Galilean explanation of time

[Robert Winn]

One of the problems of science today is misconception of time,
presenting time as a sort of force that contracts lengths, curves space,
and distorts mathematics. Time is not a force. It is a measurement of
events. So let us consider time as shown by the Galilean transformation
equations.
x'=x-vt
y'=y
z'=z
t'=t
The problem scientists have with the Galilean transformation equations
is the last equation, t'=t, because they do not see it as providing for
the result of the Michelson-Morley experiment. The disagreement with
these equations can be shown by the example of a clock in a flying
airplane. Einstein says in his Special Theory that the time of that
clock would be slower than the time of a clock on the ground.
Scientists then experimented with clocks in airplanes and found that
they did indeed have slower rates than a clock on the ground. Then
Hafele and Keating experimented with cesium clocks flown on
transcontinental jet flights and said that their experiment had shown
that if an airplane flew around the earth one way, the clocks would be
slower, but if flown around the earth the other way, the clocks would be
faster. They attributed the slower clocks to the effects of Special
Relativity and the faster clocks to the effects of General Relativity.
Then GPS satellites were put in orbit, and a clock in a GPS satellite is
faster than a clock on earth, and scientists once again found a way to
determine the time of a GPS satellite clock by combining the perceived
effects of Special and General Relativity. But it would appear that
there is a simpler way to describe all of these times. Just because
Isaac Newton described time in his theory of gravitation as being
absolute does not mean he could not have worked the problem Einstein
claimed to have solved with the Lorentz equations. My own opinion is
that Newton was a good enough mathematician that he would have
considered the problem a different way and worked it with the
transformation equations he always used, the Galilean transformation
equations. There have always been faster and slower clocks. Scientists
of the times of Galileo and Newton did not have any problem representing
these times with the Galilean transformation equations. If a clock or
any other rate of time was faster or slower than the rate of a clock
that agreed with the rotation of the earth, which was considered the
standard of time when those scientists were alive, represented by the
equation t'=t, then those scientists would have just shown another set
of Galilean transformation equations with different variables for
velocity and time. So to represent the time of a clock in an airplane,
the inverse Galilean transformation equations would be
x = x' - (-vt/n')n'
y = y'
z = z'
n = n'
n' is the time of the faster or slower clock in the airplane, (-vt/n')
is the velocity of the ground relative to the airplane. and n=n' shows
that the time of the clock that shows n' is being used in both frames of
reference. So now we can show the results of the Michelson-Morley
experiment using the Galilean transformation equations. All we have to
do is to say that x=ct and x'=cn' instead of saying that x=ct and x'=ct'
the way Lorentz and Einstein did. Then according to the Galilean
transformation equations
x'=x-vt
cn' = ct-vt
n' = t-vt\c
This value for n' is actually the same as the numerator for Lorentz's equation for t'.
t-vt/c = t-vct/c^2 = t-vx/c^2
However, there is no need for the x in this expression in the Galilean
transformation equations because there is no length contraction. The
spatial coordinates are the same in both sets of equations. To show
this, we just cancel out the (n')'s in the inverse equations, and we
have our original Galilean transformation equations.
x = x' - (-vt/n')n'
x = x' + vt
t = t'
To show how this relates to gravitation, we consider the orbits of the
planets in our solar system. Mercury is the planet that is orbiting the
fastest, being the closest to the sun, its velocity being 30 miles per
second. A clock on Mercury would be slower than a clock on earth
because earth has a slower velocity in its orbit, 20 miles per second.
But what scientists do not seem to have realized is that if we compute
n' for the time on Mercury, we are not computing it from time on earth.
Earth is the third planet from the sun, and there would be an n' for
earth's clock derived from a clock that shows t that applies to all
planets, asteroids, etc., in the solar system. To imagine this common
clock, we go out through the planets, each having a faster clock than
the planets closer to the sun, until we run out of planets and other
things that are orbiting the sun. Then we are at a point, say halfway
to the nearest star, where the gravitation of the sun is of no effect,
and a clock at that point is faster than a clock on any planet in our
solar system. If we say that the time of that clock is t, then we can
calculate the time of a clock on any planet by the Galilean
transformation equations if the velocity of the planet is shown as v
according to the time of the clock halfway to the nearest star. So then
the speed of earth in its orbit would not be v, but (vt/n'), where v is
the velocity of earth's orbit computed from the outer space clock, t is
the time of the outer space clock, and n' is the time of a GPS clock on
earth. I hope this description of time can help scientists visualize
how time relates to motion and gravitation.
Robert B. Winn