classical velocity addition: the method of adding velocities when $v << c$ ; velocities add like regular numbers in one-dimensional motion: $u = v+u'$ , where $v$ is the velocity between two observers, $u$ is the velocity of an object relative to one observer, and $u'$ 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: ${L=L}_{0} \sqrt{1 - \frac{v^{2}}{c^{2}}} = \frac{L_{0}}{γ}$

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 the Earth

proper time: $Δ t_{0}$ . the time measured by an observer at rest relative to the event being observed: $Δ t = \frac{{Δ t}_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = {γ Δ t}_{0}$ , where $γ = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

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 $λ_{obs} {=λ}_{s} \sqrt{\frac{1 + \frac{u}{c}}{1 - \frac{u}{c}}}$ where $λ_{obs}$ is the observed wavelength, $λ_{s}$ 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: ${KE}_{rel} = (γ - 1) {mc}^{2}$ , where $γ = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

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

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

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 $E = {γmc}^{2}$ , where $γ = \frac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$

twin paradox: this asks why a twin traveling at a relativistic speed away and then back towards the 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

Glossary