[DanuHoward (OP)]

So, I recently did a relativity paper at University. I learned about time dilation at relativistic speeds and such, using the example of a light clock travelling at high speeds, I was assured that this worked the same for all clocks, not just those using light to measure time.
This got me thinking about pendulum clocks.
My question is this.The period of a pendulum is meant to be proportional to sqrt(L/g), but if I had a pendulum whose period of oscillation was exactly 1s, and I moved this pendulum clock to, say, the moon, what's to say that the period of oscillation isn't still 1s, and merely time is experienced differently due to the different gravitational field, rather than the period having been increased due to the decrease in g?
How different would time be outside of Earth?
If a year is merely defined by 1 cycle around the sun, and a day by 1 rotation of the Earth, if the Earths spin or orbit were to speed up, would we even notice, or would we experience time differently?

[imatfaal]

So, I recently did a relativity paper at University. I learned about time dilation at relativistic speeds and such, using the example of a light clock travelling at high speeds, I was assured that this worked the same for all clocks, not just those using light to measure time.
This got me thinking about pendulum clocks.

  It does work - been tested to high degree of accuracy and was lovely evidence for Einstein's relativity  (1) and GPS satellites must take this into account to give accurate readings (2)

My question is this.The period of a pendulum is meant to be proportional to sqrt(L/g), but if I had a pendulum whose period of oscillation was exactly 1s, and I moved this pendulum clock to, say, the moon, what's to say that the period of oscillation isn't still 1s, and merely time is experienced differently due to the different gravitational field, rather than the period having been increased due to the decrease in g?

  Technically that proportionality is only for small swings - 25 degrees would be over 1% out.  But that is just me being pedantic.  I don't know if a pendulum clock was taken to the moon - I rather doubt it, but if one was the swing would be longer.  And it would fit with the same equation of and we could measure g with a spring balance and all would still fit.  Our wrist watch - which on the moon would be a wind-up version would show that the pendulums swing has changed. We could then time the orbit of Jupiter's moons and find that it agrees with our wristwatch and our previous knowledge.  The only conclusion is that pendulum's period has changed - not our perception of time.  There actually will be a change in time due to the different gravitational potential - but it will be very very small. 

How different would time be outside of Earth?
If a year is merely defined by 1 cycle around the sun, and a day by 1 rotation of the Earth, if the Earths spin or orbit were to speed up, would we even notice, or would we experience time differently?

  Yes just cos we define units by natural events does not imply that if those natural events were to change we wouldn't notice.  If noon occurred late or early you can bet your bottom dollar the guys at RO Greenwich or at USNO Washington (more likely Washington where the sun does occasionally shine) would notice pretty quickly; as would anyone with a wrist watch and half an eye open.  I would notice that my tendency to sleep  every night has changed - that I need to shave more or less than once a day etc



1. http://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment
2. http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

[evan_au]

We know that gravity is lower on the Moon because the movies of Lunar astronauts showed them hopping like kangaroos. Plus, the Lunar lander would have run out of rocket fuel if it had to fight a gravity field as strong as Earth's gravity.

We know that time runs at pretty much the same speed on the moon as on Earth because the Lunar astronauts didn't speak in long drawn-out sentences.

We used to define time by the rotation of the Earth, but we now have much more accurate clocks, and we know that the Earth's rotation around it's axis changes over a few years (see http://en.wikipedia.org/wiki/Leap_second#Slowing_down_of_the_Earth), and Earth's orbit changes over a period of decades and centuries as it is perturbed by the orbits of the other planets (see http://en.wikipedia.org/wiki/Earth%27s_orbit#Future).