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Glossary
# Glossary

- classical velocity addition
- the method of adding velocities when $v\text{<<}c$; velocities add like regular numbers in one-dimensional motion: $u=\mathrm{v+u}\prime $, where $v$ is the velocity between two observers, $u$ is the velocity of an object relative to one observer, and $u\prime $ is the velocity relative to the other observer

- first postulate of special relativity
- the idea that the laws of physics are the same and can be stated in their simplest form in all inertial frames of reference

- inertial frame of reference
- a reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an outside force

- length contraction
- $L$, the shortening of the measured length of an object moving relative to the observer’s frame: ${\text{L=L}}_{0}\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}=\frac{{L}_{0}}{\gamma}$

- Michelson-Morley experiment
- an investigation performed in 1887 that proved that the speed of light in a vacuum is the same in all frames of reference from which it is viewed

- proper length
- ${L}_{0}$; the distance between two points measured by an observer who is at rest relative to both of the points; Earth-bound observers measure proper length when measuring the distance between two points that are stationary relative to Earth

- proper time
- $\mathrm{\Delta}{t}_{0}\text{;}$ the time measured by an observer at rest relative to the event being observed: $\mathrm{\Delta}t=\frac{{\mathrm{\Delta}t}_{0}}{\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}}={\gamma \mathrm{\Delta}t}_{0}$, where $\gamma =\frac{1}{\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}}$

- relativistic Doppler effects
- a change in wavelength of radiation that is moving relative to the observer; the wavelength of the radiation is longer (called a red shift) than that emitted by the source when the source moves away from the observer and shorter (called a blue shift) when the source moves toward the observer; the shifted wavelength is described by the equation
11.80 $${\lambda}_{\text{obs}}{\text{=\lambda}}_{s}\sqrt{\frac{1\phantom{\rule{0.25em}{0ex}}+\phantom{\rule{0.25em}{0ex}}\frac{u}{c}}{1-\frac{u}{c}}}$$where ${\lambda}_{\text{obs}}$ is the observed wavelength, ${\lambda}_{s}$ is the source wavelength, and $u$ is the velocity of the source to the observer

- relativistic kinetic energy
- the kinetic energy of an object moving at relativistic speeds: ${\text{KE}}_{\text{rel}}=\left(\gamma -1\right){\mathrm{mc}}^{\mathrm{2,}}$ where $\gamma =\frac{1}{\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}}$

- relativistic momentum
- $p$, the momentum of an object moving at relativistic velocity; $p=\text{\gamma mu}$, where $m$ is the rest mass of the object, $u$ is its velocity relative to an observer, and the relativistic factor $\gamma =\frac{1}{\sqrt{1-\frac{{u}^{2}}{{c}^{2}}}}$

- relativistic velocity addition
- the method of adding velocities of an object moving at a relativistic speed: $\text{u =}\frac{\text{v + u}\prime}{1+\frac{v\text{u}\prime}{{c}^{2}}}$, where $v$ is the relative velocity between two observers, $u$ is the velocity of an object relative to one observer, and $u\prime $ is the velocity relative to the other observer

- relativity
- the study of how different observers measure the same event

- rest energy
- the energy stored in an object at rest: ${E}_{0}={\mathrm{mc}}^{2}$

- rest mass
- the mass of an object as measured by a person at rest relative to the object

- second postulate of special relativity
- the idea that the speed of light $c$ is a constant, independent of the source

- special relativity
- the theory that, in an inertial frame of reference, the motion of an object is relative to the frame from which it is viewed or measured

- time dilation
- the phenomenon of time passing slower to an observer who is moving relative to another observer

- total energy
- defined as $E={\mathrm{\gamma mc}}^{2}$, where $\gamma =\frac{1}{\sqrt{1-\frac{{v}^{2}}{{c}^{2}}}}$

- twin paradox
- this asks why a twin traveling at a relativistic speed away and then back toward Earth ages less than the Earth-bound twin. The premise to the paradox is faulty because the traveling twin is accelerating, and special relativity does not apply to accelerating frames of reference