Einstein’s Theory hang on the notion that Time is independent from the 3 other dimensions such as x-coordinate, y-coordinate and z-coordinate. How independent is time from them? Are it independent from the other three in the same way them are independent from each other?
Length, width and Height are independent in the sense that any object make a change in one of them doesn’t necessary imply the change of other two. Thus any object in the universe can change only one out of the three dimension without changing the other two. There is no built-in causality chain in the definition of these 3 dimension themselves to connect the change of one dimension to change of another dimension. If there is any relationship between the change of them, that relationship is formed due to something not inherent in the dimensions themselves: Gravity. It is inherently and theoretically possible a change in one dimension doesn’t imply a change in another dimension. And this theoretical possibility has been verified many times in the universe(for instance, by light traveling in straight line which only 2 out of 3 dimensions varies). They are independent of each other Mathematically in the sense that one dimension doesn’t contain the other two functionally, and description of one doesn’t give us any information of the other two. It is a complete and adequate description by each of them without referring to other. Physically they are independent from each other, in the sense that in the existing model of universe, there are no theoretical necessity that change in one dimension must cause change in any other dimension.
Time, however, is defined by periodic change of position of planets. We recognize a year by the time it take for Earth to return to its angular position from the sun(which could be verified by observing the pattern of season in weather). If there is no observable regularity in the system, then time can never be defined. Thus the definition of time is inherently depends on other three dimension. To be more accurate, time is calculated from the change of other 3 dimensions, time is a function of other three. Thus time is Mathematically and Physically impossible to be separate from the other three. Time make no sense without an implicit reference to the other three, and it is causally related to the other three dimensions. Unless we could discover phenomena that time could be referred without any implicit reference to the other three, I am strongly against the usage of time as an independent dimension in discussion of Physics. Since it is an logical and practical impossibility in existing framework of Physics and Mathematics, therefore any theory implies time is vary independently of the other 3 dimension is invalid.(i.e. Theory of Relativity)
Why does human held the illusion that time as an independent dimension to be an inherent truth? It is because of our experience that biological process is irreversible(probably built-in in the blueprint of DNA), and has regularity that we can measure. That irreversibility come from physical measure of entropy resulted from complexity inherent in any biological entity. In a sense, Life is necessary for Time to exists.
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