Relativity

What are Einstein’s postulates?

• Laws of physics remain the same in every inertial frame of reference

• Speed of light in a vacuum is the same in all inertial frames of reference and is independent of the motion of the source

What is an inertial frame of reference (IFR)

any frame of reference in which Newton’s first law holds.

What is the time dilation equation?

$\Delta t=\gamma\Delta t_0$ where $\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$, $\Delta t_0$ is the proper time

Note that \sqrt{1-\frac{v^2}{c^2}}>1 thus \Delta t>\Delta t_0

What is meant by proper time?

The time interval between two events that occurred at the same point in space.

What is the length contraction equation?

$l=\frac{l_0}{\gamma}$ where $l_0$ is the length of the object at rest and $l$ is the length of an object at speed.

Note that lengths only contract when parallel to the direction of motion.

What is $\gamma$ ?

$$\gamma=\sqrt{1-\frac{v^2}{c^2}}$$

What are the two frames S and S’ (for Lorentz transformations)?

• Frame S is the stationary frame

• Frame S’ is the frame moving at velocity, $v$

Lorentz transformation for x?

$$x^{\prime}=\gamma\left(x-ut\right)$$

Lorentz transformations for y, z?

• $$y^{\prime}=y$$

• $$z^{\prime}=z$$

Lorentz transformation for t.

$$t^{\prime}=\gamma\left(t-\frac{ux}{c^2}\right)$$

Lorentz velocity transformation

$$v_{x}^{\prime}=\frac{v_{x}-u}{\left(1-\frac{uv_{x}}{c^2}\right)}$$

Relativistic Doppler shift equation approaching observer

$f=\sqrt{\frac{c+u}{c-u}}f_0$ , f>f_0

where$f_0$ is the frequency emitted by the object, and $f$ is the shifted frequency.

Relativistic Doppler shift equation moving away from observer

$f=\sqrt{\frac{c-u}{c+u}}f_0$ ,f<f_0

where$f_0$ is the frequency emitted by the object, and $f$ is the shifted frequency.

List some of the practical applications of the doppler shift

• Weather rafar

• Military doppler radar

• police radar gun

• emission spectra of stars

• red/blue shift in astronomy/astrophysics

• velocities of astronomical entities

• Gravitational red shift

COVER LECURE 7+8