rootone said:
If 'a second' (locally) was a variable then you would need another dimension of time in order to describe it's value at some given moment.
Seconds per second?
Occams razor prefers time to be one dimensional.
Following on from Chalmoth's comment, we can also add that as a logical tautology time can only pass at "one second per second" for any particular observer.
Relativity deals with the measurement of time in one observer's frame of reference as measured by another observer in a different frame of reference, and if the observers are moving relative to one another then that is when the first observer's clock appears to slow down as observed by the second observer, and
vice versa.
That first observer however will need some kind of clock to measure that second, otherwise how would they know when that second has 'passed'? If it is physical time we are talking about, as we are, then we need some kind of physical clock to measure it by.
Many years ago I was in a postgraduate lecture on cosmology that was discussing events in the first microseconds of the universe's history, after which one of the professors in the audience asked, "What do you mean by the first second?" i.e. How do you measure it, and with what type of clock? So the OP question is a quite profound one.
If we indeed define a second by "The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom." then in order to demonstrate that that second is an unchanging unit of time we have to have an unchanging caesium atom, which might be difficult to prove in the first second when there were no caesium atoms around!
As the radiation corresponding to the transition between the two levels, n and n', of the caesium 133 atom is dependent on
\nu = \frac{2\pi^2mZ^2e^4}{h^3}\vert\frac{1}{n^2}-\frac{1}{n'^2}\vert , in order for a second to be an "unchanging unit of time" we have to demonstrate that m or e does not change over those cosmological time scales.
In GR they do not, but in alternative cosmologies such as conformal gravity theories, varying fine structure constant theories, or a mass field theory such as that of Hoyle (see for example http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1975ApJ...196..661H&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf ,) they do vary.
If the physical process that calibrates the clock is allowed to vary then that would affect the response to the question, "How long was the first second?"
It would depend on which clock you measure it by.
Garth
