Just a note, the blue lines representing the mirrors are closer together (for example, at the intersection with the x-axis) due to length contraction. Of course, at 0.2c, this will be negligible.
Take into account the Doppler effect. Your source (ship) is approaching the Earth, so the signals you see (watches on the ship) you see much faster.
https://en.wikipedia.org/wiki/Doppler_effect
While I agree with Demystifier's remark and can imagine a situation where, for example, quantum evaporation generates a different metric (with a firewall), I think that in the given example of a 'galactic collapsing shell with Earth in the middle,' there really can be no observable effects of...
Maybe I should add some remarks. This is Minkowski spacetime, and axis X,Y,T are valid only for static observer.
The motion of orange clocks is one-dinesional, along Y axe, The motion of blue clocks i also one dimensional, along X axe.
Yes, when you construct the "orange clocks tick" for different motions of orange clocks (different angle of plane 1), you receive this hyperbola (yellow, second positions of first orange miror for different orange clocks movements along Y axe).
Hyperbola is at Y-T plane, the other yellow line...
The thread "twin paradox without math" inspired me try to find fully graphical solution of length contraction.
Here is the result:
Graph is 3D as I think that is ilustrative to make all in one graph, but I am sure that it is possible to do it in 2 or 3 2D slices.
X and Y are spatial axes, T is...
Thank you.
I am thinking about next procerure:
At the beginning there is a line of the synchronized buoys in the region inside shell. Line is oriented radially and starts in the centre. Distances between buoys are regular, and matches to radial distance in flat area. Each buoy is continuously...
let's consider spherically symmetrical thin shell of dust, which is collapsing under its own gravity. There are no other forces as pressure or so except gravity, and particles of shell (dust) are in free fall. The shell has total mass M and collapse starts from rest state with diameter of the...
I know the Einstein convention of simultaneity, using light signals, which we can use also in curved spacetimes. Can you please show some other example how to meaningfully connect propper times of falling object to times of distant observer (at rest)? Thank you.
Yes, in this framework is effective to work with paradigma that interactions are happening in spacetime.
But I think that original question goes deeper, in fact, to unknown quantum gravity theory. And here, I agree with Wes, that I can imagine, that spacetime itself is gradually generated and...
Can be Einstein equation rewrited into some simpler form, when suppose only spherically symmetric (but not necessarily stationary) distribution of mass-energy ?
If yes, is there some source to learn more about it ?
Thank you.
edit: by simpler form I mean something with rather expressed...
Thank you. (I used "speed" because it corresponds to Newtonian escape velocity, But I do not need to interpret it as "speed",just ##dr / d\tau## is ok.)