The deep calls of massive whales can be heard across vast ocean distances, yet when John Spiesberger of the University of Pennsylvania attempted to measure the speed of fin whale sound waves, the results puzzled him. He eventually discovered that two waves were combining to distort the signal’s apparent speed—an effect best known from Albert Einstein’s special theory of relativity. The study’s findings have been published in the journal Physical Review E.
Knowing the speed at which the whale’s call travels allows us to pinpoint the source’s location, which is useful for biological research. (Whales, it seems, have their own reasons for wanting to know the whereabouts of others of their kind.) However, Spiesberger’s program for estimating speed based on data from multiple recording devices yielded seemingly nonsensical results.
“The first time, we got a value of around 1,000 meters per second,” Spiesberger said. The standard figure cited for seawater is 1,500 meters per second. “Then, later on, I got values that sometimes reached 3,000 meters per second. I immediately thought there was a bug in my program.”
Spiesberger eventually realized the discrepancies arose because some sound waves traveled directly to the receivers, while others reflected off the ocean surface, thereby traveling a longer path. This phenomenon is nothing new; we are all familiar with how an echo can reach us after a delay.
However, the phenomenon discovered by Spiesberger and his co-author, Eugene Terray of the Woods Hole Oceanographic Institution in Massachusetts, stemmed from the way these signals combined to create “temporal interference.” Older readers are familiar with the consequences of this phenomenon from the way radios or televisions can lose their signal when radio waves arriving via different paths interfere with one another. Younger readers might want to ask their parents about it.
A curious feature of temporal interference is that the energy peak can occur earlier than one would expect from either signal individually. “This effect sounds like a violation of the laws of physics,” said Spiesberger. “But it isn’t.”
The connection to Einstein lies in the fact that special relativity is often described as stating that nothing can travel faster than the speed of light in a vacuum. Physicists are always up for a challenge and immediately look for exceptions. Aside from the possible existence of tachyons—particles that always travel faster than light—special relativity does not rule out the possibility that electromagnetic waves could combine in such a way that the signal peak propagates faster than the speed of light. This happens even though the photons themselves continue to travel at the speed of light.
Crucially, however, this peak carries no information. If it did, it would be possible to send information into the past. “You can’t use this trick to send a message to your past self telling you to place bets on the stock market,” said Spiesberger. “Causality is not violated.”
The idea of an energy peak moving faster than the wave carrying it might seem absurd, but one can imagine a similar scenario involving an ocean wave striking a wall at an angle. The crest would hit one end of the wall first and then travel along it as more and more of the incoming wave collided with the wall. Depending on the angle between them, the point where a wave crest meets a wall can move faster than the wave itself. Let us revisit the thought experiment, replacing the ocean wave with a beam of light: the point of illumination can travel along the wall faster than the speed of light without carrying any information that would contradict Einstein’s theories.
However, while some physics instructors enjoy mentioning this possibility to challenge their students, it arises only under very limited conditions rarely found in nature. At least, this holds true for light waves; it appears that whales have been creating temporal interference in sound waves for millions of years.
Moreover, although the basic concept has been known for a century, many aspects of the effect’s mechanism remain unexplored. Last year, Spiesberger and other authors published a paper on how related effects can slow the speed of sound, utilizing what they term the “three-dimensional effective speed” of the peak energy packet. Now, Spiesberger and Terrey have presented a more rigorous mathematical description of the physics behind how temporal interference can generate apparent supersonic and superluminal energy motion.
Although Spiesberger is convinced that temporal interference is the reason his whale calls travel at varying speeds, he still considers it necessary to demonstrate this to experts.
First, he plans to reflect sound waves off a solid floor and combine them with those traveling directly to the receiver, hoping to obtain inverted models of what whales do. Then, he wants to do the same thing thousands of times faster using lasers.
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