simultaneity is redefined in special relativity because of the discovery that the speed of light is always constant. However, I think this violates Galileo's relativity, which states that you cannot know your absolute velocity or the absolute velocity of another object. You can only know their relative velocity. This is true because when you consider yourself throwing a ball on the ground and throwing the ball again on a moving train. The velocity of the ball will still be the same. So throwing a ball and measuring its speed cannot give you any clues about your absolute velocity. But Special relativity states that time and space changes, simultaneity changes, in a way that is designed to conserve the speed of light. So there will be a change in the basic setup of Galileo's experiment, and therefore would have a different result. And it seems as if there will be a difference in the velocity of the ball when thrown from the ground and on the train. But it shouldn't because it goes against Galileo's principle.I want to know why the speed of the ball would also be constant under the setups of special relativity.
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1$\begingroup$ Simultaneity only becomes relative between two inertial frames which are moving with respect to each other. Once you see another frame moving with respect to yours, you can measure your own velocity with respect to that rest frame: It is precisely the velocity you measured for that frame w.r.t. your rest frame. This works exactly the same in SR. Your train example has nothing to do with this, everything takes place within the rest frame of the train. $\endgroup$– paulinaCommented May 28 at 11:40
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$\begingroup$ There is no "absolute velocity" or "preferred inertial reference frames" in special relativity too. I think you confuse absolute velocity and maximum relative velocity due to relativistic velocity addition formula $$u' = \frac {v+u}{1+vu/c^2}$$, which is quite different concepts. There is no absolute speeds unless you have some object/phenomena scattered across all universe uniformly which you can take as a "standard reference points", like cosmic microwave background (which by the way Einstein was denying). $\endgroup$– Agnius VasiliauskasCommented May 28 at 12:01
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1$\begingroup$ FYI: When they say, "the speed of light is always constant" they mean, the speed of light relative to whoever measures it is always constant. Imagine a laser, floating in space, and imagine an apparatus that measures the speed of the laser beam. The apparatus is attached to the side of your space ship, floating near the laser. You measure the speed of the beam to be 299,792,458 m/s, and then you accelerate away, following the beam. As you continue to take measurements, you notice that you get 299,792,458 m/s every time. No matter how long you accelerate, you always will get the same number. $\endgroup$– Solomon SlowCommented May 28 at 13:18
1 Answer
Special relativity is indeed different from Galilean relativity but contains it as a limiting case, namely for velocities much smaller than that of light.
In your experiment with a ball thrown in a train versus a ball thrown on the ground in a similar fashion, the velocity of the ball as measured by you would have the same magnitude in either of these cases, and in both frameworks of Galilean and special relativity. However, in the scenario when the ball is thrown in a moving train the two theories predict different outcomes of the measurement of the velocity of the ball as measured by someone who is stationary with respect to the ground. I don't know if this is what you were asking for since your phrasing is not very clear. I mean, of course there is
a difference in the velocity of the ball when thrown from the ground and on the train
and this does NOT go against Galileo's principle.
