Minkowski ("West Coast" convention, unprimed coordinates):
##ds^2=c^2(dt)^2 -(dx)^2-(dy)^2-(dz)^2##
##ds^2=c^2(dt)^2 -(d(r \cos(\theta)))^2-(d(r \sin(\theta)))^2-(dz)^2##
Using rotating, primed coordinates for the special case of ##r## and ##z## being constant:
##\require{color} ds^2=c^2dt'^2...
This must be true, because the definition of such coordinates is based on the Einstein clock synchronization, that means on the definition, that the one-way speed of light is the same in opposite directions.
That's not completely correct. Before Einstein, when the physically relevant coordinate transformation was thought to be the GT, Maxwell's theory was thought to be strictly true in only one inertial frame - that of still ether.
Source: Chapter "6.1 Transformation of the Field Vectors" in W...
You could write Maxwell's equations in the following primed coordinates (given any inertial coordinate system x,y,z,t).
$$x' = x \ \ \ \ \ y' = y \ \ \ \ \ z' = z \ \ \ \ \ t' = t + \frac{kx}{c}$$Source:
https://www.mathpages.com/home/kmath229/kmath229.htm
Then the one-way (cordinate-)speed of...
As others mentioned, that's wrong.
The following explanation in a local scenario shows, that "gravitational" time-dilation happens also in flat spacetime.
Source:
Book "Relativity - Special, General and Cosmological", Second Edition, chapter 1.16 "Gravitational frequency shift and light...
Here is a similar thing, Reichenbach's ##\epsilon##
https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/significance_conv_sim/index.html#epsilon
Here is another explanation:
https://www.mathpages.com/home/kmath229/kmath229.htm
As others wrote, this trick does not work.
The velocity of the "reset" signal (radio or light) from O to clocks A can be split into a component in direction of the axis of the wheel and a component perpendicular to the axis.
The velocity of the "reset" signal (radio or light) from O to clocks B...
That's not completely correct. Before Einstein, when the physically relevant coordinate transformation was thought to be the GT, Maxwell's theory was thought to be strictly true in only one inertial frame - that of still ether.
Source: Chapter "6.1 Transformation of the Field Vectors" in W...
Yes. Morin calls it "Relativity without c".
Source (see chapter 11.10 on page XI-38):
https://bpb-us-e1.wpmucdn.com/sites.harvard.edu/dist/0/550/files/2023/11/cmchap11.pdf
via:
https://davidmorin.physics.fas.harvard.edu/books/classical-mechanics/
You can do this i.e. by demanding, that a velocity composition in the same direction is commutative plus a few other assumptions, as shown in the following link:
https://www.physicsforums.com/threads/only-minkowski-or-galilei-from-commutative-velocity-composition.1017275/
Then the experiment...
The principle of equivalence applies. The object is locally at rest with reference to an upward accelerated frame. This situation is equivalent to an object in an accelerated rocket in flat spacetime.
This is wrong. It is a common misconception. You have such "gravitational" time-dilation also between bow and stern of an accelerating rocket in flat spacetime.
As others asked: What is the reference you are citing?