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Sarma,
Regarding:
I think the first one i.e., x<--->t, x'<---->t' is the most obvious.
It is telling us that x and t are exchangeable. Both equations have the
dimensions of time and it indicates the equivalence of x and t.
This supposed equivalence can be only conceivably be the case if the
universe has 1 spatial and 1 temporal dimension. The experimental
evidence is that the universe has 3 observable spatial dimensions and 1
temporal dimension. In the presence of y & z dimensions a switch of x &
t is not a symmetry of nature--even if it is a symmetry of a Lorentz
boost transformation along the x direction.
David Bowman
dbowman@georgetowncollege.edu