An unexpected link between whale song and Einstein’s theory of special relativity

John Spiesberger was developing a program intended to compute the speed of sound in his whale localisation equations. The program returned 1,000 metres per second, where sound travels at about 1,500 in sea water. Then, at other times, up to 3,000. “I immediately thought there was a bug in my program”, he recounts. After a few hours spent in his code, he understood that there was none.

Two paths for the same song

When a whale emits a sound, part of it reaches the hydrophone on the seabed directly. Another part travels up to the sea surface, is reflected there, and comes back down to the same hydrophone with a slight delay. The receiver therefore receives not one signal but two, offset in time.

The configuration is a classic one in underwater acoustics, where it is known as the Lloyd’s mirror effect. What John Spiesberger, visiting researcher in the department of earth and environmental science at the University of Pennsylvania, and Eugene Terray, of the Woods Hole Oceanographic Institution, found new in it is a consequence for the timing of the arrival, and not for the intensity of the signal alone.

Publication	Physical Review E, volume 114, article 025107, 18 August 2026
Authors	John L. Spiesberger (University of Pennsylvania) and Eugene Terray (Woods Hole)
Preprint	arXiv:2510.20060, posted on 22 October 2025
Nature of the work	Theory and numerical simulation, with no experiment at this stage
Condition for it to appear	Source and receiver close to one another, and at least one of the two less than c δt / 2 from the surface
Funding	Office of Naval Research, grant N00014-23-1-2336

Why the peak arrives early

Two offset signals that superpose do not simply make a stronger or a weaker signal. They make a signal of a different shape. Where the first rises while the second falls, the sum is attenuated; where they rise together, it is reinforced. The result is a burst of energy whose summit is no longer in the same place as the summit of either of the two components.

If one then measures a speed by dividing the distance travelled by the gap between the summit at emission and the summit at reception, one obtains a value that can exceed the speed of sound. It is this quantity, which the authors write c_3d and call the peak-to-peak speed, that reached 3,000 metres per second in Spiesberger’s calculations.

Nothing runs faster for all that. The summit of a shape is not an object that moves: it is a property of the shape, and the shape changes along the way. Physicists have known this kind of result for more than a century, but until now it appeared in dispersive media, where speed depends on frequency. Here, the medium disperses nothing. That is the new point of the work, and the title of the paper puts it forward.

The speed of information stays below the limit

The simulations give a speed of information lower than c. Establishing that a burst of energy has indeed arrived requires observing it long enough to tell it apart from noise, and that delay is enough to rule out any transport of information faster than the limit. “You cannot use this trick to get your past self to bet on the stock market”, Spiesberger sums up. “Causality is not reversed.”

One detail is worth drawing out, because it is more subtle than the formulation in circulation. The authors write that the speed of information arising from the two interfering paths can exceed the one the direct path alone would give. In other words, the echo gains time compared with a model that ignores it, while remaining below the absolute limit. That is not the same statement as “faster than light”, and it is the one that counts for an acoustician.

As for light, precisely: the extension to electromagnetic waves is presented as a conjecture, not as a result. The authors write that they assume the mechanism holds for those waves as well, and that, if it does, then they prove that the speed of information remains less than or equal to that of light in a vacuum. Coverage of this work has tended to erase that conditional.

A correction published the next day

The journal Physics, published by the American Physical Society, released its summary of the paper on 18 August 2026. It corrected it on the 19th, with this note: the original wording could be understood as describing a transport of energy faster than light, and it has been rewritten to refer to the apparent motion of the summit of a wave packet.

Twenty-four hours, on the website of the publisher of the journal carrying the paper, to reword one sentence. That says enough about the difficulty of the exercise, all the more so since the title of the original paper does speak of “supersonic and superluminal energy”. The vocabulary of physics designates precise quantities here, and it misleads as soon as it is taken out of its setting.

The hyperboloids no longer hold

Then comes the practical interest, and it is considerable for anyone who listens to cetaceans. The standard method of acoustic localisation rests on differences in arrival time between several receivers. Each pair of hydrophones defines a surface on which the source may lie, and the intersection of those surfaces gives the position. Our page on passive acoustic monitoring describes these arrays.

