Postulates of Special Relativity
• The Relativity Postulate
– The laws of physics are the same in every
inertial reference frame
• The Speed of Light Postulate
– The speed of light in a vacuum, measured in
any inertial reference frame, always has the
same value of c, no matter how fast the
source of light and the observer are moving
relative to each other.
The Relativity Postulate
• The laws of physics are the same in every inertial
reference frame
– Inertia
• the tendency for an object at rest to remain at rest or an object in
motion to remain in motion
• Newton’s 1st Law (Law of Inertia)
– A body will remain at rest or move in a straight line at a constant speed
unless acted on by a net outside force
• An inertial reference frame is a frame at rest or in motion
at a constant speed
– Not an accelerating reference frame
• Not rotating
• Not free-falling
The Relativity Postulate
• The laws of physics are the same in every inertial
reference frame
– There is no preferred reference frame
– Any inertial reference frame is as good as any other
– This has interesting consequences since, according to relativity,
time is a relative quantity, too
• no absolute time – only a direction to time’s arrow
• no absolute velocity – only relative velocities
• this is a departure from Newton’s Laws where time and space are
absolute
Speed of Light Postulate
• The speed of light in a vacuum, measured in
any inertial reference frame, always has the
same value of c, no matter how fast the source
of light and the observer are moving relative to
each other.
Inertial frame
Inertial frame
Both observers measure the light to be traveling at v=c=299,792,458 m/s!!!!
Speed of Light Postulate
• The speed of light in a vacuum, measured in
any inertial reference frame, always has the
same value of c, no matter how fast the source
of light and the observer are moving relative to
each other.
– This fact was actually experimentally confirmed
before the theory of relativity was developed
• Series of experiments by A.A. Michelson & E.W. Morley over
the period 1883-1887 showed speed of light did not depend
on the motion of the inertial frame
• The wavelength (& frequency) of light do depend
on the motion of the source & observer
– Doppler shifting
Time Dilation
• Build a “light clock”
Time Dilation
• Measure “proper” time interval
– time interval in the frame of the clock
proper time interval
2D
t0 
c
Time Dilation
• Now measure time interval from another inertial
frame from which the clock appears to be in
motion
dilated time interval
2s 2 D 2  L2
t 

c
c
If L  0, t  t0
Time Dilation
t 
t0
v2
1 2
c
• Δt0 = proper time interval between
2 events as measured by an
observer who is at rest with respect
to the events and sees them
occurring at the same place
• Δt = dilated time interval measured
by an observer who is in motion
with respect to the events and sees
them occurring at different places
• v = relative speed between the two
observers
• c = speed of light in a vacuum
This effect has been experimentally verified using very accurate atomic clocks
Time Dilation
• All clocks are affected by time dilation
– light clocks, quartz-crystal clocks, mechanical
clocks, biological clocks
Twin Paradox
A pair of twins, Adam and Eve, are thinking of what will happen to
their ages if one of them goes away from Earth on a space journey.
Will Eve for example be younger, older, or have the same age as
her brother if she leaves Earth with a space-ship and then returns
after some time?
Consider what happens to Eve from two
perspectives:
• To Adam, Eve
appears to age
more slowly due
to time dilation
Adopted from Nobelprize.org website
• Eve doesn’t notice
anything unusual
– all clocks in her
frame appear to
her to run normal
Twin Paradox
A pair of twins, Adam and Eve, are thinking of what will happen to
their ages if one of them goes away from Earth on a space journey.
Will Eve for example be younger, older, or have the same age as
her brother if she leaves Earth with a space-ship and then returns
after some time?
Consider what happens to Adam from two
perspectives:
• Adam doesn’t notice • To Eve, Adam
anything unusual
appears to age
more slowly due
– all clocks in his
frame appear to
to time dilation
him to run normal
Adopted from Nobelprize.org website
Twin Paradox
• How do we resolve the paradox?
– Remember, in special relativity, observers must be in inertial
(non-accelerating) frames
– For Eve to turn her rocket around and return to Earth, she must
accelerate.
• Therefore she is not in an inertial frame the entire time.
– Adam remains in an inertial frame the entire time, so his
observations are the correct ones
• Eve will, in fact, age more slowly than her twin and be younger than
Adam upon her return to Earth
– A full treatment of relativity shows that there is no real paradox.
Eve will, in fact, see Adam age more quickly than herself over
the course of the trip.
Time Dilation & Forward Time Travel
• Traveling at close to the speed of light
allows one to age more slowly relative to
people in another reference frame
• In a sense, this allows one to travel
forward in time
Restrictions on Traveling at the
Speed of Light
E  mc
2
m
• Energy and mass are equivalent
m0
2
v
1 2
c
E
m0c
2
2
v
1 2
c
– mass can be converted to energy
– energy can be converted to mass
• Inertial mass of an object
increases without bound as vc
• Require more and more energy
to keep accelerating an object
toward c
– Requires infinite energy to reach c
Wormholes
Science Fiction:
Science:
• Wormholes
• Einstein-Rosen bridge
– Time travel
– Tunnels to alternate
universes
– Unstable structures
– May be impossible to
traverse
Wormholes
Length Contraction
L0
 vt
v
t0
L  vt0
2
v
1 2
c
v2
L  L0 1  2
c