Need review for the following claims regarding Relativity

Question

So me and one of my friend is having heated debate over validity of General relativity and special relativity. The following claims, I having hard time to understand, are they correct or not as proposed by the 'friend'.

Claim 1: SR can not be explained in terms that involve real world conditions, namely non inertial motion. It just cant work, yet there is no reason why, when all other Laws do work.

Claim 2: SR is incompatible with GR because in SR the concept of an absolute stationary frame is forbidden. But in GR such a frame of absoluteness is ESSENTIAL. In GR there is no such thing as INERTIAL. All of spacetime is curved due to the presence of mass, even if its a long way away, spacetime still has curvature, and therefore must exert non inertial forces on any other object. But in SR, nothing about the whole theory can accept the possibility of NON inertial. in SR its all 100% pure Inertial, no possibility for anything else, because as soon as you allow non inertial, then the hypothesis collapses

So the claims are mostly related to, non-inertial frames and why supposedly according to 'friend' that "STR is not compatible with GTR". For claim 1, I definitely think is a false claim as I saw validity of STR on wikipedia in non-inertial frames, but was very mathematical, so i would like more comprehensive approach. So, i would like everyone with good knowledge on relativity to review these supposed 'claim' and check their validity. I don't have much of a strong background in relativity, and am unable to understand heavy mathematical knowledge. Please help and thanks in advance!

Edit:

So many of the comments pointed out the lack of proper research, on my side. Sure I had researched about from wikipedia, especially that whether STR holds good in non-inertial forces or not. The wikipedia said about the inclusion of pseudo-forces and the delved in deeper mathematics, which was out of my reach. Second claim, was very vague so I couldn't find anything on internet regarding " But in GR such a frame of absoluteness is ESSENTIAL", so I was clueless, about its validity, and was my main doubt. Previously the question was too much rushed, and has been edited to my best of abilities by myself.

Answer 1

Your friend's arguments are nonsense. SR can deal perfectly well with accelerated motion in flat spacetime. GR does not require an absolute frame of reference, and it simplifies to SR in areas of spacetime that are locally flat.

Answer 2

Claim 1

Claim 1 is objectively wrong, as non-inertial frames are allowed in SR, but usually overlooked in introductory courses because the math is more complicated. As an example, when we are working in inertial Cartesian coordinates, the equations of motion for a free particle in Special Relativity are simply $$\frac{\text{d}^2 x^\mu}{\text{d} \tau^2} = 0,$$ where $\tau$ denotes the particle's proper time. However, once we consider a non-inertial reference frame or curvilinear coordinates, the equations of motion are
$$\frac{\text{d}^2 x^\mu}{\text{d} \tau^2} + \Gamma^{\mu}{}_{\nu\sigma}\frac{\text{d} x^\nu}{\text{d} \tau}\frac{\text{d} x^\sigma}{\text{d} \tau} = 0,$$ where $\Gamma^{\mu}{}_{\nu\sigma}$ are the so-called Christoffel symbols.

This modification does not mean Special Relativity is breaking down. This is in fact quite similar to how Newtonian mechanics requires the presence of fictitious forces in non-inertial reference frames or how Newton's second law won't assume the simple form $F_{q} = m \ddot{q}$ in non-Cartesian coordinates (see Wikipedia on this, for example).

In Relativity, changing frames of reference is analogous (in a quite literal sense) to just changing coordinates. To say Special Relativity can't deal with non-inertial reference frames is similar to saying that Newtonian Mechanics doesn't work in spherical coordinates. It is a common misconception, because people often misinterpret the equivalence principle as if it said that acceleration and gravity are the same thing, but it is still a misconception. What the principle says is that they are locally equivalent, meaning gravity still has tidal effects and acceleration has nothing to do with spacetime being curved.

Claim 2

Claim 2 is also wrong, for GR does admit inertial frames, with the difference that they are now local (i.e., defined in the vicinity of a point). Due to the equivalence principle I mentioned above, one can always pick a choice of coordinates/reference frame corresponding to a freely falling observer. These reference frames are referred to as locally inertial reference frames. Your friend is correct in saying that in a generic curved spacetime one won't be able to find an inertial frame that holds for the entire spacetime, but we can and do work with locally inertial frames and there is no problem arising from it.

Furthermore, General Relativity is formulated in the language of Differential Geometry, which emphasizes the intrinsic, physical properties of spacetime without the need to choose a particular set of coordinates or reference frames. While one can always choose a reference frame, GR is formulated in a manner that never requires you to do so until. The main point of Relativity is, ironically, not about whether things are relative, but about whether things are invariant. Good physical predictions should not depend on the reference frame we choose to work with, and Relativity ensures this to hold beautifully.

In addition, to claim Special Relativity is inconsistent while accepting General Relativity to hold is considerably weird. GR is build upon the assumption that, locally, spacetime resembles that of Special Relativity, quite similarly to how, locally, the Earth resembles a piece of flat space (even though the Earth is round, when you look at the streets around you it seems to be flat, at least for a short distance). Hence, the key concepts from SR are already implemented in GR. In addition to this, SR is precisely what we get from GR when we assume the absence of a gravitational field, so in situations where gravity is negligible (for example, inside particle accelerators like the Large Hadron Collider), General Relativity predicts that spacetime will be well described by Special Relativity.

Summary

In summary, none of the claims your friend presented are flaws in Relativity. They are misunderstandings, but quite natural ones. Before I started diving deep into the math I also thought that SR was not enough to deal with acceleration and propagated the same mistakes, but once you start doing the calculations these things get cleared out and you notice how everything falls in place beautifully.