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Galilean principle of relativity is for sure not absolutely true, isn't it?

Say one has a pool full of water within a spaceship, if the spaceship is accelerated and then acceleration stops, one can look at the ripples in the pool, analyze their form and then tell, up to a certain degree of preciseness, if there was acceleration, how long ago, what was the force accelerating? nop? and now say, the types of materials analyzable and measuring equipment become more and more available, then it can get to a point that some type of liquid-gas within the space ship can be analyzed by some sort of newly discovered particles, and one can tell if the spaceship was accelerated up to 100 million years ago up to a 1000 years plus minus preciseness. Is there a basic physical law that denies that possibility?

Now, doesn't the special principle of relativity start at its very first sentences, by relying on the Galilean principle of relativity?

If there is any well informed math-physics guy here, who also thinks that this is not a die-hard joker question-view, then, can you please try to explain to me, how does this change the very mathematical basics of SR?

Say one has a pool full of water within a spaceship, if the spaceship is accelerated and then acceleration stops, one can look at the ripples in the pool, analyze their form and then tell, up to a certain degree of preciseness, if there was acceleration, how long ago, what was the force accelerating? nop? and now say, the types of materials analyzable and measuring equipment become more and more available, then it can get to a point that some type of liquid-gas within the space ship can be analyzed by some sort of newly discovered particles, and one can tell if the spaceship was accelerated up to 100 million years ago up to a 1000 years plus minus preciseness. Is there a basic physical law that denies that possibility?

Now, doesn't the special principle of relativity start at its very first sentences, by relying on the Galilean principle of relativity?

If there is any well informed math-physics guy here, who also thinks that this is not a die-hard joker question-view, then, can you please try to explain to me, how does this change the very mathematical basics of SR?

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