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Day is usually defined as the period when sunlight reaches the ground in the absence of local obstacles.
On the day of the equinox, the center of the Sun spends a roughly equal amount of time above and below the horizon at every location on the Earth, so night and day are about the same length.
In reality, the day is longer than the night at an equinox.
There are two reasons for this:
First, from the Earth, the Sun appears as a disc rather than a point of light, so when the centre of the Sun is below the horizon, its upper edge is visible.
Sunrise, which begins daytime, occurs when the top of the Sun's disk rises above the eastern horizon.
At that instant, the disk's centre is still below the horizon.
Second, Earth's atmosphere refracts sunlight.
As a result, an observer sees daylight before the top of the Sun's disk rises above the horizon.
Even when the upper limb of the Sun is 0.4 degrees below the horizon, its rays curve over the horizon to the ground.
In sunrise/sunset tables, the assumed semidiameter (apparent radius) of the Sun is 16 minutes of arc and the atmospheric refraction is assumed to be 34 minutes of arc.
Their combination means that when the upper limb of the Sun is on the visible horizon, its centre is 50 minutes of arc below the geometric horizon, which is the intersection with the celestial sphere of a horizontal plane through the eye of the observer.
These effects make the day about 14 minutes longer than the night at the equator and longer still towards the poles.
The real equality of day and night only happens in places far enough from the equator to have a seasonal difference in day length of at least 7 minutes, actually occurring a few days towards the winter side of each equinox.
The times of sunset and sunrise vary with the observer's location (longitude and latitude), so the dates when day and night are equal also depend upon the observer's location.
At the equinoxes, the rate of change for the length of daylight and night-time is the greatest.
At the poles, the equinox marks the transition from 24 hours of nighttime to 24 hours of daylight (or vice versa).
========,3,Geocentric view of the astronomical seasons.
In the half-year centered on the June solstice, the Sun rises north of east and sets north of west, which means longer days with shorter nights for the northern hemisphere and shorter days with longer nights for the southern hemisphere.
In the half-year centered on the December solstice, the Sun rises south of east and sets south of west and the durations of day and night are reversed.
Also on the day of an equinox, the Sun rises everywhere on Earth (except at the poles) at about 06:00 and sets at about 18:00 (local solar time).
These times are not exact for several reasons:
***LIST***.
========,4,Day arcs of the Sun.
Some of the statements above can be made clearer by picturing the day arc (i.e., the path along which the Sun appears to move across the sky).
The pictures show this for every hour on equinox day.
In addition, some 'ghost' suns are also indicated below the horizon, up to 18° below it; the Sun in such areas still causes twilight.
The depictions presented below can be used for both the northern and the southern hemispheres.
The observer is understood to be sitting near the tree on the island depicted in the middle of the ocean; the green arrows give cardinal directions.
***LIST***.
The following special cases are depicted:
========,3,Celestial coordinate systems.
The vernal equinox occurs in March, about when the Sun crosses the celestial equator south to north.
The term "vernal point" is used for the time of this occurrence and for the direction in space where the Sun is seen at that time, which is the origin of some celestial coordinate systems:
***LIST***.
Strictly speaking, at the equinox the Sun's ecliptic longitude is zero.
Its latitude will not be exactly zero since the Earth is not exactly in the plane of the ecliptic.
Its declination will not be exactly zero either.
(The ecliptic is defined by the center of mass of the Earth and Moon combined).
The modern definition of equinox is the instants when the Sun's apparent geocentric longitude is 0° (northward equinox) or 180° (southward equinox).
See the adjacent diagram.
Because of the precession of the Earth's axis, the position of the vernal point on the celestial sphere changes over time, and the equatorial and the ecliptic coordinate systems change accordingly.
Thus when specifying celestial coordinates for an object, one has to specify at what time the vernal point and the celestial equator are taken.
That reference time is called the equinox of date.
The autumnal equinox is at ecliptic longitude 180° and at right ascension 12h.
The upper culmination of the vernal point is considered the start of the sidereal day for the observer.
The hour angle of the vernal point is, by definition, the observer's sidereal time.
Using the current official IAU constellation boundaries – and taking into account the variable precession speed and the rotation of the celestial equator – the equinoxes shift through the constellations as follows (expressed in astronomical year numbering in which the year 0 = 1 BC, −1 = 2 BC, etc.
***LIST***.
========,3,Cultural aspects.
The equinoxes are sometimes regarded as the start of spring and autumn.
A number of traditional (harvest) festivals are celebrated on the date of the equinoxes.
========,2,Equinoxes on other planets.
Equinox is a phenomenon that can occur on any planet with a significant tilt to its rotational axis.
