On Thursday, March 15, 2018 at 2:40:38 PM UTC-6, Gerald Kelleher wrote:
once you recognize Sir Isaac's absolute/relative time as nothing more than the
equalizing facility between variations in natural noon and the average 24 hour
day you can't discuss it in any other terms and certainly not relativity.

Let's try to take this one step at a time.

How can one speak of an "average 24 hour day", unless one can measure the lengths
of the 1,491 days over a four-year period, and then average those lengths?

Historically, sundials did divide the day into 24 hours before people had
pendulum clocks. There were water clocks and burning candles with graduations -
and later hourglasses - to measure uniform time, but they were not very
accurate.

But in a practical sense, if one wanted to find out how long to make a pendulum
for a clock giving the "average 24 hour day", one would have to do something
like this:

Start with a pendulum clock which tells time in some *arbitrary* unit, not
related to the calendar or the Sun at all. Then keep track of how many times the
pendulum went back and forth between, say, noon on February 29 and noon on
February 29 four years later. To ensure the count is accurate, take note of
where the hands of the clock are at intervals during this period as well,
perhaps even every day.

Perhaps the arbitrary interval chosen will be a crude approximation to the day,
so that one can meaningfully say that the pendulum clock lost 2 hours, 12
minutes, and 4 seconds over four years. And so the pendulum is adjusted
proportionately, and one now has a standard for clocks that give the average 24
hour day.

My point here is that you have claimed a wrong solution to the "chicken and the
egg" problem. Yes, sundial time long preceded average clock time. But average
clock time still had to be constructed using clock time in an independent unit
to measure sun time. So while variable sun time *historically* precedes uniform
mechanical time, uniform mechanical time still *logically* precedes sun time.

If one lived on Mars, one's sundials would undergo an Equation of Time that
oscillated with a period of one *Martian* year, which is about two Earth years.
Uniform clock time is shared between Earth and Mars, sun time is unique to each
planet.

So clock time, although the _size of its unit_ is derived from an average of
solar days, is much more than a derived equalization; it is fundamental. It is
the ground on which motion and action can be described and measured.

And now that we have said that time is not allowed to vary with the Sun, are we
"certainly" unable to accept that something else, after all, can cause it to
vary? Must we reject Einstein's "Theory of Relativity"?

Well, when he first came out with it, a lot of scientists were quite
uncomfortable with such a radical notion. But we don't have the choice of
rejecting it; it's proven by experiment. And, while it does add a complication,
the complication it adds is a necessary one *when it is relevant*, and it can be
ignored otherwise.

You would burden us with an unnecessary and irrelevant complication that cancels
out anyways.

John Savard