I can't understand inertial reference frames

[rcgldr]

Ok, why not just think of an inertial frame of reference as an abstract concept? It may not be reality, but it's close enough to be useful for a lot of applications.

 

[vanesch]

Ok, why not just think of an inertial frame of reference as an abstract concept? It may not be reality, but it's close enough to be useful for a lot of applications.

Yes, of course, there's no problem with that. I'd even say that it is the starting point for doing Newtonian physics: you start with the postulate that there exists an inertial frame, you name it and you say that it is called x,y,z,t, and then you can do things in it.
The conceptual confusion is to think that this corresponds to some kind of absolute space, which it doesn't of course.

As long as things are abstract, and you SAY that x,y,z,t is an inertial frame, and you SAY which forces are acting upon which object, there's no problem, and this is what's usually done in textbooks (and textbook problems).
The difficulty resides in giving an *operational definition*: to define a lab procedure in all generality that will guarantee you that you have an inertial frame. And without such an operational definition, there's no LINK between the abstract, mathematically invented set of coordinates x,y,z,t and any number you could get out of any measurement procedure: in other words, without an operational definition of an inertial frame, Newtonian mechanics makes no empirically testable predictions.

In practice this is not a problem, because "a coordinate set at the surface of the earth" or "a coordinate set through the center of the earth, pointing to the fixed stars" or "a coordinate set through the center of the sun" turn out to be quite good. But clearly those are "accidental" cases and they have a circumstantial ad hoc definition. If you take that as a definition of "inertial frame" it would imply, for instance, that there's no Newtonian mechanics before the formation of our solar system :-)

The fundamental problem is that there are no "free particles" on which "no forces act", because on all things acts at least the force of gravity, and maybe others - which you might ignore.

 

[loom91]

Ok, why not just think of an inertial frame of reference as an abstract concept? It may not be reality, but it's close enough to be useful for a lot of applications.

The question is not whether it's a reality or whether classical physics is more useful than GTR. This is theoretical physics, usefullness is a very minor consideration. The problem is that the concept of inertial reference frame is not internally self-consistent. It has a circular definition.

Q:What is an inertial reference frame?
A:It is a reference frame in which particles free of forces are unaccelerated.
Q:What is force?
A:Force is the time-derivative of momentum IN AN INERTIAL REFERENCE FRAME.

You see the problem? It is not possible to opertionally determine a particle to be free of forces, but even before that the very definition of inertial reference frames is problematic. Irrespective of whether or not classical mechanics with galilean relativity can be formulated in E^3xE^1, it remains that it is theoretically impossible to determine anyhting's velocity against it without assuming the existence of ether. Classical mechanics is defnitely usefull, but all the usefullness in the world won't save a theory in theoretical physics if it's not the right picture of the world. That's why the field is called theoretical physics and not applied enginnering.

Molu