I have been trying to come to grips with the principle underlying the Resonance. This topic has been discussed before

ahci.watchprosite.com

but I am not sure there is a conclusion yet. The following is what I have collected from the literature for your comments.

I think that calling the watch „Resonance“ is strictly speaking probably a bit of a misnomer. Resonance usually means that a system is made to oscillate through small external periodic driving forces that correspond to its natural “resonant” frequencies, produce large amplitude oscillations. Examples are soldiers marching over a bridge or a singer shattering a glass; in each example the driving events are small compared to the large oscillations that they induce.  I don’t think that this is likely to happen in the Resonance; if we would disconnect one of the balance wheels from the going train, I doubt that there would be enough energy transmitted from the other balance wheel to make it move.

Rather, the Resonance is an example of coupled oscillators. Each of the two halves of the movement drives a balance wheel that is carefully regulated to oscillate at a frequency that is very closely matched to that of the other balance wheel. In this situation, even minute amounts of energy transmitted between the two oscillators can move them into synchronization.

This was first noticed by none other than the inventor of the pendulum clock and the balance spring himself, Christiaan Huygens. In 1665, he was sick in bed, when he observed two large pendulum clocks designed to be used at sea that were close to one another. These were large clocks, each in a four-foot long case with a weight of approximately 100 pounds at the bottom of the case (to keep the clock standing upright aboard a ship). Importantly, they were regulated to beat as nearly at the same frequency as possible at the time. Huygens now observed that the pendulum clocks swung in exactly the same frequency and in anti-phase (180 degrees). When he disturbed one pendulum, the antiphase state was restored within a half-hour (about 1800 beats) and remained indefinitely. At first Huygens thought that air flow between the two clocks caused this phenomenon; but he showed that this could not be right by blocking air flow by a piece of paper between the clocks. He conducted a careful series of experiments that convinced him that the true reason were minute vibratons transmitted through the wooden beam on which both clocks were mounted. He was excited about the potential of this finding for timekeeping at sea (to solve the longitude problem). As Journe also writes in the catalogue, having two oscillators in anti-phase movement has timekeeping advantages since many movements will tend to slow down one balance and speed up the other and these will tend to cancel out if resonance is not broken. So Huygens wrote a letter to the then newly-founded Royal Society with the delightful (IMO) title

“Of an odd kind of sympathy” .

So maybe we could call the watch the Sympathique which would be a very fine name I think.

Unlike Huygens, the Royal Society took a very dim view of his finding:

“Occasion was taken here by some of the members to doubt the exactness of the motion of these watches at sea, since so slight and almost insensible motion was able to cause an alteration in their going”.

So how does this work? Bennett et al., in a paper (Proc. R. Soc. Lond. A 2002 458, 563-579) from which I have quoted the above, reconstructed Huygen’s experiment and showed that it were indeed the mechanical movements of the beam that caused the synchronisation. This paper is available online under 

rspa.royalsocietypublishing.org .

Interestingly, these authors found that antiphase synchronisation only occurred when the pendulum is very light compared to the case; in that sense it was fortuitous that the cases were made so heavy for the clocks Huygens studied. If the relative weight of the pendulum were increased a phenomenon occurred in which one clock stopped beating altogether: “beating death”.

The reason the clocks move into antiphase, according to Bennett et al., is friction. If the pendulums are moving in-phase, they move the beam together, which causes some friction that dampens the movement. Conversely, if the pendulums move in opposite directions, their forces on the beam cancel each other out, and no dampening occurs. So over time, although the movement of the beam is tiny, anti-phase motion wins out over in-phase.

There are some cool youtube videos showing that the same mechanism can be used to synchronize several metronomes simply by putting them on a movable “base” plate.

www.youtube.com

Note that if there are more than two metronomes, both in-phase and anti-phase patterns are possible.

Does this apply to the Resonance? I would think the answer is probably yes. Using slow-motion video (although of low quality at 250 pics per seconds, posted below) the two balances are indeed moving in synchrony and in anti-phase (BTW I think the reason the hands on the left dial are not turning backwards is that the escape wheels are not mirror images of each other, but are teethed the same direction on the left and right). Although instead of pendulums here we have balance wheels mounted perpendicular to the base plate they transmit force to the pinion on which they are mounted. It is probably safe to assume that the balances in the Resonance are similarly “light” compared to the base plate as Huygens pendulums are compared to the clock case, although I have no numbers on this. Alternatively one could think about the air flow again since the wheels are so close to each other. One would have to repeat Huygens experiments and put a thin sheet of paper between then but I am not going to remove the back of my watch to try that!

I think that having a watch based on coupled oscillators is extraordinarily satisfying since the same principle underlies complex behaviour in physical systems such as lasers and superconductors, but also the beating of the heart and even the function of the human brain and hence, mind on some level. To have this instantiated in a mechanical device on the wrist is genius. By the same token, I am highly motivated to try and really understand what is happening. So I would greatly appreciate comments by Purists-in-the-know about the account above to figure out what I got wrong or correct. Thanks!

Andreas