Download Special Relativity

Special Relativity
How does light behave in moving reference frames?
Some lingering questions remain…
Maxwell’s equations
describe and predict
electromagnetic
phenomena
amazingly well.
but…
1) What is the medium for electromagnetic
waves?
2) In what frame of reference is the speed of
light 3.00 x 108 m/s?
Luminiferous ether?
Hypothesized as medium for light
Hypothesized as frame of reference for light
• Does a microwave work on a fast-moving spaceship?
• Does a motor work?
If there is an ether, it’s odd.
• Does not noticeable interact with matter
• Is it dragged by Earth or is there an ethereal wind through
which the Earth (and everything else) travels?
Michelson-Morley Interferometer
In 1880’s, Albert
Michelson and Edward
Morley designed an
experiment to test the
speed of the ethereal
wind.
Swimmers’ analogy
Stationary relative
to ether?
• waves should
constructively
interfere.
Moving relative to
ether?
• waves should
destructively
interfere
Null results
Michelson and Morley discovered
no evidence of the Earth’s
motion through ether.
Consequence of no ether
1. No ‘absolute’ frame of
reference
2. If no ‘absolute’ frame, laws of
physics (including electricity
and magnetism) work in all
reference frames
3. If laws of physics work in all
reference frames, speed of light
is the same in all frames of
reference
Speed of light is the same
regardless of reference
frames?
Postulates of special relativity
1st postulate:
All laws of nature are the same in
all uniformly moving frames of
reference
•
Sometimes called “inertial reference
frames”
2nd postulate:
The speed of light in empty space
is the same, regardless of the
motion of the source or the
motion of the observer
Frames of reference
(with a ball)
The thrower throws the ball at, say,
10 m/s in each situation.
The receiver perceives the ball to
travel at
1)
2)
3)
10 m/s (truck at rest)
>10 m/s (moving towards)
<10 m/s (moving away)
https://www.youtube.com/watch?v=
BLuI118nhzc
Frames of reference & light
1) What happens if you travel at the
speed of light and turn on a
flashlight? Does that light travel at
twice the speed as the ‘slow’ light?
2) Imagine an electric current
traveling down a wire. It induces a
magnetic field. Would you detect
a magnetic field if you traveled the
same speed as the electric
current?
Frames of reference
(with a flashlight)
The person on the truck shines a
flashlight at the person standing on
the ground.
The person on the ground
perceives the light to travel at
1)
2)
3)
3 x 108 m/s (truck at rest)
3 x 108 (moving towards)
3 x 108 (moving away)
Explaining null results
Hendrik Lorentz proposed a
mathematical trick as a solution
• Trick = hypothesis with no physical
explanation
Suppose that objects contract
(i.e., shrink) in the direction of
their motion
What if length contraction not a trick?
Einstein’s insight: if speed
of light is the same in all
reference frames,
1. Clocks aren’t
2. Rulers aren’t
Read the original paper here:
https://www.fourmilab.ch/etext
s/einstein/specrel/www/
Time and distance in stationary frames
Person on high-speed
rocket ship measures
time with a light clock, a
device in which light
bounces back and forth
between two mirrors
𝑑
𝑑
𝑡= =
𝑣
𝑐
Time and distance in moving frames
Person NOT on the ship
observes the following:
Moment 1
Moment 2
Moment 3
Time and distance in moving frames
Person NOT on the ship
observes the following:
𝑑 = 𝑐𝑡0
𝑑 = 𝑣𝑡
Moment 1
Moment 2
Moment 3
Time and distance in moving frames
𝑐𝑡
2
= 𝑐𝑡0
2
By Pythagorean Theorem
So, 𝑐𝑡
2
− 𝑣𝑡
So, 𝑡 2 1 −
So, 𝑡 =
𝑣2
𝑐2
= 𝑡0 2
𝑡0
2
𝑣
1−
2
𝑐2
= 𝑐𝑡0
2
+ 𝑣𝑡
2
Time dilation
𝑡=
𝑡0
If physics works regardless of
reference frame, then
observers note that time
slows downs for events in
moving reference frames.
• At everyday speeds (v << c), v/c ~0, so
time dilation is barely noticeable.
NOT “seems to slow”, but
really and actually and
counterintuitively slows
• At relativistic speeds, (v some
appreciable fraction of c), time dilation
is significant.
•
2
𝑣
1−
𝑐2
Length contraction
Length contracts in direction of
travel.
𝐿 = 𝐿𝑜 1 −
𝑣2
𝑐2
Measurement between frames
Measurements of time and length between one frame of
reference and another will agree only on the speed of light.
Time: 𝑡 =
𝑡0
2
1−
𝑣
2
𝑐
Length: 𝐿 = 𝐿0 1 −
In relativity, we see the term
1
𝑣2
1−𝑐2
𝑣2
𝑐2
occurs so frequently,
we abbreviate it with the Greek letter gamma, 
Other implications
Relativistic momentum
Relativistic kinetic energy
𝑝=
𝑚𝑣
2
𝑣
1−𝑐2
KE =
𝑚𝑐 2
2
−
𝑚𝑐
2
𝑣
1−𝑐2
Using relativity to explain
electromagnets
Imagine an electric current traveling
down a wire. It induces a magnetic
field. Would you detect a magnetic
field if you traveled the same speed as
the electric current?
Think about…
Joe Burpy is 30 years old. He has a
daughter who is 6 years old. If Joe
leaves on a Greyhound space bus
which takes a 5-year (space bus
time) round trip at 0.99 c.
a) How old will Joe be when he
returns?
b) How old will his daughter be?
More…
Minute Physics:
• Special relativity:
https://www.youtube.com/watch?v=ajhFNcUTJI0
• Energy & mass equivalence:
https://www.youtube.com/watch?v=hW7DW9NI
O9M
• How far away is tomorrow:
https://www.youtube.com/watch?v=s5S-hA9uKEM
• Adding velocity:
https://www.youtube.com/watch?v=IM630Z8lho8
• Breaking speed of light:
https://www.youtube.com/watch?v=lR4tJr7sMPM
• Why you can’t go speed of light:
https://www.youtube.com/watch?v=NnMIhxWRG
Nw
New York University – Physics Dept:
http://www.physics.nyu.edu/~ts2/Animation/special_r
elativity.html#