Yes, but don't forget that a worldline is not something real. Nor is a coordinate system.
I haven't said anything that
requires coordinates to be real. It's just a simple fact that 1) we need coordinates for various practical reasons, 2) coordinate-dependent statements are very sensitive to the choice of coordinate system, and 3) Einstein used coordinates, and many of the statements you quote by Einstein on the speed of light and time dilation are, in fact, only true in the particular coordinate systems Einstein worked them out in.
I haven't downplayed it. See
gravity works like this where I say the Riemann-curvature rubber-sheet analogy is depicting the varying speed of light.
I've already told you that the rubber sheet analogy is, at best, a gross oversimplification of the Riemannian geometry Einstein formulated general relativity in terms of. It's little more than a simple picture we show kids. Case in point: it only depicts curvature in
space instead of
spacetime. That's important, because the weak field metric (that we recover Newtonian gravity as well as some GR effects like time dilation from) is actually intrinsically
flat in its spatial sections. The spatial part is just the Euclidean metric of flat space, and it's only in allowing some curvature in spacetime when you bring the time dimension into consideration that you recover Newtonian gravity and gravitational time dilation. Your thread OP has no basis in how Riemannian geometry is actually used in GR. Concerning the Riemann curvature itself, Einstein already explained its basic significance better and more accurately than you do in your thread:
Albert Einstein said:
The mathematical importance of this tensor is as follows: If the continuum is of such a nature that there is a co-ordinate system with reference to which the $$g_{\mu\nu}$$ are constants, then all the $$B^{\rho}_{\mu\sigma\tau}$$ vanish. If we choose any new system of co-ordinates in place of the original ones, the $$g_{\mu\nu}$$ referred thereto will not be constants, but in consequence of its tensor nature, the transformed components of $$B^{\rho}_{\mu\sigma\tau}$$ will still vanish in the new system. Thus the vanishing of the Riemann tensor is a necessary condition that, by an appropriate choice of the system of reference, the $$g_{\mu\nu}$$ may be constants. In our problem this corresponds to the case in which,* with a suitable choice of the system of reference, the special theory of relativity holds good for a finite region of the continuum.
--------------------
* The mathematicians have proved that this is also a sufficient condition.
Of course, by "mathematicians" in the footnote, Einstein is referring to the mathematicians who worked on and proved theorems about Riemannian geometry, and that's where you should go if you want to learn more about the Riemann and other curvature tensors than Einstein covers in his own paper. Needless to say, there's nothing in Einstein's paper or any of the mathematical literature about the Riemann curvature (a tensor with 20 independent components!) being obtainable by a simple plot of clock rates.
I try not to have any beliefs.
Your track record says otherwise. You have expressed strong beliefs on space, time, light, gravity, time travel, electromagnetism, and other topics, usually without the slightest hint you're open to the possibility you might be wrong in any of your beliefs. Instead of "proposed explanation of gravity" and "I've shown X under condition Y, in future I hope to generalise what I've shown here to Z", with you it's "Gravity works like this".
Case closed.
Since we're having fun quoting science celebrities anyway, let's bring in Richard Hamming, who
gave a famous speech in 1986 on effective research habits based on his over 40 years of research experience. Contrast your own attitude with what Hamming has to say about really good researchers:
Richard Hamming said:
There's another trait on the side which I want to talk about; that trait is ambiguity. It took me a while to discover its importance. Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance. But most great scientists are well aware of why their theories are true and they are also well aware of some slight misfits which don't quite fit and they don't forget it.
