had through out our physics history, from Galileo to Newton and then to Einstein's statement of it in his 1905 paper, all seemed to implicitly assume that for constant velocity motion the fact of it being an inertial frame came whole sale. In an opposite manner when discussing accelerating frames these are usually thrown into the bin of non-inertial frames as well. However, there are cases that do not relegate this sort of strict intuitive dichotomy in that you can view accelerated inertial frames from a non-inertial reference frame (linearly or in rotational motion) and such that the people outside the non-inertial frame will claim that their laws of physics remained valid despite this relative acceleration you perceived. 

Its as if the definition of an inertial frame that includes not just the statement of the invariance of some collection of laws of physics but also of a constant velocity has exceptions that do not warrant such a strict adherence to only constant relative velocities. Even Newton proclaimed in a strangely familiar manner in Corollary 6 of his Principia that,

Quote

If bodies, any how moved among themselves, are urged in the direction of parallel lines by equal accelerative forces, they will all continue to move among themselves, after the same manner as if they had been urged by no such forces. 

Then the question arises as to why we prefer to distinguish two different frames of reference where one is part of a homogeneous influence of forces (non-inertial) and the other is inertial (perceived from the other frame to be accelerated) when the physics conspires to not have us distinguish them. It seems then that you can extend this argument to any magnitude of homogeneous forces or any dependency on direction/magnitude, so long as its homogeneous, such that any general kinematical motion could be further relegated also to being inertial. It seems to be fairly redundant and i'm curious if Newton or others ever attempted to specify why inertial reference frames were so relegated usually to only constant velocities if they even noticed these sorts of equivalent situations.

For Newton's own gravitational theory this relativization and treatment of 'gravitationally' accelerated motion can be performed creating a Classical geometrical version of Newtonian gravitation called Newton-Cartan gravity. Entirely from arguments based on the above corollary along with assumptions regarding the WEP and SEP (Weak and strong gravitational equivalence principles). You don't have to see it as the inclusion then of a warped spacetime but merely as a redefinition and generality of inertial frames that responds to corollary 6 by making all such equivalent frames a part of the definition of being inertial.  

This is a curiosity to my Classical intuitions as they have always then betrayed me into thinking about constant velocity inertial motion as a strict given when these exceptions screamed for Occam's razor to be applied to them. Perhaps an approach that emphasizes the relativity of inertial frames in many cases, as is the case here, would be more amenable in certain teaching settings for a gentler transition from Special Relativity into General Relativity which wouldn't be too distinct in core concepts when going from Newtonian gravitation to Newton-Cartan theory. 

The key point being that kinematical motions are somewhat of a byproduct of being inertial or non-inertial and may be sometimes necessary but not sufficient to make a distinction between them. 

What are your thoughts? 

[mathematic]

My thought - MEGO!

[MigL]

The argument has always been there that gravity could be considered a fictitious force.
Not because the FoR it is apparent in is rotating, but because it is being 'warped' by the mass/energy/momentum in that frame.
The fact that rotating frames give rise to forces which are seen to disappear  ( fictitious ) when viewed from an 'outside' frame makes me wonder; what 'outside' frame could you view space-time from, to determine that gravity ( the 'warping ) is fictitious ?

edit
Is MEGO=my eyes glaze over ???

Edited August 31, 2021 by MigL