Most dramatic of these is Saturn, where the equinox places its ring system edge-on facing the Sun.
As a result, they are visible only as a thin line when seen from Earth.
When seen from above – a view seen by humans during an equinox for the first time from the "Cassini" space probe in 2009 – they receive very little sunshine, indeed more planetshine than light from the Sun.
This lack of sunshine occurs once every 14.7 years on average.
It can last a few weeks before and after the exact equinox.
The most recent exact equinox for Saturn was on 11 August 2009.
Its next equinox will take place on 6 May 2025.
One effect of equinoctial periods is the temporary disruption of communications satellites.
For all geostationary satellites, there are a few days around the equinox when the sun goes directly behind the satellite relative to Earth (i.e.
within the beam-width of the ground-station antenna) for a short period each day.
The Sun's immense power and broad radiation spectrum overload the Earth station's reception circuits with noise and, depending on antenna size and other factors, temporarily disrupt or degrade the circuit.
The duration of those effects varies but can range from a few minutes to an hour.
(For a given frequency band, a larger antenna has a narrower beam-width and hence experiences shorter duration "Sun outage" windows.)
========,1,preface.
Eugene Paul "E. P." Wigner (; November 17, 1902 – January 1, 1995), was a Hungarian-American theoretical physicist, engineer and mathematician.
He received half of the Nobel Prize in Physics in 1963 "for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles".
A graduate of the Technical University of Berlin, Wigner worked as an assistant to Karl Weissenberg and Richard Becker at the Kaiser Wilhelm Institute in Berlin, and David Hilbert at the University of Göttingen.
Wigner and Hermann Weyl were responsible for introducing group theory into physics, particularly the theory of symmetry in physics.
Along the way he performed ground-breaking work in pure mathematics, in which he authored a number of mathematical theorems.
In particular, Wigner's theorem is a cornerstone in the mathematical formulation of quantum mechanics.
He is also known for his research into the structure of the atomic nucleus.
In 1930, Princeton University recruited Wigner, along with John von Neumann, and he moved to the United States.
Wigner participated in a meeting with Leo Szilard and Albert Einstein that resulted in the Einstein-Szilard letter, which prompted President Franklin D. Roosevelt to initiate the Manhattan Project to develop atomic bombs.
Wigner was afraid that the German nuclear weapon project would develop an atomic bomb first.
During the Manhattan Project, he led a team whose task was to design nuclear reactors to convert uranium into weapons grade plutonium.
At the time, reactors existed only on paper, and no reactor had yet gone critical.
Wigner was disappointed that DuPont was given responsibility for the detailed design of the reactors, not just their construction.
He became Director of Research and Development at the Clinton Laboratory (now the Oak Ridge National Laboratory) in early 1946, but became frustrated with bureaucratic interference by the Atomic Energy Commission, and returned to Princeton.
In the postwar period he served on a number of government bodies, including the National Bureau of Standards from 1947 to 1951, the mathematics panel of the National Research Council from 1951 to 1954, the physics panel of the National Science Foundation, and the influential General Advisory Committee of the Atomic Energy Commission from 1952 to 1957 and again from 1959 to 1964.
In later life, he became more philosophical, and published "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", his best-known work outside of technical mathematics and physics.
========,2,Early life.
Wigner Jenő Pál was born in Budapest, Austria-Hungary on November 17, 1902, to middle class Jewish parents, Elisabeth (Einhorn) and Anthony Wigner, a leather tanner.
He had an older sister, Bertha, known as Biri, and a younger sister Margit, known as Manci, who later married British theoretical physicist Paul Dirac.
He was home schooled by a professional teacher until the age of 9, when he started school at the third grade.
During this period, Wigner developed an interest in mathematical problems.
At the age of 11, Wigner contracted what his doctors believed to be tuberculosis.
His parents sent him to live for six weeks in a sanatorium in the Austrian mountains, before the doctors concluded that the diagnosis was mistaken.
Wigner's family was Jewish, but not religiously observant, and his Bar Mitzvah was a secular one.
From 1915 through 1919, he studied at the secondary grammar school called Fasori Evangélikus Gimnázium, the school his father had attended.
Religious education was compulsory, and he attended classes in Judaism taught by a rabbi.
A fellow student was János von Neumann, who was a year behind Wigner.
They both benefited from the instruction of the noted mathematics teacher László Rátz.
In 1919, to escape the Béla Kun communist regime, the Wigner family briefly fled to Austria, returning to Hungary after Kun's downfall.
Partly as a reaction to the prominence of Jews in the Kun regime, the family converted to Lutheranism.
Wigner explained later in his life that his family decision to convert to Lutheranism "was not at heart a religious decision but an anti-communist one".
On religious views, Wigner was an atheist.