relativity simplified
DESCRIPTION
Special and General theories of relativity simplifiedTRANSCRIPT
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