4 Time: the new paradigm

Time: the new paradigm.  The measurement of time has undergone a fundamental and important shift in the last 100 years, largely due to Albert Einstein’s work. The chronometer, which needed to be wound every day with 7 turns of the key  indicated Greenwich Mean Solar time. As the name implies, Mean Solar time is an average of the irregular motion of the Sun. It is in fact calculated from sidereal time, which is time measured by the stars. The GPS ignores mean solar time and functions on sidereal time.  Astronomers scan the skies in sidereal time, not mean solar.

The gyrocompass depends on a gyroscope to indicate true north instead of magnetic north . True north is the star Polaris within about 1 degree of azimuth.  Magnetic north varies across the globe because the magnetic poles are in continual motion under the influence of sunspots and internal magnetic turbulence. A gyroscope consists basically of a spinning wheel. If it has sufficient mass and rotates with sufficient angular velocity it develops what is called inertia in space. If the rotor is supported in gimbals with freedom to move in all directions, the spin axis remains pointing towards any star at which it is aimed.  If pointed at a circumpolar star it will describe a circle in the sky, but of course the star is stationary in the inertial frame of reference and so is the free gyroscope. It is you that is moving in the opposite direction in spacetime, travelling around a small circle or almucantar. One apparent rotation of the free gyroscope represents one rotation of the Earth around the celestial pole. Gyroscopic inertia is what enables you to ride a bicycle without falling over, so long as you lean into the curve when rounding corners.

A free gyroscope is converted into a compass that points true north by counteracting its tendency to point at a particular star and redirecting it towards Polaris. Different brands of gyrocompass  employ different methods but a common strategy is to counteract unwanted precession with pots of mercury linked together in north-south pairs. As the spin axis precesses, weight is transferred between the mercury pots, restoring the spin axis to a north-south alignment. A ship’s motion across the more-or-less spherical surface of the sea also introduces unwanted precession and needs to be counteracted if the ship is to maintain a steady course on the golden spiral.  It is found that an applied torque with a period of 1 hour 24 minutes of solar time dampens the oscillation from this cause. This is called Schuler tuning after the engineer who discovered it. The period of 84.4 minutes is the period of a pendulum of length equal to the planet’s radius, which is the period of a satellite orbiting near sea level.

II n mid 19th century, French physicist Leon Foucault used a very large pendulum to counter the ancient belief that the stars revolve around Oceania.  Not only did the pendulum bob swing back and forth but the plane of its swing also rotated for no apparent reason. He experimented with gyroscopes and found similar properties supporting the idea that the world is rotating, not the stars. An intriguing discovery was that the period of rotation was not 24 hours per day except at N or S pole. It is a function of cosec of observer’s latitude; different in different latitudes.  At the equator it does not rotate at all and in latitude 45 degrees it rotates in nearly 34 hours. At Paris, where Foucault conducted his experiment in 1851, the pendulum rotates in 31 hours 48 minutes of mean solar time. In general, the number of sidereal hours in a day = 24 /sin observer’s latitude.   Only at the poles are there 24 sidereal hours in a day = 23h, 56m 04s of mean solar time. This fact was proved in the year 2000 by a university research team from Sonoma State University in the USA. They  set up a Foucault pendulum at the South Pole . Inside the Antarctic and Arctic circles there is one sidereal day in a tropical year so a mean solar day is 24/365 hours or nearly 3 minutes 57 seconds of sidereal time.

It is important to distinguish between sidereal time and mean solar time. Schuler tuning of a gyroscope compensates for the effect discovered by Foucault. It has to be adjusted as the ship changes latitude. You also need to adjust your personal clock with changes in latitude or longitude. The easy way to do it nowadays is with  GPS, which indicates spacetime automatically.

