Mechanical clocks and time dilation

[exmarine]

Does anyone know if any mechanical clocks have ever been accurate enough to show time dilation? (That would be a clock with a spring-mass harmonic oscillator.) Is there any reason to suspect they might not show the same thing as the atomic clocks? (Pendulum clocks would not, for example. They would show the opposite effect by slowing down with an increase in altitude, and in fact would stop in a geodesic orbit.)

How about electronic clocks with crystal oscillator controlled frequencies? Early satellites surely had these onboard for their transmitters I would think. Would they have been accurate enough to detect time dilation? After accounting for Doppler, etc., it seems there would have been a small downshift in their transmission frequencies. (Well, maybe an upshift depending on altitude and speed, etc.)

Thanks.

 

[phinds]

Does anyone know if any mechanical clocks have ever been accurate enough to show time dilation? (That would be a clock with a spring-mass harmonic oscillator.) Is there any reason to suspect they might not show the same thing as the atomic clocks?

ANY clock that keep accurate time will show exactly the same time (and time dilation) as any other clock. Do you seriously think that time dilation can be dependent on what kind of clock is used? Sure, if a clock is INaccurate, it might show something differently, but so what?

 

[russ_watters]

(Pendulum clocks would not, for example. They would show the opposite effect by slowing down with an increase in altitude, and in fact would stop in a geodesic orbit.)

An accurate pendulum clock at high altitude (but not in orbit) would show both the impact of the lower g and time dilation.

But no, none are accurate enough for that.

 

[exmarine]

An accurate pendulum clock at high altitude (but not in orbit) would show both the impact of the lower g and time dilation.

But no, none are accurate enough for that.

 

[exmarine]

Thanks.
But wouldn't the pendulum clock SLOW DOWN with an increase in altitude, exactly the opposite of the atomic clocks which speed up? In fact, they would stop at infinity - zero gravity.

 

[Ibix]

Yes. You could use a wristwatch - I think their oscillators work against springs, so they'll operate even in zero g.

 

[Herman Trivilino]

Does anyone know if any mechanical clocks have ever been accurate enough to show time dilation?

Sure, but it would be by sheer luck, because they're not precise enough!

Let me explain. Before even attempting to detect time dilation put some very precise mechanical clock next to a very precise atomic clock and see if you can keep it in sync by adjusting its mechanism. You'll find that the best you can hope for is an occasional match, it'll be fast sometimes and slow others. There's a limit to how well you can do, and this limit is due to what's called precision.

If we repeat the above with a pair of precise atomic clocks we find we can keep them in sync with each other much better than we can a pair of mechanical clocks. So we say the atomic clocks are more precise than the mechanical clocks. Thus if we are interested in accurate time keeping we need a standard to use for comparison purposes. We would use the atomic clocks to establish that standard simply because they are more precise.

So returning to the original comparison we see that sometimes the mechanical clock will be accurate but most times it won't. Using any clock to determine anything requiring higher precision than it's capable of will be futile. Time dilation measurements of the type we're able to conduct with our current technologies require, as far as I know, a greater precision than can be achieved with a mechanical clock. But I could be wrong about that.

 

[jtbell]

Does anyone know if any mechanical clocks have ever been accurate enough to show time dilation?

According to the Guinness world-records people, the most accurate mechanical clock ever built (in 2015) lost about 5/8 second over 100 days. I leave it as an exercise to calculate the speed that produces time dilation at this rate.

http://www.techtimes.com/articles/4...ars-ago-is-most-accurate-mechanical-clock.htm

This is a pendulum clock, so it probably wouldn't do for gravitational time dilation. Even using it to measure speed-induced time dilation would probably be tricky.

 

[Vanadium 50]

Sure, but it would be by sheer luck, because they're not precise enough!

Alternatively, we can't get them moving fast enough.

 

[jbriggs444]

Alternatively, we can't get them moving fast enough.

Get 'em going fast enough and even a muon makes a clock accurate enough to detect time dilation.

 

[exmarine]

According to the Guinness world-records people, the most accurate mechanical clock ever built (in 2015) lost about 5/8 second over 100 days. I leave it as an exercise to calculate the speed that produces time dilation at this rate.

http://www.techtimes.com/articles/4...ars-ago-is-most-accurate-mechanical-clock.htm

This is a pendulum clock, so it probably wouldn't do for gravitational time dilation. Even using it to measure speed-induced time dilation would probably be tricky.

Wow, about a quarter million miles per hour? Here to the moon in one hour. Thanks!

 

[russ_watters]

Thanks.
But wouldn't the pendulum clock SLOW DOWN with an increase in altitude, exactly the opposite of the atomic clocks which speed up?

Yes, but the overall amount would reflect both effects. It wouldn't slow down as much as you would expect if you ignored GR. Just like a GPS clock in orbit that shows both the effects of SR (slow down) and GR (speed up) separately.

 

[PAllen]

For a pendulum, local g can be measured independently, e.g using a sensitive scale and a standard test mass (or by far more sophisticated methods that don't depend on clocks). Then, a standard pendulum clock should be defined as one whose readout is adjusted for locally measured g. Then, in principle, you would detect time dilation with such a clock. Note that for the local correction for local g you are not specifically depending on Newtonian gravity. Any theory which includes local universal free fall would produce the same correction. In particular, GR does not predict a different local correction. The correction is to measure a second defined by some local fundamental physics, and to have local clocks of different design be consistent. What GR predicts is that after local correction, two pendulum clocks at different altitude would show gravitational time dilation (the higher one be faster via comparison by signals, for example).

 

[jtbell]

According to the Guinness world-records people, the most accurate mechanical clock ever built (in 2015) lost about 5/8 second over 100 days. I leave it as an exercise to calculate the speed that produces time dilation at this rate.

Wow, about a quarter million miles per hour?

That's about right, after converting from 114 km/s which was my result. For comparison, the orbital speed of the International Space Station is about 7.6 km/s.

 

[Herman Trivilino]

The thing is, we routinely make measurements of particles that travel at much faster speeds than 114 km/s. I was trying to think of a way that a mechanical clock could be used to detect time dilation for these particles. Like using a wrist watch to time laps around the LHC.

But seriously, traveling at nearly the speed of light, it would take about a microsecond to complete a lap, if I did my arithmetic correctly. Now, 5/8 of a second every 100 days is about one microsecond every 10 seconds. So if you timed laps for 10 seconds you would be on the verge of being able to detect variations that small with a mechanical clock. That's 10 million laps!

You could do something like sending a beam of muons around the ring, count of course the number of laps, but also count how many muons are in the beam every 10 seconds. After a minute or so it seems you'd have more than enough data to detect the effects of time dilation with your mechanical clock.

 

[PAllen]

The thing is, we routinely make measurements of particles that travel at much faster speeds than 114 km/s. I was trying to think of a way that a mechanical clock could be used to detect time dilation for these particles. Like using a wrist watch to time laps around the LHC.

But seriously, traveling at nearly the speed of light, it would take about a microsecond to complete a lap, if I did my arithmetic correctly. Now, 5/8 of a second every 100 days is about one microsecond every 10 seconds. So if you timed laps for 10 seconds you would be on the verge of being able to detect variations that small with a mechanical clock. That's 10 million laps!

You could do something like sending a beam of muons around the ring, count of course the number of laps, but also count how many muons are in the beam every 10 seconds. After a minute or so it seems you'd have more than enough data to detect the effects of time dilation with your mechanical clock.

But I think the OP was interested in the clock having its rate affected per some other observer, not measuring time dilation of a decay process using a mechanical clock.