Whether a non-inertial frame is absolute

[etotheipi]

It's also really important not to ignore the fact that the reason we care about particular abstract structures is the predictions they make about the actual world. If the abstract structure you call "classical mechanics" didn't make such predictions, and didn't have many people believing for about two centuries that those predictions were exact, it would not be called "classical mechanics".

But all this is precisely by construction. The universe isn't actually a four-dimensional affine space, et cetera; these are just artefacts of attempts to build a mathematical theory that resembles certain aspects of reality. That doesn't make it any less abstract! Once formulated it exists independently of any puny reality

 

[etotheipi]

So let a scientific theory $(F,I)$ consist of an abstract mathematical framework $F$ and a minimal interpretation $I:P\rightarrow R$ mapping predictions $P\subset F$ to real world experimental results $R$. Now we are in no danger of conflating $F$ with $R$, and yet we can see that $F$ by itself is insufficient to form a theory.

I enjoyed reading that, but it is certainly not a proof of anything. It's because all these terms are ill-defined anyway, and this whole disagreement is really one of opinion more than anything else

 

[Dale]

I enjoyed reading that, but it is certainly not a proof of anything. It's because all these terms are ill-defined anyway, and this whole disagreement is really one of opinion more than anything else

It does show that insisting that a scientific theory contain more than merely an abstract mathematical framework in no way implies that we are conflating the abstract framework with real world things.

If you want to make an argument that your use of the word “theory” is better than mine then you need to avoid strawman arguments like the “conflate the real world” argument.

The point is really what @PeterDonis said. I don’t care about most abstract mathematical frameworks. I only care about the abstract mathematical frameworks that can be mapped to the outcomes of experiments. Furthermore, in order to use the scientific method I need both the framework and the mapping. The framework by itself neither helps me design nor analyze an experiment. So since I always use them together in science then as a scientist I want a word to refer to them together. That word is “theory”.

If you wish to recommend the word theory apply only to the framework then to convince many scientists you will also need a word to refer to the framework and the minimal interpretation together. Then you will have to explain why the term “mathematical framework” is insufficient for describing the abstract math part. Finally you will have to convince a large enough group of scientists to drop the use of “mathematical framework” adopt “theory” instead and replace the current usage of “theory” with whatever term you invented above.

To do that will require some good practical reasons why your new terminology is beneficial. So far I don’t see any benefit to it.

 

[PeterDonis]

But all this is precisely by construction. The universe isn't actually a four-dimensional affine space, et cetera; these are just artefacts of attempts to build a mathematical theory that resembles certain aspects of reality. That doesn't make it any less abstract! Once formulated it exists independently of any puny reality

Nobody is disputing any of this with regard to the mathematical structures alone. You don't need to explain to us that abstract mathematical structures are not the same as the real world phenomena that we use them to model. We all know that. That is not the point at issue.

The point at issue is the usage of the word "theory". Nothing that you have said, as far as I can see, gives any justification for your usage as opposed to the usage @Dale and I have described (and which I think is the usage most physicists would agree with). Saying that abstract mathematical structures are different from real world phenomena, by itself, is not an argument for your preferred usage. To make it into one, you would have to show evidence that using the word "theory" to describe the mathematical structures plus the predictions they make plus the operational rules for comparing predictions with data, causes people to confuse abstract mathematical structures with real world phenomena. You have produced no such evidence. Do you have any?

 

[italicus]

@feynman1
let’s imagine you are driving your car on a rectilinear motorway , at constant speed. Ignore, for a short time, that the Earth isn’t an inertial reference frame. At a certain moment, you accelerate the car. LEt’s suppose that the acceleration wrt the motorway is constant, as measured by an observer standing aside.
You’ll feel a force in your back, applied by the seat. That force is exerting on you what can be called “proper acceleration”. In classical mechanics , there is no difference between proper acceleration and coordinate acceleration, the one measured by the observer. So you experience a proper constant acceleration.
But when you come to Special Relativity, which can manage objects which are accelerated wrt to a coordinate frame, there is a substantial difference between proper acceleration $\alpha$ and coordinate acceleration ${du}/{dt}$ . It can be shown that the relation between them is :

$$ \alpha = \gamma(u)^3 {du}{/{dt} }$$

here $\gamma(u)$ is the Lorentz factor , which increases with the speed “u” .

The LHS is the proper acceleration, which can be assumed constant, for example. So the coordinate acceleration ${du}/{dt}$ cannot increase indefinitely, and the speed of the object ( for example a space ship) cannot reach the speed of light.

This is called “hyperbolic motion” , because the line of universe on a Minkowski diagram is an hyperbole. This was studied by Wolfgang Rindler deeply. Look for “Rindler coordinates” .

Sorry for my bad English.