Modern Physics
Outline
•
•
•
•
•
Special Relativity (Einstein)
Quantum Mechanics
Modern Particle Physics
Gravity/General Relativity
Cosmology/Big Bang Theory
Relativity
• Before we get to special relativity, need to
know what “normal” relativity is.
• Relativity refers to how 2 different observers
can view a physical situation
– They are in 2 different reference frames relative to
each other
Alice and Bob
• Alice is standing on a train platform while Bob
is in the front of a train passing the platform
• Bob throws a ball from the front towards the
back (assume a straight line at a constant
speed) and no gravity
• What does each observer see?
Bob
• From his point of view, he and the train are
moving together, so he doesn’t notice the
movement.
• It takes a time of t = L/v to reach the back of
the train
– L = length of train
– v = velocity of ball
Alice
• From her point of view, the back of the train is
moving towards Bob as he throws it so it
needs to cover less distance
• However, it appears that he releases it slower
because the 2 velocities partially cancel
• t = (L – ut)/(v-u)
– u = velocity of train
Alice and Bob
• Alice says: t = (L-ut)/(v-u)
• Bob says: t = L/v
• Who’s right?
• Solve Alice’s expression for t:
– t(v-u) = L-ut  ut terms cancel  vt = L  t = L/v
• They get the same answer!
– Both will observe the ball hitting the back wall at the
exact same time  of course!
Galilean relativity
• This principle of velocities adding or
subtracting based off one observer moving
Galilean relativity
• The physical results/observations do not
change, just the words you use to describe
them
– Alice says it’s moving slower but had less distance
to cover
Special Relativity
• Einstein in 1905 submitted 2 postulates about
light being special
Postulate #1: The laws of physics are the same
in all inertial reference frames (frames that only
differ by a constant speed)
Postulate #2: The speed of light is the same in
all inertial reference frames
Back to Alice and Bob
• Same setup, but instead of a tennis ball, make
Bob shine a laser to the back and figure out how
long it takes to hit the back
• Bob: t = L/c
• Alice: t= (L-ut)/c
– Speed of light is the same in all reference frames
– Ball appears to move slower to Alice before, not light
Alice and Bob - SR
• Bob: t = L/c
• Alice: solve for t = L/(c+u)
• Alice will say (observe) that the time it takes
the laser to reach the back of the train is LESS
than Bob
Another Example
• https://www.youtube.com/watch?v=wteiuxyq
toM
Special Relativity
• What do these mean?
• It means that 2 different observers can get 2
different answers
– Things don’t happen at the same time
– Simultaneous events don’t have to remain that
way
– Time is no longer a constant but depends on the
motion
Mirror Clock
Mirror Clock
Comparison of Mirror Clocks
• 1st one: t = w/c
• 2nd one: (ct’)2 = (vt’)2 + w2
t’ =
𝑤
1
𝑐 1−𝑣 2 /𝑐 2
Call g=
1
1−𝑣 2 /𝑐 2
 t’ = gt
Time dilation
• g = Gamma factor or Lorentz factor
– Always bigger than 1
– Gets asymptotically bigger as v  c
• Says: Time measured by moving clock is
bigger (takes longer) than time measured by
stationary one
– Moving clocks tick slower
Nice Theory, but….
• This idea was based on the 2nd postulate of SR
• Is it right?
• Short answer: yes, we have measured these
effects
– http://en.wikipedia.org/wiki/Hafele%E2%80%93K
eating_experiment
Basic Results from Special Relativity
• Time is not a constant – depends on relative
motion
• Space is also not constant
– Sort of the opposite of time dilation  length
contraction
• Simultaneous events in one frame don’t stay
that way in another
More results
• Since speeds can’t add beyond the speed of
light, speeds are also relative between frames
• Affects kinetic energy, momentum, etc as well
• ALL of mechanics is slightly modified by the
Lorentz gamma factors
– As long as v/c < 0.1-0.2, then gamma ~1 and no
real modification
Energy
• Einstein’s theory gives a formula for the
energy of an object in terms of momentum
and mass, etc.
𝐸=
𝑝2 𝑐 2 + 𝑚2 𝑐 4
Energy
• If you are not moving  p =0
E = mc2
• If moving slowly (p is small), use an identity
1+𝑥~1+
1
𝑥
2
for small x
2
1
𝑚𝑣 2
2
𝐸 ~ 𝑚𝑐 +
• https://www.youtube.com/watch?v=NnMIhxWRGNw
Twin Paradox
• Your twin gets in a rocket and leaves Earth at a
high rate of speed for years and then turns
around and comes home
• What happens?
• Your reference frame: You are stationary and
your twin is moving  aging slower
Your reference frame
• You are stationary and your twin is moving 
aging slower
• You will be older when your twin returns
Twin’s reference frame
• Twin is at rest and you (and the Earth) are moving
away from it
• Your time slows down and you age slower
• When the twin returns home, you are younger
and the twin is older
• How do we resolve this paradox?
Resolution
• Travelling twin was not always in a inertial
reference frame because he has to turn
around  must decelerate/accelerate and
that changes how time is perceived in a
different way
• The two situations aren’t actually symmetric