Rapidity

Rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates.

Rapidity equals the arctargent of the ratio between the velocity and the speed of light.

Formula

QuantityVariable["θ", "Rapidity"] == ArcTanh[Quantity[1, "SpeedOfLight"^(-1)]*QuantityVariable["v", "Speed"]]

symbol	description	physical quantity
θ	rapidity	"Rapidity"
v	velocity	"Speed"

Forms

Examples

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Get the resource:

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Get the formula:

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Use some values:

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$FormulaData[ ResourceObject[ "Rapidity"], {QuantityVariable["v","Speed"] -> Quantity[1.`*^8, ("Meters")/("Seconds")]}]$

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External Links

http://en.wikipedia.org/wiki/Lorentz_transformation#Rapidity

Source Metadata

Creator:
Date: 1908

Publisher Information

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