my post i really about discussing the difference that a mathematical representation does to physics. for example, let's take for example a system which can be be represented by quaternions and by complex numbers. if we can represent a physical theory by quaternions which aren't commutative as oppose to complex numbers, does it have an impact on the theory itself? or in other words we can represent a physical theory by distinct mathematical appraoches which aren't the same and in someway even contrdict eachother, then which representation should we approve? does ockham's razor should put to the test here?