Einstein's theory of relativity was all about the relativity of measurement. I will present here an extention to this idea, the relativity of unit of measurement. At first, anyone agrees that the laws of physics don't change one bit, if we would use one day instead of the meter stick any other unit of length. This is a very profound principle of physics. At first this looks rather trivial. Nature does not have preferred units of measurement, so all choices for units are more or less arbitrary. The outcome of General Relativity was that we need to think of the cosmos as expanding. Suppose now, we would choose a unit of length, that was exactly proportional to the expansion of space. So, in other words, in this new measuring unit system, the expansion of space would not be a known phenomena. Since speed of light still is constant, this would also mean we need to have a new time unit. In this new time unit we have to adopt the idea that the age of the universe is infinite. It is clear then that in more then one way, we have a new phyics, just be choosing a new measuring unit of length, and changing other units of measurement accordingly! Physical phenomena would not be the same. The expansion of space would be an unknown phenomena. On the other hand a new phenomena would occur, the contraction of all material forms (from galaxies to atoms and below). Does this change of physical behaviour mean that Nature does have a preferred set of measuring units? Is the physics of the new measuring units an - although different - but still valid form of physcis? If so, what would these new physcis laws be like?