Re: Grandfather Clocks and Relativity



On Jan 29, 4:26 pm, "Tom S." <nos...@xxxxxxxxxx> wrote:
"Barry" <Sir...@xxxxxxxxxxx> wrote in messagenews:1170107537.725468.243800@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx



On Jan 29, 3:43 pm, "Tom S." <nos...@xxxxxxxxxx> wrote

. Anyway, your comments make me think that
maybe the ratio of the two masses that David refers to is the ratio
of the mass of the pendulum to the mass of the descending weights.

I think he was referring to the mass of the pendulum and the mass of
the main gravitational source that's accelerating the pendulum
(usually the Earth).

BarryThat's what I thought at first, too. If so, then I really don't understand
what David is saying.


First David writes:

______________
A pendulum clock is a clock who's timing mechanism is based on the
ratio of two masses. Neither mass needs to be the size of the earth.
_______________

Meaning that any two masses can be used to make a pendulum. One of
them doesn't need to be the Earth.
That seems O.K.

Then he writes:

________________
Furthermore, I can be in an inertial reference frame that is far
removed and has zero relative velocity with respect to a large mass
like the earth, and I can setup a pendulum clock there that ticks off
seconds at the same rate as all other clocks I construct.
______________

He can make a bunch of clocks that all keep the same time.
That seems to be O.K.

Finally, he writes:
_________________
The ratio of the masses doesn't change in the pendulum clock with
an
observer's relative velocity wrt the clock.
______________


Each of the two (relativistic) masses will change by the same factor
as viewed from other inertial frames. Hence the ratio of their
(relativistic) masses will be the same in all inertial frames.

That also seems to be O.K.

Going back to his original post, he wrote:
__________________
Einstein said ideal clocks in different inertial frames run at
different rates, but this does not apply to pendulum clocks.
Einstein's notions of time and space must apply to all clocks. How
was the exception for pendulum clocks resolved?
___________________

The answer seems to be that to an inertial or accelerating *observer*,
a pendulum clock will behave like any other clock.

However, should it be the pendulum *system* that's accelerating, The
answer would be a little different.

We know that T = 2pi(L/g)^0.5, and for accelerating pendulum
*systems*, "g" would effectively be greater so I would expect the
pendulum to *physically* speed up - ceteris paribus.



Barry

.

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