It is not surprising that you use non-standard terminology, but its imprecision can cause some confusion.
I'm going to use the language and terminology of space-time diagrams in an attempt to clear things up, but you might have to draw a few such diagrams to make sense of it.
A beam of light...
You already noted that the light is faster than the ship. Thus, the light should reach the Earth first, followed by the ship. This comes simply from the relation velocity = distance * time, or time = distance / velocity. As of yet, this doesn't even involve relativity.
You can put specific...
Momentum in GR is complicated, as is energy in GR. There are several concepts of energy, and momentum, in GR, not just one, that can be applied in different situations. If this seems unsatisfying to you, I would agree, though that's probably a matter of personal opinion.
There is a...
Einstein has used the idea of "shrinking" or "expanding" rulers in his popularization, "Relativity: The Special and General theory". See for instance https://www.bartleby.com/lit-hub/relativity-the-special-and-general-theory/xxiv-euclidean-and-non-euclidean-continuum. Einstein, however, uses...
Possibly. My main thought is that the approach (which is of course your approach) in "Relativity on Rotated Graph paper" is a promising approach to those who want to learn a useful amount about Special Relativity but are intimidated by the math. But to use this approach does require the...
I've felt for some time that a primer on space-time diagrams and light clocks would be very helpful, but I was (and am) too lazy to do an exposition. Perhaps someday? But I can outline a sort of "homework exercise", a series of tasks that one can do to break down the larger task of "drawing a...
I'm not sure I understand your point. What specific geometric entity (tensor, scalar) is "path curvature" supposed to represent in this context?
I was initially thinking you were making some point about space-time curvature being specific to a space-time manifold, (as opposed to a more...
It's fairly easy to say that curvature can be related to relative acceleration between nearby geodesics per unit distance between said geodesics - which has units of (m / s^2) for the acceleration, and units of meters for the distance between them. When we divide the acceleration by the...
I'd like to "upvote" A.T.'s observation, force / unit mass is the same thing as acceleration. This illustrates that forces don't really play a fundamental role in GR. As early as Gallileo, it was noted that all test masses fall at the same rate. This means we can just as easily talk about the...
This is a valid (and IMO good) way of looking at things, but a reference to your source would be helpful to settle any fine details. Such as:
That part is probably a misunderstanding of what was said, though it's possible the video itself was wrong, which is why it would be helpful to cite...
When you reach 99 percent of the speed of light in one direction (we'll call it the x direction), you'll have some momentum in the x direction ##\gamma \, m \, .99 \, c##, where m is your mass.
If you start to accelerate in the y direction, if you maintain the same momentum in the x direction...
Consider a spaceship accelerating at a constant acceleration of (approximately) 1 earth gravity, about 10 m/s^2, also approximately 1 light year / year^2.
This sort of motion, the motion of an object with a constant "proper acceleration" is called "hyperbolic motion". While there are wikipedia...
If you are familiar with the idea of the conservation of charge being expressed by the vanishing of a divergence in a vacuum, namely ##\nabla \cdot E = {\rho} / {\epsilon}## then we have a divergence in GR that vanishes (the divergence of the stress-energy tensor), and thus we can say that it's...
Possibly relevant are the remarks about optical extinction in the "experimental tests of relativity" FAQ stickied in PF, namely http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Optical_Extinction
So what is of interest here is how we measure "the speed of light through...