PH 103

Dr. Cecilia VogelLecture 14

Review

Outline Consequences of Einstein’s

postulates time dilation simultaneity

Einstein’s relativity 1st and 2nd postulates of special

relativity equivalence principle of general

relativity

Some Consequences

Can be derived from constancy of speed of light:

Time interval between two events is different measured by different observers.

Order of events may be different measured by different observers.

Length of object or length of a trip is different measured by different observers.

Recall Classical Relativity Suppose two observers time the pretzel

you throw and catch. One observer on plane, one on Earth. Same pretzel.

Go-stop. t=5 s

Go------------------------------stop. t =?

Recall Classical Relativity

At any point, let the velocity of the pretzel measured by the plane observer be vp.

The velocity measured by Earth observer is vplane + vp. Earth observer measures faster speed:

pretzel goes farther, faster, but same time (5s)

Compared to this frame,

in this frame, the pretzel goes...farther

Now Einstein’s Relativity That worked for pretzels, what about light? Person on super-plane shines light at mirror. Suppose two observers time the light that

shines and reflects. One observer on plane, one on Earth. Same light.

Go-stop. to=5 s

Go-------------stop. t=?

Now Einstein’s Relativity

Compared to this frame,

in this frame, light goes...

At any point, the velocity of the light measured by the plane observer is c

And the velocity measured by Earth observer is c, so Earth observer measures:

Light goes farther, same speed→

farther

longer time!

t>5s

Time Dilation Generalize result:

t and to are both the time between same events measured by different observers

v is relative speed of the two observers Notice that if v<<c, the two times are

. Hard part: which time is which?

21 cv

ott

Time Dilation

Units comment If velocities are given as a fraction

of c, then the “c”units cancel.

Example: If v= 0.8 c, then (v/c) =(0.8c/c) = 0.8 (no units)

21 cv

ott

Proper time What’s the difference between t and to? to is the “proper time”

It is always less than any other measured time. Definition: proper time is time in frame in which

the two events occur at same place Events are

single instant in time, single point in space, Events don’t move. They don’t have reference frame. Occur in all frames

Time interval is time between two events One event makes you start your timer other even makes you stop you timer.

Proper time What’s the difference between t and

to? to is the “proper time”

Definition: proper time is time in frame in which events occur at same place

For example If the two events happen to someone or

something, their frame measures proper time your heartbeatIf someone is at both events, (or same x away)

their frame measures proper timeperson taking trip

particle’s lifetime

you and the clock on the wall

Time Trip Nikos travels to a planet 12 light-years

away at a speed of 0.6 c. Juan stays on Earth. Each measures the trip to take a different amount of time. Note:

A light-year is distance light travels in a yr 1 light-year = (c)(1yr) = 1c-yr Consistent units: distance in light-years,

speed as fraction of c, time in years

The values in example are relative to EarthIn that frame (in any one frame), the laws of physics hold, including d = vt

Ex: 12c-yr/24yr = 0.5c

More Example If Nikos makes a 12 light-year trip at

0.6c, Juan sees him moving at 0.6c for 20 years. d = vt = (0.6c)(20 y) = 12c-yr.

Nikos sees himself moving at

Nikos sees the planet getting closer at 0.6c for 16 years.

d = vt = (0.6c)(16y) = 9.6 c-yr Both are measuring the distance

between Earth and planet, yet the distances are different!

Proper Length What’s the difference between the

two lengths? One is the “proper length”

It’s always longer than any other measured length.

Def: proper length is length in frame in which object (or ends of trip) is at rest

For example Object, or anyone at rest relative to it,

measures object’s proper length. Your own height Length of ship you are riding on

Someone measures the proper length between two objects, if both are at rest relative to them

person on either planet, for a trip between planets

Just How Proper is it? If there is a proper time and a proper

length, is there a proper reference frame?

NO!!!!!!! Proper time of trip in example: Nikos Proper length of trip in example: Juan Proper time of astronaut’s heartbeat:

Astronaut Astronaut’s heartbeat looks SLOW to you.

Proper time of your heartbeat: You Your heartbeat looks SLOW to astronaut.

Simultaneity How do we know whether 2 events are

simultaneous? If signals coming from events arrive

at the same time, the events might not have been simultaneous

how long did it take the signal to get here?

signalarriveevent vdtt /demo

signalarriveevent vdtt /

If tarrive, d, and v the same,conclude tevent same

If tarrive, is smaller and d/v also smaller, can conclude tevent same

signalarriveevent vdtt /veraser+vthrower

Veraser-vthrower

cdtt arriveevent /

If tarrive is earlier and d/v is same, must conclude tevent is earlier!

one observer says two events are simultaneous,other says they are not!!

SIMULTANEITY IS NOT ABSOLUTE