Animal navigation and biological rhythms: the inertial theory by Antonio B. Nafarrate

Abstract
The Coriolis acceleration (or force when acting on a mass) can be used to define an inertial bicoordinate map over the surface of the Earth. These coordinates closely correspond to geographic latitude and longitude measured in units of time; in addition the Coriolis force can generate a clock frequency or time base to “calibrate” the biological rhythms.  The elementary detectors are intramolecular rotors or oscillators acting as inertially controlled ion gates forming part of “tunnel” proteins bridging cellular bilayer membranes.  The precessional monitors of these rotors generate the frequencies that encode the space-time coordinates. From an evolutionary standpoint the simplest and earliest application of this inertial model is in a non-statolithic gravity sensing system (detection of the local vertical), followed by sensing of the Earth rotation (timing information) and evolving later into the fully developed bicoordinate navigation system necessary in any animal species capable of migrating or homing.

Introduction
In spite of the large existing body of knowledge and the large numbers of investigators working in the study of animal navigation or biological rhythms science still has no answers to the fundamental questions on these subjects. Several of the models proposed for animal navigation involve the use of a “clock”, suggesting an interaction between navigation and rhythms; in this model both problems are shown to be essentially connected through the same physical mechanism.

The idea that animals use inertial navigation is not new; among the earlier proponents are Darwin (1), Ising (2), Yeagley (3) and Barlow (4). This model in addition to the concepts used in these earlier models brings a whole new focus to the way that organisms make use of bio-inertial sensors to gain spatio-temporal information.

The inertial theory
An inertial device such as the Foucault pendulum has a particular period of rotation of its plane of oscillation for each latitude; at either pole this period is equal  to the duration of the true sidereal day (23h 56min 4.0996s) and it becomes  infinite at the equator with opposite sense of rotation in the North from the South hemisphere; from these is clear that at least in theory it is possible to measure latitude using a Foucault pendulum, a chronometer and some sort of simple binary rule or cue to decide among North or South hemisphere.

The inertial device that measures longitude does not exist. Because of the geometry problem only changes of longitude can be measured from an arbitrary meridian with the use of a spinning top, a chronometer and again a binary rule or simple cue to decide whether the longitudinal changes are in the East or the West direction. It works as follows: a spinning top anywhere on the Earth, except at either pole, even under ideal conditions will always have some precession because of the contradictory tendencies of falling “asleep”(alignment of the rotational axis with the vertical or local direction of gravity) and the conservation of angular momentum that demands that the axis of rotation should continue pointing to the same direction in space in spite of the rotation of the Earth; as a result a given spinning top will precess with a certain frequency related to the velocity of the motion of the top as it is carried by a rotating Earth (tangential velocity), if in addition the top is transported East or West with some other velocity the precessional frequency will be shifted by the mechanical analog of the well-known Doppler effect of acoustic and optics.

It was shown that a spinning stationary top precesses with a certain frequency because of the Earth rotation, if this frequency is copied by a non-inertial oscillator (neuronal chemical in an organism) the frequency of this oscillator can be used to monitor changes in the inertial oscillator indicating longitudinal displacements; furthermore the frequency in the stationary case identical for both types of oscillators is a suitable “time base” or clock reference frequency useful to time other events of biological interest associated with the Earth rotation. To keep track of the longitudinal displacements only is needed a simple integration of the frequency shifts and it will be shown below that this can be achieved in a surprisingly easy manner.

The comparison of frequencies is usually done by the ”beat” or interference methods ;if an inertial oscillator and a non-inertial one are tuned to the same frequency in the stationary condition and then they are displaced eastwards or westwards at a certain velocity the mechanical Doppler frequency shifts towards lower or higher frequencies respectively experienced by the inertial oscillator will have it beat with the neuronal or chemical non-inertial oscillator, the maxima and minima of amplitude of the beat frequency will happen at nearly equidistant points along any parallel of latitude independent of the velocity of the displacement, counting the beats is equivalent to counting units of distance if simple mathematical linearity is assumed. It is easy to see that this process of velocity integration reduces itself to something similar to counting steps.

Magnetism
After a long history of contradictory reports there is now solid evidence that magnetic fields similar in strength and even weaker than the geomagnetic fields interact with living organisms, the emerging picture is showing two different types of detection one polar and the other axial (5). The polar form can be traced to the chains of magnetite crystal domains (or similar magnetic compounds) described by Blakemore (6), the axial form does not have an accepted explanation at this time, but in the context of the inertial model supplies the strongest evidence of the existency of spinning tops as gravitational-inertial sensor that because of their actual nature (intramolecular rotors or oscillators) are perturbed by magnetic fields.

