OK I am just going to dump this here for now as I am busy with other things, but will be back again later:
A baseball pitcher can throw a ball with a mass of 0.15 kg at over 90 mph, so I can safely use a ball with a mass of 0.2 kg and have it thrown at 70 mph (28 m/s)
The kinetic energy KE of that ball is 1/2 mv^2 = 78.4 J
Let’s say this is a very efficient pitcher so that is the amount of energy he puts into the throw.
Now, according to SR enthusiasts and various other complete whackos, “you can’t tell which is moving!”
“It could be the ball or it could be the entire earth depending on which reference frame you choose!”
The concept of reference frames is a very useful one, but when it is carried to extremes, you get the above kinds of absurdities.
I am about the prove that you can know which one is moving at 28 m/s and I will not resort to absolute motion, just Newton’s Laws.
IF the earth was moving at 28 m/s, with respect to the ball, it would have a kinetic energy of
1/2 MV^2 where M is the mass of the earth, 5.98E24 kg
That works out to 2.34E27 J, but we only started with 78.4 J
I call that a clear case of violating conservation of energy!
So, this idea of relative motion and “you can’t tell” what is really moving can be nicely resolved just by energy considerations. Actually, all you need is common sense, but that is something that SR enthusiasts seem to completely lack.
If I had a sailor come on deck and ask me if it really is the ship moving through the water and not the other way around, I would be tempted to thrown him overboard!
To determine the actual velocity of the planet earth, resulting from the throw, according to Newton’s Laws, we can use the fact that momentum is also conserved. Before the throw, the total momentum of ball and earth was zero and it must be zero after the throw.
That is, (0.2 kg) (28 m/s) + (5.98E24 kg) (V_earth) = 0
And V_earth works out to the incredibly small velocity of 9.36E-25 m/s
The KE of the earth then is 2.62E-24 J an incredibly tiny amount, but not zero.
So, there is relative motion but the 28 m/s only applies to the baseball and it is the baseball that will have some tiny amount of time dilation. The baseball that is thrown will be found to be ever so slightly “younger” than the one the umpire is keeping in his vest, by applying the Lorentz transform.
The exact same reasoning can be applied to the space-faring twin without all the cartoonish space time diagrams and “deep” philosophical ruminations.
None of what I have written here overturns SR and I rely a great deal on the GPS and have no doubt at all that time dilation is real. I do have a reasonable doubt that velocity time dilation is reciprocal and I would very much like to see some experimental evidence to either support it or debunk it.