Special and general theories of

relativity

Relativity

Invariance of Physical Laws

• Einstein’s first postulate: Principle of relativity– The laws of Physics are the same in every inertial

frame of reference• Einstein’s second postulate– The speed of light in vacuum is the same in all

inertial frames of references and is independent of the motion of the source.

ImplicationsSimultaneity

Time dilation and length contractionEquations for momentum and

kinetic energy have to be revised

an occurrence that has a definite position and time

Relativity of Simultaneity

event

Can 2 events be simultaneous?

Relativity of Simultaneity

Two events that are simultaneous in one frame of reference are not simultaneous in a second frame of reference that is moving relative to the

first.

Relativity of Simultaneity

It follows that the time interval between two events may be different in different frames of reference

Consider pulse of light bouncing between two mirrors (retroreflectors)

d

Consider path of pulse of light in moving frame of reference: Light Clock

dct vt

Relativity of time intervals

• For the one in the moving train:

Δt0= 2d/c• For the observer outside the train:

Δt= Δt0 / √ [1-(u2/c2)] Cannot happen–u=c–u>c

Time dilation

Proper time

Relativity of time intervals

Example

You are on earth as a spaceship flies past at a speed of 0.990c (about 2.97x108m/s) relative to the earth. A high intensity signal light ( perhaps a pulsed laser) on the ship blinks on and off; each pulse lasts 2.20x10-

6s as measured on the spaceship. What do you measure as the duration of each light pulse? 15.6x10-6s

Twin Paradox

γ= 1/√[1-(u2/c2)] and from Δt= Δt0 / √[1-(u2/c2)]

Therefore Δt= γΔt0 This equations for time dilation suggest an

apparent paradox

10% the speed of light

86.5% the speed of light

99% the speed of light

99.9% the speed of light

Relativity of length

Lengths parallel to the relative motion

Δt0= 2l0/c

l= lo√ [1-(u2/c2)]Length contraction

Example

A crew member on the spaceship on the previous example measures its length, obtaining the value of 400m. What length do observers on earth measure?56.4m

Example

The two observers mentioned in the previous example are 56.4m apart. How apart does the spaceship crew measure them to be?

7.96m

Relativistic Momentum

p=movClassical

momentum

p=mov/√[(1-v2/c2)]Relativistic momentum

Relativistic Momentum

Mass m is observed to

increase

m= mo/√[1-(u2/c2)]

Mass inc formula

Relativistic Work and Energy

E2=(m0c2)2+(pc)2

Total energy, rest energy, and momentum

Newtonian Mechanics & Relativity

The general theory of relativity

Inertial forces and

gravitational forces

principle of

equivalence

gravitational red shift

bending of light by gravity

You are on top of the Eiffel tower, holding the bucket, and step off. While falling towards the ground, do you see the cork move towards the top of the water, towards the bottom of the bucket, or stay where it is relative to the bucket and the water?

acceleration gravity

Inertial forces

force produced by the reaction of a body to an

accelerating force

equal in magnitude and

opposite in direction to the

accelerating force.

Gravitational forces

Force exerted by two

interacting bodies with

mass

Principle of equivalence

the fundamental

basis for the general theory of relativity

Inertial forces

The complete equality of gravitational and

inertial mass, gravity, and acceleration

Gravitational forces

Bending of light by Gravity

Bending of light by Gravity

Bending of light by Gravity

Gravitational Time Dilation

Einstein's theory of General

Relativity says:

Time slows near massive

objects

Time flows at different rates everywhere

The Gravitational Red Shift

Light rising against gravity

loses energy