The following interpretation of the experimental results of Lindauer and Martin (7) with honey bees constitutes a dramatic illustration of the previous statement. Lindauer and Martin measured with incredible patience and accuracy several millions of bee dances and found that the bees were making an error or “missweisung” (actually the bees were never wrong, the error was in the human expectations of what the bees were supposed to do), the human model for the dances predicted the proper result when the beehive was magnetically shielded or the geomagnetic field was compensated by using Helmholtz coils.                                              It will be shown that in the combined influence of the gravitational and geomagnetic field the bees dance as if using an electrically charged spinning top to detect the direction of the vertical and for this reason the “pure” mechanical precession is perturbed by the magnetic Larmor precession. Lindauer and Martin´s summary of results indicate the following:

1-    The magnetic field does not introduce any error when the dance vector direction is along it. The inertial theory claims that this happens because the electromagnetic component of the top is “asleep” along the magnetic field and the Larmor precession is zero and the mechanical precession (gravitational-inertial) shows itself “pure” without error in a full agreement with human expectations (the Karl von Frisch model)

• The error is largest when the dance vector is perpendicular to the geomagnetic field.

Again the claim of the inertial theory is that the sum of two vectors (the mechanical angular velocities of precession) shows the largest misalignment with the direction of either component just about when the Wiltschko’s (8) model for the magnetic compass of European robins.

Experimental evidence
Over the years a wealth of information pointing to the inertial nature of the navigational system in animal has accumulated but the data that did not fit the “orthodox” school of thinking was easily swept under the rug, and this is in part the reason why Able (9) describes the study of this subject in chaos and turmoil, and indeed it is true because of the lack of comprehensive model to introduce order in a large and ever growing pile of data.

Besides the example already described of the axial form of magnetic detector, the strongest evidence for inertial navigation is the papers that show lunar influences in the orientation and timing of diurnal species (10-12). Within the framework of generally accepted physical science the Moon has only two types of influences over the Earth and its terrestrial inhabitants, one is the inertial-gravitational (mechanical forces; best example: the tides) and the other is electromagnetic, in turn the electromagnetic influence can be divided into optical (direct response to lunar light through the visual system; included here is most of the poetic-romantic influence) and electromagnetic (non-visual). While the electromagnetic lunar influences indeed exist and have been measured they are of an intensity and periodicity such that they add a very small modulation or contribution to solar influences of the same nature and for that reason it is unlikely that lunar rhythms in living organisms are driven or synchronized through electromagnetic cues, on the other hand the situation reverses for mechanical influences where the Moon dominates and the Sun is the lesser contributor. In summary when an organism shows lunar periodicities and visual cues can be ruled out, suspect mechanical effects, if a rhythm has solar frequency components check for electromagnetic effects.

An intriguing hint to the relation between gravity and timing comes from the chemical-hormonal fact that the hormone that mediates the gravitational response of plants, indole acetic acid and the hormone associated with circadian rhythmicity in the pineal gland of vertebrates, melatonin belong to the same chemical family of indoles with serotonin and tryptophan.

Conclusions
There is evidence that animal migration routes are genetically encoded, the just described method of inertial navigation that reduces latitude and longitude to time differences or steps counting lend itself for very simple encoding, the coordinates of a migration path are given by sets of three numbers (date, longitude and latitude) all in time units. Counting in some early cultures was made with the help of beads tied on stings, and today our civilization stores and manipulates information though stings of        data encoded in a variety of physical ways, hence it should not surprise anyone that genetic “stings” can be used as counters. When migrating species expand their range they add new path to their ancestral route as if adding or splicing a new section to their route specification gene.

One of the strongest and earliest opponents to the concept of inertial navigation is Matthews (13) others who follow mainly repeated Matthews’s mistake clearly seen in his book Bird Navigationwhen the Coriolis acceleration is discussed, Matthews’ asserts that the Coriolis acceleration can only provide one coordinate and not a bicoordinate grid necessary for complete map information; curiously enough this inertial model is very similar to Matthews “all solar model” and his concept of astronomical grids. Matthews’ solar model is a daylight version of celestial navigation and it has a profound connection with this form of inertial navigation though a path only recognized early this century by Einstein’s relativity; all the laws of physics have the same form when formulated with respect coordinate axis formed by the axis of telescopes pointing the stars or by the spinning axis of gyroscopes pointing to the same stars, and if this would have been known in the late 1800’s the Michelson and Morley experiment would then have been superfluous, because it would have been recognized that an optical (electromagnetic) experiment could not circumvent the limitations known from Newtonian mechanics that prevent  measuring absolute velocities.

It is to Matthews credit his belief in a simple navigational system and his clear statement that “time is longitude, longitude is time” (13), and this model adds that latitude is also time and both can be defined inertially.

This inertial form of navigation and timing makes use of very basic physical mechanisms available for living organisms at their most early evolutionary stages, and for this reason simple primitive species can amaze us with nearly incredible navigational performances.

Note: A more detailed expanded version of this paper with its additional impact in all areas of biology is under preparation; interested persons are encouraged to contact the author.

References

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13-  Matthews, G.V.T. Bird Navigation, 2^ndedn. Cambridge University Press, London ( 1968)