>> That the notion of "straight" versus "nonstraight" is *not* >> dependent on a coordinate system. > >It's definitely the case for "straight" trajectories, which are for >example straight relative to an inertial system but not relative to a >rotating system.
That's mistaken. Whether a trajectory is straight (or unaccelerated) is *not* relative to a coordinate system. If it is straight, it is straight in all coordinate systems. What varies from coordinate system to coordinate system is the *equation* describing a straight path. For Cartesian coordinates, the path x(s), y(s) satisfies:
(d/ds)^2 x = (d/ds)^2 y = 0
For non-cartesian coordinates, the equation of a straight path is more complicated.
>I understand why he agreed to call the clock exercise a "paradox" and >an "objection" against his theory,
His dialog was a response to critics. The fact that he responded doesn't amount to admitting the critics were right. He's explaining why they are *not* right.
>which required to be solved. It appears that you still don't >understand why,
And the fact that you can't give a coherent answer to the question: why is the twin paradox a consistency challenge for Einstein's generalized principle of relativity seems to me to mean that you don't understand why, either.
>> >> The modern way of looking at it is that "inertial forces" are >> >> felt whenever the observer is accelerating *relative* to freefall. >> >> Einstein originally thought of the equivalence principle differently: >> >> He thought that an object accelerating in a gravitational field felt >> >> two different kinds of forces: (1) inertial forces due to acceleration= >, >> >> and (2) gravitational forces. These two forces canceled in the case >> >> of freefall. >> >> >??? I strongly doubt that. Reference please! >> >> I cannot find an online reference, but it occurs in a discussion >> by Einstein of his "elevator" thought experiment. > >As far as I remember, he held that an object accelerating in a >gravitational field feels no force at all; does it make a difference?
Right. The modern explanation is that an object in freefall is *not* accelerating; it is moving inertially. Einstein's original explanation (if I'm remembering it correctly) was that the object feels *two* forces that cancel each other: A downward force due to gravity, and an upward "inertial" force.
>> >Good, we are making progress. :-) >> >Einstein held that, as he put it, acceleration is "relative": >> >according to his theory we may just as well claim that the traveler is >> >*not* physically accelerated, contrary to Langevin's and your claim. >> >> No, you are confused. As I have said, there are two different notions >> of "acceleration": (1) proper acceleration (acceleration relative to >> the local standard for freefall) and (2) coordinate acceleration >> (acceleration relative to whatever coordinate system you are using). >> Einstein and I are in complete agreement that for the traveling >> twin, proper acceleration is nonzero, while coordinate acceleration >> is zero (using the appropriate noninertial coordinate system). So >> where is the disagreement? There is none. > >There is no disagreement on that point. What about the induced >gravitational field?
That's just the ordinary inertial forces associated with an accelerated observer. Calling them a gravitational field is to remind you that in Einstein's theory, there is no difference between a gravitational force and inertial forces. They are both manifestations of accelerating relative to the local notion of freefall.
>> >He thought to solve the problem by saying that at the turnaround >> >(according to the stay-at-home), the traveler may consider himself as >> >remaining in place against an induced gravitational field that >> >appears. >> >> And certainly he may, in the sense that he may choose a coordinate >> system in which he is always at rest. The notion of being at rest >> is relative to a coordinate system in relativity. > >He only may do so if his induced gravitational field can be held to >be, as his theory claims, "physical", and propagating according to the >same laws of physics as all other gravitational fields.
And that is the case. It's important to distinguish "gravitational field" from "gravity". They aren't the same thing. There are two different phenomena at work in the modern view of gravity:
(1) Spacetime is *curved* by matter. What this means is that at each point in spacetime, there is a local notion of "freefall" or "inertial motion". Curvature means that this notion varies from point to point, rather than there being a global notion of an inertial frame.
(2) Acceleration relative to the local notion of freefall results in inertial forces. This effect is exactly like Newtonian physics, where acceleration results in inertial forces. The difference is that in Newtonian physics, there is a consistent *global* notion of freefall or inertial motion, while in General Relativity, freefall varies from place to place.
For effect (2), there is no distinction between "gravitational force" and any other inertial force. They're all inertial forces due to acceleration relative to the local notion of freefall.
There is no "propagation" of effect (2). If you start accelerating, you instantly feel inertial forces. Inertial forces don't propagate in any physical sense. On the other hand, effect (1) has a very definite dynamic to it, which is describe by Einstein's field equations. Curvature is influenced by the presence of mass/energy/momentum.
>> If you are asking, not about General Relativity, but the General >> Principle of Relativity: that isn't a theory of physics, it is >> a heuristic, or a philosophical position, or metaphysics. It has >> no physical meaning, except to the extent that it guides us in >> coming up with better theories of physics. > >I rarely saw a more aggressive criticism against Einstein's >theory. :-)
The generalized principle of relativity is not a theory.