The gyroscope is also important in general physics because it demonstrates the inertial frame of reference, which is the only frame of reference in which Newton’s laws are valid. In fact, the free gyroscope contradicts Newton’s law that says a mass moves in the direction of an applied force. If a torque is applied to the axis of a spinning gyroscope the reaction is perpendicular to the applied force. This is precession, the same kind of force that affects Oceania, which is a rather large gyroscope. There is a time lag of 90 degrees or 6 hours between action and reaction. This point should be added to Newton’s first law. For every action there is a reaction 6 sidereal hours later in the perpendicular direction. The word ‘hour’ is open to interpretation. There are many different kinds of hour, not just the ratio of solar time to sidereal. Six hours is a right angle in any frame of reference, but the word ‘hour’ has different meanings depending on your point of view.  Doesn’t time fly when you’re having fun!

The phenomenon can be compared with the propagation of an electromagnetic field. Magnetism and electricity are intimately linked. Moving magnetic lines of force always give rise to electric lines of force, which are perpendicular to the plane of the magnetic lines of force. The combination of the two fields is called an electromagnetic radiation field and covers the range from ultraviolet, through the visible spectrum to infrared.

Because of gravitational interference by other planets, the direction of Oceania’s spin axis changes relative to the stars at a rate of about one degree every 72 years. The two points where the ecliptic and the equinoctial intersect are called the equinoxes, when day and night are of equal duration. The northern hemisphere spring equinox is by convention the reference point for measuring date and time. It is called the First point of Aries. Over 2000 years ago the northern hemisphere spring equinox coincided with the constellation Aries.It has now drifted into the constellation Pisces and is about to enter Aquarius, as we have been informed by the song This is the Dawning of the Age of Aquarius. There is nothing to see at the so-called first point of Aries.  We need to rename the northern hemisphere vernal equinox Aquarius, the southern vernal equinox Virgo, the Tropic of Cancer Taurus and Tropic of Capricorn Sagittarius. They are all past their use-by date.

A free gyroscope is a sidereal clock indicating local sidereal time in your location, where the length of a sidereal day depends on your latitude. It is  negative, or anti-clockwise, in the southern hemisphere.  It delivers a dynamic illustration of sidereal time and if pointed at an equatorial star like Mintaka in Orion it indicates World Sidereal time, WST. From that, all the rest can be calculated. Any observer equipped with a sextant can measure local Sidereal Time with no need for any kind of clock so long as an equatorial star like Mintaka is visible. A free gyroscope aimed at Mintaka measures World Sidereal Time for an observer in any latitude and every observer’s time scale is unique. The clock on your wall and the watch on your wrist do not measure any kind of time. Foucault demonstrated that and Einstein did the mathematics that introduced the word spacetime to the world.

Writing in Navigation News in December 1997, professor Wade Allison of Keeble College, Oxford said;

‘Why, even given an advanced knowledge of physics, is it so difficult to measure position and time? The brief answer is that many of the laws of physics conspire to give as little meaning as possible to the concepts of absolute position and absolute time. They make a virtue out of confounding the aspiring navigator!

Inertial navigation

Inertial navigation systems require three mutually perpendicular gyroscopes that detect acceleration in any direction, enabling the navigator or a feedback loop to apply corrections and stay on track, even underwater. Newton’s laws are valid only in the inertial frame of reference and there is a serious problem with the first law. There is no such thing as a ‘straight line’ on a sphere and what is a state of rest? Did Newton mean a loxodrome or a geodesic, or possibly an almucantar? A free gyroscope is ‘at rest’ relative to the stars when its rotor is spinning at high speed and its spin axis is pointing at a star revolving around the sky. When lying in bed asleep you are not ‘at rest’ but hurtling through space aboard a planet orbiting the Sun and spinning on its own axis. Far from being ‘at rest,’ why don’t we all get giddy? On the basis of this unanswered question, ancient astronomers like Claudius Ptolemy rejected the idea that Oceania is in motion. The world is obviously stationary and Sun, Moon and stars revolve around it. It’s a reasonable proposition until confronted with the evidence of a Foucault pendulum or free gyroscope. It was only thoroughly discredited in the year 2000 with the Foucault pendulum at the South Pole, which should be recognised as one of the great scientific experiments of all time. The claim that Sun, Moon and stars revolve around Oceania is unsustainable in the 21st century unless you are a fegger. There are still plenty of them around and more graduating from high school every year.