“Absolute, true, and mathematical time, of itself and from its own nature, flows equably without relation to anything external, and by another name is called ‘duration’; relative, apparent, and common time is some sensible and external (whether accurate or unequable) measure of duration by means of motion, which is commonly used instead of true time, such as an hour, a day, a month, a year.” (Isaac Newton)
At 14 mins and about 30 seconds into the Royal Institute lecture below, Professor Sean Carroll refers to the t coordinate in Minkowski space-time as ‘floating somewhere in the background of your mind’.
However, as it is a coordinate, surely it must have a location in time and / or space?
I think Professor Carroll is unable to define it any further because he is unable to consider the possibility of Absolute Time. Consequently, he cannot say where it is and so fudges the issue.
I believe that the t coordinate has a very physical reality within my Theory of Universal Absolutivity, and that it lies at rest on the ever-expanding 2D membrane of Absolute Time in which the 4D (Relative) space-time universe resides.
My thinking here is that tau is a variable whereas t is an Absolute Time co-ordinate.
As Professor Carroll explains, Minkowski space-time is embedded within Einstein’s equation for gravity e.g. within the metric tensor:
Therefore, it seems to me to be logical to assume that Absolute Time is implicit within the equations of both Einstein and Minkowski despite the latter’s declaration that:
“Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality”
My interpretation of our reality is, therefore, 5 Dimensional. There is the Relative dimension of 4D space-time, and a 5th dimensional space of Absolute Time through which the 4D space-time universe travels via the ever-expanding instant of the 2D membrane. This is how we are able to progress nano-second by nano-second into the future.
Einstein argued that if the Speed of Light is a universal constant (as suggested by Maxwell’s equations), then Time has to be variable. Otherwise, a moving torch would record a higher speed of light than a stationary one. However, by use of Lorentz transformations, Einstein (1905) was able to argue that time could dilate and space could contract, thus compensating for the additional movement / speed of the torch. This was then turned into 4D Space-Time by Minkowski (1907).
Obviously, Einstiein was not wrong … but perhaps he was only partially correct?