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A start will be made by extending Newtonian physics to replace special relativity.
To see special relativity in action, read Plus article What's so special about special relativity?
Numerous experiments using very high-speed objects have shown that Special relativity is correct.
To get the velocity of recession of a galaxy from its redshift, you should use the formula given by special relativity.
First, special relativity has no need of an ether.