Researchers prove Huygens was right about pendulum synchronization | Hacker News Reader

Researchers prove Huygens was right about pendulum synchronization

phys.org

42 pointsdnetesn17 comments

"Another new discovery is that pendulum clocks are not only synchronous but also move more slowly over time and thus are not very reliable timekeepers."

Wait, what? That's surely not a "discovery"...

Not sure if this is what you mean, but pendulum clocks work because the pendulum "... swings back and forth in a precise time interval dependent on its length, and resists swinging at other rates."[0]

[0] https://en.wikipedia.org/wiki/Pendulum_clock

The fact that a particular mechanism resists the effects of friction doesn't mean it's unaffected by them.

I don't think that's quite right - friction obviously causes the pendulum swing to slow down, but even as it slows the frequency of the swing remains constant (because the amplitude changes to compensate for the slowed swing) So until the swing actually stops due to friction, the pendulum will continue to keep time. There are of course exceptions, for example if the friction is actually changing (due to air pressure / humidity changes) the clock will go out of sync.

This is observable in real life pendulum clocks and I didn't think it was an area of debate - am I missing something here?

Actually friction changes the frequency, see [1]. Moreover there is this general idea in spectroscopy (whether of atoms or of pendulum clocks) that to precisely measure a frequency you need the smallest dissipation possible (check wikipedia about linewidth-lifetime relations, Q-factors, etc). Basically the precision with which you can measure a frequency is 1/lifetime_of_the_phenomenon. Higher dissipation means lower precision.

See [1] https://en.wikipedia.org/wiki/Harmonic_oscillator#Damped_har...

edit: If this change of frequency is calibrated it is not an issue, but this calibration is not trivial and friction is something a lot less stable than the other physical properties that govern the clock.

But (approximating at small angles), the pendulum's period is constant. Friction will have the effect of reducing the distance that it swings, but the amount of time it takes to swing it doesn't change.

That's a simplified model of a pendulum and isn't completely accurate, but even if your pendulum has a 30° swing its true period is only 1.7% off of the approximation.

And pendulum clocks don't just let the pendulum lose energy to friction until they swing down and stop. Take a look at this deadbeat escapement: https://en.wikipedia.org/wiki/Anchor_escapement#/media/File:... (one of several pendulum mechanisms)

There are three main actions going on here. 1) A weight is hung so that its downward force is trying to drive the escape wheel's rotation. 2) The side face of the anchor (swinging part w/ pendulum attached) moves in front of the escape wheel tooth and stops it. This locks the motion of the clock mechanism to one tooth per swing (and is the reason the weight doesn't just drop immediately). 3) As the anchor swings off the dead face, the tooth applies a slight push to the sloped impulse face at the end of the anchor. That repeated nudge transfers potential energy from the weight to the pendulum swing, and keeps its swing distance consistent against friction losses.

Mechanical clocks are actually pretty clever.

See my response to grahamburger. Friction does not only cause decay of the amplitude, it also changes the frequency.

edit: But you are right, the mechanical clocks are still pretty amazing and quite precise given the limitations of the technology.

>Interestingly, when the clocks are synchronized, the common oscillation frequency decreases, i.e. the clocks become slow and inaccurate.

From the abstract of the referenced paper. Apparently the effort required to keep the clocks synchronized slows them both down, and they collectively keep worse time.

Relevant video: https://www.youtube.com/watch?v=5v5eBf2KwF8

More than relevant, it's a fantastic video of 32 out-of-phase metronomes sitting on a shared surface "magically" coming into (seemingly) perfect sync over several minutes. Thanks!

I have observed crystals and oscillation circuits syncing up on PC boards because of tiny noise on the power supply. This is a direct analogy of the Huygens observation.

Were those crystals and oscillations circuits independently driven by the power supply, or were they mutually connected?

The only thing connected was the power line. I have heard of oscillation circuits with no common power syncing up because of RF from coils.

Such effects have been pretty thoroughly studied in the quantum mechanics of Bosons. Bosons are particles or quasi-particles that follow Bose-Einstein statistics, including photons and phonons, i.e. quantised electromagnetic and acoustic vibrations, respectively. This phenomenon of pendulum synchronization on a shared acoustic surface is not completely unlike that of photon synchronization in a laser cavity.

Of course, the clocks need to have compatible internal time constants (pendulum length) for this to work.

How close do the natural frequencies need for this to happen? There must be some relation between how tightly coupled they are and how close their frequencies must be. Is it a sharp cut-off? What happens near the breaking point?

Easier to explore in electronic systems than kinetic ones, as we did in a lab in college. You get some fun phenomena, with chaos and fractals arising: https://en.wikipedia.org/wiki/Arnold_tongue

Good points. This would certainly be interesting to figure out.

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