Log-log plot of γ (blue), v/c (cyan), and η (yellow) versus proper velocity w/c (i.e. momentum p/mc). Note that w/c is tracked by v/c at low speeds and by γ at high speeds. The dashed red curve is γ − 1 (kinetic energy K/mc2), while the dashed magenta curve is the relativistic Doppler factor.
In relativity, proper velocity (also known as celerity) w of an object relative to an observer is the ratio between observer-measured displacement vector and proper time τ elapsed on the clocks of the traveling object:
It is an alternative to ordinary velocity, the distance per unit time where both distance and time are measured by the observer.
The two types of velocity, ordinary and proper, are very nearly equal at low speeds. However, at high speeds proper velocity retains many of the properties that velocity loses in relativity compared with Newtonian theory.
For example, proper velocity equals momentum per unit mass at any speed, and therefore has no upper limit. At high speeds, as shown in the figure at right, it is proportional to an object's energy as well.
Proper velocity w can be related to the ordinary velocity v via the Lorentz factor γ:
where t is coordinate time or "map time".
For unidirectional motion, each of these is also simply related to a traveling object's hyperbolic velocity angle or rapidity η by
In relativity, propervelocity (also known as celerity) w of an object relative to an observer is the ratio between observer-measured displacement vector...
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Majewski, Steven R. (2006). "Stellar motions: parallax, proper motion, radial velocity and space velocity". University of Virginia. Archived from the original...
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Proper speed may refer to: PropervelocityProper motion Peculiar velocity This disambiguation page lists articles associated with the title Proper speed...
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nerve conduction velocity (CV) is the speed at which an electrochemical impulse propagates down a neural pathway. Conduction velocities are affected by...
The relative velocity, denoted v → B ∣ A {\displaystyle {\vec {v}}_{B\mid A}} (also v → B A {\displaystyle {\vec {v}}_{BA}} or v → B rel A {\displaystyle...
Virginia-based web development consulting group Phase velocity, speed of propagation of a wave Propervelocity, an alternative way of measuring motion in relativity...
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