On 7/5/17 2:48 PM, Robert Winn wrote:
> Well, but I am using the Galilean transformation equations, the correct equations for relativity, and Galileo's definition of a second, notwithstanding the hyperfine transitions of Cs133 atoms. In other words, there are variations even in hyperfine transitions of atoms. So what I can do instead of what you suggest is take a sufficiently long time in which the earth rotates and average out a value for a Galilean second that would satisfy scientists and say, a Galilean second is equal to a particular number of hyperfine transitions of a Cs133 atom under certain conditions of gravitation, etc., and scientists should be able to agree, Well, that would be close enough for modern science of today, although maybe not for some future time.
> Then we could talk about Galilean seconds as they are used in the Galilean transformation equations. This is just a suggestion. I know how touchy scientists are about this, but I thought I would suggest it anyway.
Well, let's investigate this a little bit.
Let's say you wanted to design a little system with a spring and a
massive ball in an evacuated tube, and you want it to oscillate at a
certain rate. Fortunately, to do this design, you can actually use some
knowledge of physics. There's things called laws of physics, and there's
one here that says that the period of the oscillation of this system is
going to be
T = 2*pi*sqrt(m/k), where m is the mass of that ball, and k is the
stiffness of the spring, which you get by pulling on the spring with
some known force and measuring how far it stretches. So if we wanted to
actually design this system to oscillate at a rate of once every 0.50
seconds, we could do it using this physical law and then choosing the
spring and the ball appropriately. Physical laws are such handy things
for designing objects and avoiding a lot of trial and error -- which is
what DESIGNING means, after all.
Now, here's the thing. Let's say we put one of these spring-mass systems
up on a satellite and let it oscillate. Will it be oscillating at once
per half second as designed? It should be, if the law of physics is any
good. Let's say there is some other system on board that is counting on
it ticking at 0.50 seconds.
But let's take your scheme of making sure that all clocks, regardless of
where they are in a gravitational field or how fast they're moving, are
synchronized with some ground master clock that is ticking away so that
86,400 of its ticks corresponds to an "average" earth day? Will the
spring oscillate at 0.50 seconds according to this earth clock? No, it
will not.
Oddly enough, it WOULD oscillate at 0.50 seconds if compared to a local
atomic clock. But as you observed, this local atomic clock on the
satellite doesn't show the same elapsed time as the ground atomic clock.
Now, I know what you're going to say, because you've said it before.
You're going to say that the rate of the mass-spring system's
oscillations is ALSO affected by the difference in speed and
gravitation, the same way the local atomic clock is. So what that means
is you're saying that the law T = 2*pi*sqrt(m/k) just doesn't work for
a mass-spring system up in a satellite and you have to find some other
law to design by. Or maybe because you don't know what the law should be
up there, you just have to do it by trial and error.
So there's an important trade-off here. What you've gained is that all
the clocks everywhere, even in satellites, are all ticking together in
synchronization with the ground clock. But you've lost your ability to
design anything using any laws of physics, because those laws don't seem
to work up there in the satellite. Your spring mass system just doesn't
oscillate at 0.50 seconds by the ground clock, even though the law of
physics says it should.
So what have you really gained, in the long run? What's so good about
having all those clocks running in synchronization always, when you've
lost the ability to design things using laws of physics?
What MIGHT be better -- and just consider this as a possibility -- is to
say that the laws of physics are the same and still work, but only
against a local clock. And if you want to see how it works against a
ground clock, well then, you know how to translate the rate as measured
by the local clock compared to the rate of the ground clock.