How Does Motion Impact Pendulum Clock Accuracy?

[mangaroosh]

Hey guys, I've been trying to find out about the expected effect of acceleration and/or motion on a pendulum clock; I asked this question in the mechancial engineering section of PF but didn't get any replies. It pertains to Einsteinian relativity also, specifically the effect of motion on clocks. I understand that a pendulum clock would not be precise enough to measure time dilation, but can we hypothesise an idealised, infinitely precise pendulum clock for the sake of explanation?


If a pendulum clock is put on a train and the train accelerates to an inertial speed, will that clock tick at the same rate as a similar clock left behind in the train station (at rest on earth)? If not, does anyone know by how much it would change?

Also, if a pendulum clock was built on a train traveling at an inertial speed, such that it didn't undergo acceleration, would it be expected to tick at the same rate as a clock in the train station?

Am I right in presuming that a pendulum clock would not work in deep space?

Also, if acceleration is the same as gravity, or at least has the same effect, would a pendulum clock accelerating in deep space start to tick, given the correct orientation?


Apologies for the glut of questions, it's just something I've been wondering about.

 

[DrewD]

A pendulum clock requires acceleration in the direction that the pendulum "hangs". On Earth that is from gravity. In deep space, it would have to be accelerated by something else.

Lets not consider the real life difficulties of measuring precision or bumpiness of the track. The clock's ticking would be mechanically altered while the train accelerated. Since the net force is pulling in a different direction, that would change the pendulum's swing. General Relativity would come into play too. Once moving inertially, the only difference would be due to SR (assuming uniform gravity). How much depends on the speed of the train.

Doesn't matter where the clock is built, SR will affect it the same way. Certainly the accelerating and decelerating would change the total time elapsed, but not the rate at which it ticks after it has come to rest.

Of course in real life, the only thing that would be noticed are the classical mechanics effects from jostling the change in direction of net force. There is no general answer to that question. You would have to check specific situations individually.

 

[russ_watters]

Both the acceleration and deceleratiion would increase the tick rate. During inertial motion, there is no effect. [Edit] Er, actually, a pendulum clock in a train moving at constant speed is traveling in a curved path around the Earth so it is not experiencing as much g.

Both of these are of course referring to clock error, not time rate (relativistic) effects.

 

[mangaroosh]

Both the acceleration and deceleratiion would increase the tick rate. During inertial motion, there is no effect. [Edit] Er, actually, a pendulum clock in a train moving at constant speed is traveling in a curved path around the Earth so it is not experiencing as much g.

Both of these are of course referring to clock error, not time rate (relativistic) effects.

thanks Russ.

if we were to assume that the clock was not traveling a curved path, but a strictly linear path, would the pendulum clock tick at the same rate as a clock at rest on earth; and has this actually been verified?

 

[mangaroosh]

A pendulum clock requires acceleration in the direction that the pendulum "hangs". On Earth that is from gravity. In deep space, it would have to be accelerated by something else.

Thanks Drew.

In the deep space example, if the motion were linear, would the pendulum clock have to be oriented in the direction of motion in order to work; and would it stop working if the motion became inertial?

Lets not consider the real life difficulties of measuring precision or bumpiness of the track. The clock's ticking would be mechanically altered while the train accelerated. Since the net force is pulling in a different direction, that would change the pendulum's swing. General Relativity would come into play too. Once moving inertially, the only difference would be due to SR (assuming uniform gravity). How much depends on the speed of the train.

Doesn't matter where the clock is built, SR will affect it the same way. Certainly the accelerating and decelerating would change the total time elapsed, but not the rate at which it ticks after it has come to rest.

If we were to ignore SR for a second though, would a pendulum clock on board a train traveling at an inertial speed tick at the same rate as a similar clock at rest on Earth (assuming no acceleration in either); has this been tested at all?

Of course in real life, the only thing that would be noticed are the classical mechanics effects from jostling the change in direction of net force. There is no general answer to that question. You would have to check specific situations individually.

cheers

 

[Dale]

would it stop working if the motion became inertial?

Yes, a pendulum doesn't tick in 0 g.

 

[harrylin]

[..] If a pendulum clock is put on a train and the train accelerates to an inertial speed, will that clock tick at the same rate as a similar clock left behind in the train station (at rest on earth)? If not, does anyone know by how much it would change? [..]

That goes beyond the capabilities of SR, because the pendulum clock system includes the Earth and SR does not account for the effect of motion in a gravitational field. Einstein already indicated this complication in his 1905 paper, by specifying that his time clock retardation prediction concerned balance clocks. In a footnote to the English translation this was later clarified as follows:

"Not a pendulum-clock, which is physically a system to which the Earth belongs. This case had to be excluded."

Perhaps someone else can provide the prediction of GR...

 

[russ_watters]

if we were to assume that the clock was not traveling a curved path, but a strictly linear path, would the pendulum clock tick at the same rate as a clock at rest on earth; and has this actually been verified?

I'm not sure what shape the path would have to be to keep a constant g(there may not be one), but it wouldn't be linear and I'd be surprised if anyone bothered to try. It has no scientific value that I can see.

 

[mangaroosh]

thanks guys!

 

[harrylin]

thanks guys!

I pointed out that the pendulum clock system includes the Earth. Regretfully you did not understand that, for you next wrote in a wrong thread:

I'm wondering if there are any issues that mean we couldn't use such an idealised pendulum clock? Is the fact that it wouldn't work in an inertial reference frame in deep space sufficient reason to exclude it?

I'll thus rephrase what I said in other words: a pendulum clock as physical system consists of the clock proper plus a big mass such as the earth. Such an idealised pendulum clock system would certainly work in deep space, but it's extremely impractical to shoot a clock that is fixed to a huge mass into deep space. And it would be impossible to do that experiment on earth, as the not co-moving Earth would still be affecting its operation.