**The Length of A Position Vector**

In special relativity the location of a particle in 4-dimensional spacetime is given by its world line

where is the position in 3-dimensional space of the particle, is the velocity in 3-dimensional space and is the speed of light.

The "length" of the vector is a Lorentz scalar and is given by

where is c times the proper time as measured by a clock in the rest frame of the particle and the metric is given by

- .

This is a time-like metric. Often the Minkowski metric is used in which the signs of the ones are reversed.

- .

This is a space-like metric. In the Minkowski metric the space-like interval is defined as

- .

We use the Minkowski metric in the rest of this article.

Read more about this topic: Lorentz Scalar, Simple Scalars in Special Relativity

### Famous quotes containing the words length and/or position:

“Whoever aims publicly at great things and at *length* perceives secretly that he is too weak to achieve them, has usually also insufficient strength to renounce his aims publicly, and then inevitably becomes a hypocrite.”

—Friedrich Nietzsche (1844–1900)

“When asked whether or not we are Marxists, our *position* is the same as that of a physicist or a biologist who is asked if he is a “Newtonian” or if he is a “Pasteurian.””

—Ernesto “Che” Guevara (1928–67)