A coordinate singularity occurs when an apparent
singularity or discontinuity occurs in one coordinate frame that can be removed by choosing a different frame.
An example is the apparent (longitudinal) singularity at the 90 degree latitude in spherical coordinates. An object moving due north (for example, along the line
0 degrees longitude) on the surface of a sphere will suddenly experience an instantaneous change in longitude at the pole (i.e., jumping from longitude 0 to longitude 180 degrees). In fact, longitude is not uniquely defined at the poles. This discontinuity, however, is only apparent; it is an artifact of the coordinate system chosen, which is singular at the poles. A different coordinate system would eliminate the apparent discontinuity, e.g. by replacing the latitude/longitude representation with an
-vector representation.
Stephen Hawking aptly summed this up, when once asking the question, "What lies north of the North Pole?".
What is Cosmology?
wiseGEEK.com. Accessed 15 Feb 2013. In a related discussion, he mentions this again
; accessed 15 Feb 2013.
See also
*Chronometric singularity
A chronometric singularity (also called a temporal or horological singularity) is a point at which time cannot be measured or described.
An example involves a time at a coordinate singularity, e.g.a geographical pole. Since time on Earth is meas ...
*Imaginary time
Imaginary time is a mathematical representation of time which appears in some approaches to special relativity and quantum mechanics. It finds uses in connecting quantum mechanics with statistical mechanics and in certain cosmological theories.
M ...
* Mathematical singularity
In mathematics, a singularity is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity.
For ex ...
* No-boundary proposal
References
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Mathematical analysis