Information about Simultaneously

Simultaneity is the property of two events happening at the same time in at least one reference frame.

The noun Simult means a supernatural coincidence, two or more divinely inspired events that occur at or near the same period of time that are related to each other in both noticeable and unnoticeable characteristics [Latin simul, at the same time; see sem-1 in Indo-European Roots + English -taneous(as in instantaneous)].

• In criminal law, for a criminal violation to be established, it must be shown that there was simultaneity of actus reus and mens rea.
• In mathematics, a system of equations or a set of simultaneous equations share variables; a solution is a set of variable values for which all these equations are satisfied together.
• In music, see: simultaneity (music).
• In modern physics two events may be simultaneous with respect to a time event as follows:

A central event (0,0) is used to anchor a spacetime plane {(x, t) in RxR} = ST where x measures distance in units of 30 centimeters and t measures time in nanoseconds. Space events satisfy |x| > |t| and the time events satisfy |x| < |t|.

Now a space event e is simultaneous with the origin (0,0), with respect to a time event z, if e and z are hyperbolic-orthogonal points in ST.

Two events g and h in ST are simultaneous with respect to z if their difference g - h in ST is hyperbolic-orthogonal to z.

• In marketing, simultaneity is one of the characteristics of a service which differentiates it from a product. It refers to the idea that the production and consumption of a service occur simultaneously, making it impossible to produce and store a service prior to consumption.
• Important ideas and inventions are often created 'simultaneously' by independent, contemporary individuals when 'the time is ripe'. (Note: a coincidence does not prove a relationship.) This phenomenon is referred to by the saying 'Great minds think alike' — though it is not limited to great minds. In modern times it has led to many patent squabbles and 'who was first' controversies. Some examples:
• The theory of evolution was developed independently by Charles Darwin and Alfred Wallace
• Calculus arose in different forms in the work of Newton and Leibniz
• Hyperbolic geometry, developed by János Bolyai and Nikolai Lobachevsky
• Early work on radio transmission by Hertz, Marconi and Tesla.

See also

• equation
• relativity
• relativity of simultaneity
• synchronization

Notes and references

• Peter Galison. Einstein's Clocks, Poincaré's Maps. New York, W. W. Norton, 2003. ISBN 0-393-02001-0. Excellent insights into the climate that surrounded Einstein at the time that he created special relativity.