This construction assumes one thing: that the sound travelled at the same speed towards each receiver. Under that assumption, the surfaces are hyperboloids, and the geometry is simple. If the effective speed differs from one receiver to another, the hyperboloid is no longer the right surface, and the intersection falls in the wrong place. That is what interference with the surface echo produces, since it does not shift in the same way the signals received by hydrophones placed differently.

Spiesberger had described the general surface, valid when the speeds differ, in a 2004 paper: the isodiachron. Twenty-two years later, he identifies a physical mechanism that makes this generalisation necessary in a very ordinary case, that of an animal singing near the surface. The error made by sticking to hyperboloids amounts, according to the University of Pennsylvania press release, to hundreds of metres.

When the group velocity falls to zero

The 2026 result has a twin, posted two years earlier and signed by Spiesberger with six co-authors, entitled Slowing and stopping the speed of sound. The same interference mechanism produces the opposite effect there: the group velocity can fall by several orders of magnitude, and vanish when source and receiver draw closer together while both stay near the surface. It is the value of 1,000 metres per second that had first surprised Spiesberger, pushed to its extreme.

For this situation the authors propose an image that may be found bold: that of “three-dimensional acoustic black holes” at the receivers, by analogy with the event horizon where the speed of light vanishes. It is in this 2024 text, and not in the 2026 one, that the consequence for localisation is stated most clearly: group velocities that differ by orders of magnitude from one receiver to another invalidate the geometric interpretation by hyperboloids.

The experiment remains to be done

It has to be said plainly: at this stage there is neither a measurement at sea nor a laboratory experiment. There is a theory and its numerical implementation. The authors themselves conclude that their results should be readily accessible to experimental verification, which is one way of admitting that it has not taken place.

Spiesberger says he will begin with the simplest arrangement: microphones and a hard floor serving as the reflecting surface, an airborne replica of the underwater set-up. If the acoustic version behaves as expected, an optical version would follow, with a beam splitter sending one beam towards a reflector and the other straight to a detector. He adds that he does not know which of the two will be the easier to measure.

Consequences for passive listening to cetaceans

One thing is reassuring: the effect diminishes with distance, because the delay between the two paths becomes negligible beside the total travel time. A fin whale heard a hundred kilometres away on a single hydrophone, as our page on the detection range of cetacean sounds recalls, is not concerned.

The case at risk is the reverse, and it is precisely the one of greatest interest: an animal close to the receivers and close to the surface. That is the configuration of fine-scale monitoring, in coastal waters or on a tight array, when the aim is to know not that a whale is there, but exactly where it is. It is also the configuration of the work documenting reactions to noise, such as that on fin whales faced with seismic surveying, where a few hundred metres of difference change the reading of avoidance behaviour.

This result should therefore be read as a warning about method rather than as a revolution. Nothing requires revising what is known of cetacean acoustic emissions. A position computed from differences in arrival time for an animal at the surface, a short distance from an array, does on the other hand now deserve a caveat that no one had formulated until now.

One remark remains, and Spiesberger insists on it himself. “Most of us do not hear a whale song and think: there, that is special relativity in action.” The result was not sought. It came out of a debugging session, in a program written to find out where animals are.

Sources: J. L. Spiesberger and E. Terray, “Supersonic and superluminal energy and speed of information via temporal interference in a dispersionless environment”, Physical Review E 114, 025107, 18 August 2026 (preprint arXiv:2510.20060); J. L. Spiesberger et al., “Slowing and stopping the speed of sound”, arXiv:2409.13769, 2024; J. L. Spiesberger, “Geometry of locating sounds from differences in travel time: Isodiachrons”, Journal of the Acoustical Society of America 116, 3168-3177, 2004; Ryan Wilkinson, “Whale Calls Reveal an Unexpected Wave Effect”, Physics 19, s107, 18 August 2026, with its correction of 19 August 2026; University of Pennsylvania press release.