Physicists motivate the need of departure from Newtonian mechanics into the space-time of Einstein’s theory of relativity, by stating that Newtonian mechanics requires absolute space and time, and this is an unreasonable request. Therefore Newton’s mechanics has to be replaced by Einstein’s.
But this argument is not correct: There is no absolute space and time in Newtonian mechanics, since Newton’s laws are invariant under Galilean (coordinate) transformations between systems moving with constant velocity with respect to each other (see above picture), and thus there is no special coordinate system which could represent absolute space. Further, relativity of time is evident since any time can be chosen as initial time.
Newtonian mechanics thus does require absolute space and time, only the distinction between space and time of the Galilean transformation, in contrast to the mixture of space and time into the space-time of the Lorentz transformation of the special theory of relativity.
The difference between Newton and Einstein is not absolute space and time vs relative space and time, but separation between space and time vs mixture of space and time.
What is then the reality of physics? Can space be traded for time and time be traded for space? Can we prolong our lives by moving to a smaller apartment? Can we gain in weight by giving up a bit of time?
Nothing in our experience indicates that space can be turned into time or vice versa. The mere idea seems to be far beyond any form of imagination. Yet this idea is embraced by modern physicists as a sign of deep understanding of the reality we live in.