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This is the continuation of a discussion in https://www.physicsforums.com/showthread.php?t=431068".

Where does SR end and GR begin, in today's textbooks (not internet forums)? Do accelerating frames (coordinate systems) belong to also to SR, or is GR needed?

I say that they belong solely to GR, and find my view disputed with 4.5 : 4.5 people supporting each view.

I'm not an expert in history/philosophy of science or wherever this question belongs, so maybe I'm simply wrong. I'll argue nevertheless until someone convinces me.

Let me state also that in my opinion, if we want to separate theories, it makes sense to say flat spacetime->SR, curved spacetime->GR. I don't dispute that.

But I say that this is not how it is actually handled, and that the other position (which I believe is still the "official" one) also makes sense.

We had these quotes:

Now for the different objections:

But in relativity, fictitious forces mean

I say that SR excludes this kind of weird coordinates. You deal with it using general covariance and the mathematical apparatus of GR. This is GR. I know of no example where an accelerating frame is handled correctly in detail without using different line elements, as in GR.

I can certainly show that it all started with my position in 1915, and I've seen that there's a majority in internet forums for your position. But I've missed the change you proclaim in the literature, or even in Wikipedia. I still see GR and SR tied with the respective principles of covariance.

Where does SR end and GR begin, in today's textbooks (not internet forums)? Do accelerating frames (coordinate systems) belong to also to SR, or is GR needed?

I say that they belong solely to GR, and find my view disputed with 4.5 : 4.5 people supporting each view.

Granted, but I had more responses to that innocuous comment than to most of my disputed positions regarding real physics. So it seems people are interested.DaleSpam said:it probably is not horribly important to draw the line anyway.

I'm not an expert in history/philosophy of science or wherever this question belongs, so maybe I'm simply wrong. I'll argue nevertheless until someone convinces me.

Let me state also that in my opinion, if we want to separate theories, it makes sense to say flat spacetime->SR, curved spacetime->GR. I don't dispute that.

But I say that this is not how it is actually handled, and that the other position (which I believe is still the "official" one) also makes sense.

We had these quotes:

where I fully agree with DaleSpam:bcrowell said:Misner, Thorne, and Wheeler, Gravitation, 1973, p. 163, "Accelerated motion and accelerated observers can be analyzed using special relativity."

Penrose, The Road to Reality, 2004, p. 422, "It used to be frequently argued that it would be necessary to pass to Einstein's general relativity in order to handle acceleration, but this is completely wrong. [...] We are working in special relativity provided that [the] metric is the flat metric of Minkowski Geometry M."

It is undisputed that SR can handle accelerated motion, as long as it is described in an inertial coordinate system. I need to see a quote concerning accelerated frames, not accelerated motion.DaleSpam said:Neither of these quotes refer to SR handling a non-inertial frame.

Now for the different objections:

I don't think it's unnatural. An essential part of SR is what you must (or mustn't) read into its standard coordinates. You deal with inertial frames, and you use phrases like "the speed of light is constant". You teach Lorentz transformations, and you say you understood SR when you can handle them intuitively.Fredrik said:we're left with Minkowski spacetime, which can be defined mathematically in at least three different ways: as a vector space, an affine space, or a manifold. But regardless of which of these options we choose, there's nothing that forces us to throw out non-inertial coordinate systems. In fact, it's quite unnatural to do so.

The "accelerated frame" is a human made definition, not something you can establish by experiment. So I think it's ok to let humans define whether a theory can handle a certain human-made definition.Passionflower said:What a theory can handle or not can be established by experiments. It has nothing to do with human made definitions.

If I did, that was not my intention.atyy said:Hmm, reading carefully, I see you have indeed classed the twin paradox as a general relativistic problem ... really?

Yeah, general covariance (ofatyy said:General covariance (of the equations of motion) isn't the key principle of general relativity is it?

*all*equations) the key principle of GR. Human made, agreed, but that's what defines GR. At least, that's my position.I'd say youbcrowell said:SR classifies frames as privileged and non-privileged by exactly the same criteria as Newtonian mechanics. Exactly as in Newtonian mechanics, the laws of physics are form-invariant in different privileged frames, but have a different and more complicated form in the non-privileged frames. Exactly as in Newtonian mechanics, we can choose to use the non-privileged frames if we wish.

*almost*have a point here. But there's one thing: Newton deals with accelerating systems by introducing fictitious forces, letting the meaning of coordinates unchanged.But in relativity, fictitious forces mean

*geometry*. You can't have fictitious forces without all sorts of weird coordinate transformations, i.e. time dilation, horizons, problems in defining large scale distance and such. You're in the same mess then whether spacetime is flat or not, you need the generally covariant formulation.I say that SR excludes this kind of weird coordinates. You deal with it using general covariance and the mathematical apparatus of GR. This is GR. I know of no example where an accelerating frame is handled correctly in detail without using different line elements, as in GR.

That's your position, but I haven't seen your evidence yet.bcrowell said:There has been a historical evolution of our understanding of the best way to define the distinction. The definition in terms of curved versus flat spacetime has been widely accepted for decades, but it wasn't understood in 1905, or even in 1915.

I can certainly show that it all started with my position in 1915, and I've seen that there's a majority in internet forums for your position. But I've missed the change you proclaim in the literature, or even in Wikipedia. I still see GR and SR tied with the respective principles of covariance.

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