2. Brief Overview
• 1879: Einstein born Ulm, Germany.
• 1885 - 1925: Michelson and Morley began a series of
puzzling experiments which made the Newtonian
Universe impossible.
• 1900: Max Planck shocked the physics community with
the concept of quantization
• 1905: The miracle year in physics: Einstein published
papers on Brownian motion as well as the seminal papers
on his theory of relativity. He developed the Special
Theory of Relativity in which he described how space and
time are relative or related to each other.
• 1915: Einstein extended his discussion of relativity to
include gravity and thereby explained the problem of
Mercury. He developed the general theory of relativity
which dealt with gravity and acceleration and a 4
dimensional space in which everything is related to each
other.
• 1919: Eddington confirms Einstein's prediction
concerning deflection of starlight.
• 1915 - 1925: Einstein was a co-leader in the birth and
development of quantum mechanics
• 1925 - 1935: Einstein and Bohr engaged in a fascinating
series of "debates" over the interpretations of physics
especially the notion of determinism (God does not play
dice)
• 1930 - 1955: Einstein searches for a unified theory of the
universe
• 1933 - Hubble and Humanson discover the recessional
nature of galaxies - Einstein's theories of the universe
take shape.
• 1955: Einstein dies, Princeton, N.J.
4. Einstein and Relativity
Einstein (1879 – 1955) noticed
that Newton’s laws of motion are
only correct in the limit of low
velocities, much less than the
speed of light.
Theory of Special Relativity
Also, revised understanding
of gravity
Theory of General Relativity
5. Two Postulates Leading to Special
Relativity
1. Observers can
never detect their
uniform motion,
except relative to
other objects.
This is equivalent to:
The laws of physics are the same for all
observers, no matter what their motion, as
long as they are not accelerated.
6. Two Postulates Leading to Special
Relativity
2. The velocity of
light, c, is
constant and
will be the
same for all
observers,
independent of
their motion
relative to the
light source.
7. If c were not absolute, you’d see car A reach the collision
point before car B! You would see a different event!
10. Basics of Special Relativity
The two postulates of special relativity
have some amazing consequences.
Consider thought experiment:
Motion of Assume a light source moving with velocity v
“stationary” relative to a “stationary” observer:
observer
v’ v v
c t’ c t
Light c t’
source
v t
Seen by an observer
moving along with the light Seen by the
source “stationary” observer
11. Basics of Special Relativity
Now, recall that the speed of light, c,
is the same for all observers.
The times t and t’ must be different!
Then, the Pythagoras Theorem gives:
(c t)2 = (c t’)2 + (v t)2
or
t’ = ( t)/ c t’ c t
where = 1/(1 – [v/c]2)1/2
v t
is the Lorentz factor.
This effect is called time dilation.
12. Einstein’s Twin Paradox
• A set of Twins (5 yo) • Bob Saget places
Ashley on a
spaceship that will
travel at 80% the
speed of light.
v/c
• c = speed of light
• One decides to visit • d= distance
Epsilon Eridani
which is 10 LY away • t = time
13. Einstein’s Twin Paradox
• Velocity (v) is v = 4/5c = 0.8c
therefore…
• β = 4/5 = 0.8
= 1/(1 – [ ]2)1/2 (β² = 0.8² = 0.64)
1 - β² = 1 - 0.64 = 0.36
and the √ of 0.36 is 0.6 !!
= 1 ÷ 0.6 = 1²/³ = 5/3
14. Without Relativity…..
• d = vt or t = d/v
• d is light years traveled
• v is velocity.
• t is time.
• t = 10/0.8c = 12.5 years each
way.
• There and back makes the trip
12.5 x 2 or 25 years!!
15. With Relativity…..
• Mary-Kate’s view of her sister on the
spaceship:
• Ashley’s spaceship clock is running slow by…
• γ = 5/3 !!
• Therefore Ashley’s clock reads 25 years ÷ γ
• 25 ÷ 5/3 = 15 years!!
16. With Relativity…..
• Ashley’s view on the spaceship:
• Ashley sees distance of planets contracted by
γ = 5/3
• In Ashley’s frame distance is
• 10 light years ÷ 5/3
• 6 light years.
• Therefore t = d/v = 6/0.8 = 7.5 years each way.
• There and back is 7.5 x 2 = 15 year trip for
Ashley!!
17. The Physical Result of the Trip
25 years later…
• Ashley ages only 15 • While Mary-Kate ages
years… the full 25 years!
19. Other Effects of Special Relativity
• Length contraction: Length
scales on a rapidly moving
object appear shortened
• Relativistic aberration:
Distortion of angles
• The energy of a body
at rest is not 0.
Instead, we find
E0 = m c2
21. General Relativity
A new description of gravity
Postulate:
Equivalence Principle:
“Observers can not
distinguish locally
between inertial forces
due to acceleration and
uniform gravitational
forces due to the
presence of massive
bodies.”
22. The General Theory of
Relativity Explained
• Einstein Discovered in his
General Theory of Relativity
that gravity and acceleration
are the same phenomenon.
Imagine an elevator and a
person standing in it.
What would happen to the person if
the elevator free-falls?
The person would be floating in the
elevator while it is free-falling.
Now Imagine that person in a
space ship far away from any
gravitational force. He would be
floating in the ship.
If the ship the person is in accelerates
at the right amount of speed, the
person would feel the same as if
gravity was pulling on him.
23. Another Thought Experiment
Imagine a light source on board a rapidly
accelerated space ship:
Time Time
a
Light
source
a a a
g
As seen by a As seen by an observer
“stationary” observer on board the space ship
24. Thought Experiment
For the accelerated observer, the light
ray appears to bend downward!
Now, we can’t distinguish between
this inertial effect and the effect of
gravitational forces.
Thus, a gravitational force
equivalent to the inertial force
must also be able to bend light!
27. General Relativity Effects
Near Black Holes
At a distance, the
gravitational fields of a black
hole and a star of the same
mass are virtually identical.
At small distances, the much
deeper gravitational potential
will become noticeable.
28. General Relativity Effects
Near Black Holes
An astronaut descending
down towards the event
horizon of the BH will be
stretched vertically (tidal
effects) and squeezed
laterally.
This effect is called
“spaghettification”
29. General Relativity Effects
Near Black Holes
Time dilation
Clocks starting at
12:00 at each point.
After 3 hours (for an
observer far away Clocks closer to the
from the BH): BH run more slowly.
Time dilation
becomes infinite at
the event horizon.
Event Horizon
30. General Relativity Effects
Near Black Holes
Gravitational Red Shift
All wavelengths of emissions
from near the event horizon
are stretched (red shifted).
Frequencies are lowered.
Event Horizon
32. Thought Experiment (Conclusion)
This bending of light by the gravitation of massive
bodies has indeed been observed:
During total solar eclipses:
The positions of stars apparently close to the sun are
shifted away from the position of the sun.
New description of gravity as
curvature of space-time!
33. Another manifestation of bending of light:
Gravitational lenses
A massive galaxy cluster is bending and
focusing the light from a background object.
34. Other Effects of General Relativity
• Perihelion advance
(in particular, of
Mercury)
• Gravitational red shift: Light from sources near
massive bodies seems shifted towards longer
wavelengths (red).
35. Conclusion Click Me
• Einstein published two theories that
extended Newton’s Laws of motion and
gravity:
• The Special Theory of Relativity explained
how motion was relative to the observer and
the speed of light is constant to all
observers.
• The General Theory of Relativity says that a
gravitational field is a curvature of space-
time caused by the presence of a mass.
• The curvature of space-time was confirmed
by Mercury’s precession and a solar eclipse.
