Preamble: Jet-lag, is a physiological condition associated with the disruption of a body's circadian rhythm found to occur after long-distance trans-meridian (east–west or west–east) travel on high-speed aircraft. Jet-lag is believed to result from the disruption in a traveler's normal cycle of eating, sleeping, and exposure to light. However, the recent discovery of the CLOCK gene points to a cause that operates - at least partially - at the cellular level. Looking for a more fundamental cause, an analogy may be found with the phase shifts in the oscillation and rotation period of coupled oscillators when they are subjected to changes in acceleration. In Topic VI: Molecular Precession, Gravitation, and Circadian Rhythms, it was shown how the precession rate of spinning elements depends on the gravitational environment in which those molecules reside.

Hypothesis: When a body travels on a jet plane, it becomes subjected to non-trivial changes in both gravitational and centrifugal acceleration that has a trans-meridian (east–west) dependence. For a typical flight aboard a commercial airplane, it is shown that the acceleration for a westbound traveller is a(t)=0.9962 a(0), and for an eastbound traveller a(t)=0.9954 a(0). A change in acceleration, relative to a(0), the acceleration their body had adjusted to before departure, is know to alter the precession rate of spinning molecules. Conjecture is presented below that links the cause of jet-lag to the cumulative phase shift produced when the precession rate of cell molecules is subjected to the sustained artificial acceleration typically endure on trans-meridian flights.

Background. Jet-lag is a chronobiological problem similar to problems found in shift work and the circadian rhythm sleep disorder. Jet-lag, medically referred to as either desynchronosis or circadian dysrhythmia, is considered to be a condition within a larger family of more serious conditions associated with disruptions in biological rhythm such as obesity, diabetes, cardio-metabolic syndrome, and hypertension. The focus of this conjecture will be limited to problems associated with jet travel.

All plants, insects and animals possess a circadian rhythm that corresponds in period with the 24-hr rotational period of the earth. Experiments with mammals indicate that this internal circadian rhythm is substantially controlled by the suprachiasmatic nucleus (SCN) that resides in the hypothalamus.*. The means and method by which the SCN maintains body rhythm was initially believed to be linked to the body's exposure to daylight and darkness. However, with the discovery of a gene called CLOCK and related genes such as Per {1,2,3} and Cry {1,2}, it was demonstrated how the circadian rhythm is expressed at the cellular level. The SCN is now believed to be the master regulator of a more complex system that is ultimately driven by contributions from each cell.*[article citations needed].

Conjectural Summary
The conjecture outlined here is that jet-lag is caused by exposure to small but sustained artificial acceleration imposed on a traveller by their rapid trans-meridian displacement. The 'artificial' (or 'changed') character of the acceleration is defined relative to the acceleration environment that associated with the point of departure which the traveller's body has previously adapted to. The change in acceleration is both gravitational and centrifugal in nature, and they act to alter the oscillation and/or precession period of molecules in the cell. The degree to which the oscillation/precession phase is shifted during the flight defines the severity of the effects associated with jet-lag.

The combined change in the centrifugal and gravitational acceleration of a traveller aboard an airplane cruising at an altitude h and speed v(e), relative to the normal values they have adapted to when standing on the earth, {g, h=0 and v(e)=v(0)}, may be approximated by:

In the above equation: G, is the gravitational constant; M is the mass of the earth; r(0)=radius of the earth at equator; and v(e) is the eastbound velocity.

(Note that the above equation has been simplified to reflect the change only for a body travelling parallel to the equator; it does not reflect the natural change in centrifugal acceleration of a body at different latitudes - or, more generally, changes that reflect specific paths between latitudes. Also truncated from this equation are variables that define the contributions from the sun and the moon; these bodies produce an acceleration of relative magnitude <0.0005 g with day/night and monthly variation - their contributions will be added in later.)

Of course, the magnitude of change is a function of the specific altitude, speed and path of the airplane; more properly, we should integrate the change over the full path from takeoff to landing. However, for long flights - such as we might endure when travelling from, say, California to Great Britain, we can compute the expected change experienced during the majority of the flight path - a time when a typical commercial airline is cruising at a constant speed of ~ 250mps and an altitude of ~ 12,000 m. During these periods, the weight of a travelling body W* relative to the weight of the body at rest on the surface of the earth W(0) is different for a westbound traveller than it is for an eastbound traveller because the westbound traveller is travelling in a direction opposite to the earth's rotation while the eastbound traveller is moving with the earth's rotation. The respective weights of the westbound and eastbound traveller are shown below - every molecule, every protein, every organelle in the cell are subjected to these inertial changes when flying. (The calculation of these values is provided further below).

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The energy exchanged between coupled systems is substantially dependent on their inertial properties. When the inertial properties change, so too does the rate at which energy can be shuffled back and forth between systems - these changes have to be managed by the cell if it is to maintain its normal rhythms. When our biological rhythms are regular, the anticipated energy needed by the cell to perform activities can be planned for, with small differences borrowed locally from [the ADP/ATP banking system]. But, subject our body to a sustained period of artificial acceleration - such as occurs when we travel aboard an airplane - and the shuffling of energy is thrown off rhythm. Our circadian rhythm becomes phase shifted, and our system becomes jet-lagged.

The diagram below illustrates the centrifugal acceleration, a(t), experienced by a traveller flying above the equator west to east at a speed v(e) and altitude h, relative to the acceleration, a(0), of a person at rest on the surface of the earth.

Each activity we subject our bodies to during the day produces an acceleration that shuffles small amounts of energy between all systems that are coupled to each other. These are small pools of angular momentum called atoms coupled to other small pools of angular momentum that react to even smaller pools of rotational activity called photons. On an average day, the cumulative energy change is…well, average. And – therefore - predictable. The anticipated energy we will need to perform future activities can be planned for by our biological rhythms, with small differences borrowed locally. But, subject our body to a sustained period of artificial acceleration - such as occurs when we travel aboard an airplane - and the shuffling of energy is thrown off rhythm. Our circadian rhythm becomes phase shifted. Our system becomes jet-lagged.

[this follow up on this topic will be posted in early 2018]

[The diagrams below were used in Topic VI: Molecular Precession, Gravitation, and Circadian Rhythms it was shown how the precession rate of spinning elements depends on the gravitational environment in which those molecules reside.]

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