Fig 7-8

During the first half of the nineteenth century, an illustrated nautical book appeared in France containing advise to mariners on how to deal with a host of dangerous situations encountered at sea. Some involved coping with adverse weather conditions and natural hazards, whilst others dealt with close encounters with other vessels. The Dutch physicist Sipko Boersma noticed that this handbook contained a peculiar warning to sailors of something that is reminiscent of the Casmir effect en.wikipedia.org/wiki/Casimir_effect that we have just described.

Sailors are warned that when there is no wind and a strong swell building, then two large sailing ships will start to roll. If they come close together and lie parallel to one another then they are at risk. An attractive force will draw the two ships together and there will be a disaster if their riggings collide and become entangled. The sailors are advised to put a small boat in the water and two one of the ships out of the range of the attractive influence of the other. This sounds like a strange warning. Is there any truth to it? Remarkably, it turns out that there is. The attractive force between the ships arises in an analogous way to the force of attraction between the Casimir plates although there is no quantum physics or zero point fluctuations of the vacuum involved – ships are too large for those effects to be big enough to worry about. Instead the waves of zero point energy, the ships feel the pressure of the water waves.

The analogy is quite clear. Although we were dealing with radiation pressure between Casimir’s plates, the same ideas apply to other waves as well, including water waves. In Figure 7.8, we see the situation of two ships, oscillating from side to side in the swell. The rolling ship absorbs energy from the waves and then re-emits this by creating a train of outgoing water waves. If the principal wavelength of these waves is much bigger than the distance between the two ships then they will rock together in time like a pair of copy-cat dancers. However, the waves that they radiate towards each other will be exactly out of phase. The peaks of one ship’s waves will coincide with the troughs of the other ship’s waves. The net result is that they will cancel each other out. As a result, there is virtually no radiated water-wave energy in between the two ships, and the pushing together of the ships, caused by the outgoing waves from the other sides of the ships, is not balanced. Thus, rolling ships will approach one another, just like atoms in a sea of vacuum fluctuations.

The calculations show that two 700-ton clipper ships should attract one another with a force equal to the weight of a 2000-kilogram mass. This is a reasonable answer. It is a force that a large boat of rowers could overcome by concerted effort. If the force were ten times bigger then all such efforts would be hopeless, whereas if it were ten times smaller the attraction would be negligible and no action would be needed to avert a collision. Boersma also discovered that the attractive force between the boats is proportional to the square of the maximum angle that they swing back and forth in the swell. In breezy conditions these oscillations will die out fairly quickly as the sails take up their energy. Thus we see the reason for the warning about the naufragous effect of coming too close to another ship is fairly calm conditions. ~ Pages 211-213