Lorentz Transformations

Functions
template<typename T >
T	EGXPhys::LorentzFactor (const T &velocity)
	Calculates the Lorentz factor, \(\gamma\). The factor by which time, length, and relativistic mass changes due to movement of an object. More...
template<typename T >
T	EGXPhys::LorentzFactorViaMomentum (const T &momentum, const T &restMass)
	Calculates the Lorentz factor, \(\gamma\). The factor by which time, length, and relativistic mass changes due to movement of an object. More...
template<typename T >
T	EGXPhys::LorentzFactorViaEnergy (const T &energyTotal, const T &energyRest)
	Calculates the Lorentz factor, \(\gamma\). The factor by which time, length, and relativistic mass changes due to movement of an object. More...
template<typename T >
T	EGXPhys::LorentzFactorViaRapidity (const T &rapidity)
	Calculates the Lorentz factor, \(\gamma\). The factor by which time, length, and relativistic mass changes due to movement of an object. More...

Detailed Description

Function Documentation

LorentzFactor()

template<typename T >

T EGXPhys::LorentzFactor

(

const T &

velocity

)

Calculates the Lorentz factor, \(\gamma\). The factor by which time, length, and relativistic mass changes due to movement of an object.

\[\gamma=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}\]

\[\gamma=\frac{1}{\sqrt{1-\beta^2}}\]

See https://en.wikipedia.org/wiki/Lorentz_factor

Equation taken from

Parameters

velocity

\(v\) \((\frac{m}{s})\) velocity of relativistic object.

Returns

\(\gamma\) (dimensionless) Lorentz factor.

LorentzFactorViaEnergy()

template<typename T >

T EGXPhys::LorentzFactorViaEnergy	(	const T &	energyTotal,
		const T &	energyRest
	)

Initial value:

{
        return sqrt(1.0+pow(momentum/(restMass*NISTConst::c),2.0)))

Calculates the Lorentz factor, \(\gamma\). The factor by which time, length, and relativistic mass changes due to movement of an object.

\[\gamma=\frac{E_{total}}{E_{rest}}\]

\[\gamma=\frac{\gamma m_0 c^2}{m_0 c^2}\]

See https://en.wikipedia.org/wiki/Lorentz_factor

Equation taken from

Parameters

energyTotal	\(E_{total}\) \((J)\) Total energy of relativistic object.
energyRest	\(E_{rest}\) \((J)\) Rest energy of relativistic object.

Returns

\(\gamma\) (dimensionless) Lorentz factor.

LorentzFactorViaMomentum()

template<typename T >

T EGXPhys::LorentzFactorViaMomentum	(	const T &	momentum,
		const T &	restMass
	)

Calculates the Lorentz factor, \(\gamma\). The factor by which time, length, and relativistic mass changes due to movement of an object.

\[\gamma=\sqrt{1+(\frac{p}{m_0 c})^2}\]

See https://en.wikipedia.org/wiki/Lorentz_factor

Equation taken from

Parameters

momentum	\(p\) \((\frac{kg m}{s})\) momentum of relativistic object.
restMass	\(m_0\) \((kg)\) Rest mass of relativisitc object.

Returns

\(\gamma\) (dimensionless) Lorentz factor.

LorentzFactorViaRapidity()

template<typename T >

T EGXPhys::LorentzFactorViaRapidity

(

const T &

rapidity

)

Calculates the Lorentz factor, \(\gamma\). The factor by which time, length, and relativistic mass changes due to movement of an object.

\[\gamma=Cosh(w)\]

See https://en.wikipedia.org/wiki/Lorentz_factor

Equation taken from

Parameters

rapidity

\(w\) (dimensionless) rapidity of relativistic object.

Returns

\(\gamma\) (dimensionless) Lorentz factor.