When Concorde is in supersonic cruise at Mach 2 the airframe heats up causing the aircraft to expand in length by 12.5 centimetres. This does not happen to the passengers.
However, if you speak to a physicist he (or she) will tell you that a) the faster you go the bigger you get and b) time slows down when you go really fast. This second point has actually been proved by setting two atomic clocks to exactly the same time, sending one into space for a few orbits round the earth and then bringing it back down and comparing the times. Believe it or not, the clock that went into space ran slower than the clock on earth. Proving the point that time it not constant (only the speed of light is constant).