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.

Both observers measure the light to be traveling at v=c=299,792,458 m/s!!!!

Inertial frame

Inertial frame

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

c

Dt

20 =Δproper time interval

Time Dilation• Now measure time interval from another inertial

frame from which the clock appears to be in motion

c

LD

c

st

2222 +==Δdilated time interval 0 ,0 If ttL Δ>Δ≠

Time Dilation

2

2

0

1c

v

tt

−

Δ=Δ

• 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

• To Adam, Eve appears to age more slowly due to time dilation

• Eve doesn’t notice anything unusual – all clocks in her

frame appear to her to run normal

Consider what happens to Eve from two perspectives:

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?

Adopted from Nobelprize.org website

Twin Paradox

• To Eve, Adam appears to age more slowly due to time dilation

• Adam doesn’t notice anything unusual – all clocks in his

frame appear to him to run normal

Consider what happens to Adam from two perspectives:

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?

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

• Energy and mass are equivalent– mass can be converted to energy– energy can be converted to mass

• Inertial mass of an object increases without bound as vc

• Require more and more energy to keep accelerating an object toward c– Requires infinite energy to reach c

2mcE =

2

2

0

1cv

mm

−

=

2

2

20

1cv

cmE

−

=

WormholesScience Fiction: Science:

• Wormholes–Time travel–Tunnels to alternate

universes

• Einstein-Rosen bridge–Unstable structures–May be impossible to

traverse

Wormholes

Length Contraction

2

2

0

0

1cv

tv

tvL

−

Δ=

Δ=

0tvL Δ=

2

2

0 1c

vLL −=