simple general theory of relativity

2. GENERAL RELATIVITY
AND
GRAVITATION
Presented By,
M.Gomu
E.Esakki
II M.Sc Physics
The M.D.T Hindu college
Pettai.

3.  2015 marks an important milestone in the history of
physics: one hundred years ago, in November 1915,
Albert Einstein wrote down the famous field
equations of General Relativity. General Relativity is
the theory that explains all gravitational phenomena
we know (falling apples, orbiting planets, escaping
galaxies...) and it survived one century of continuous
tests of its validity. After 100 years it should be
considered by now a classic textbook theory, but
General Relativity remains young in spirit: its central
idea, the fact that space and time are dynamical and
influenced by the presence of matter, is still mind-
boggling and difficult to accept as a well-tested fact of
life.

4.  Prior to Einstein, Issac Newton’s laws were used to
understand the physics of motion. In 1687, Newton
wrote that gravity affects everything in the Universe.
The same force of Gravity that pulled an apple down
from a tree kept the Earth in motion around the sun.
But Newton never puzzled out the source of Gravity.

6. Philosopher David Hume’s 1738 “A Treatise of
Human Nature” was a big influence on
Einstein’s thinking about the space and time.
Hume was an empiricist and skeptic, believing
that scientific concepts must be based on
experience and evidence, not reason alone. He
also held that time did not exist separately from
the movement of objects.
 “ It is very well possible that without these
philosophical studies I would not have arrived at
the solution”, Einstein wrote.

7. There are really three theories of relativity:
 Relativity pre-Einstein(Galileo)
 Special Theory of Relativity(1905)
 General Theory of Relativity(1915)

8. Relativity is concerned with the question:
What is the nature of space and time?

9. Absolute space and Absolute time:
 Suppose that you are on an airplane. At 12:00, you
leave your seat to talk a friend a few rows in front of
you. At 12.15, you return to your seat. You might say
that at 12:15, you were at the same point in the space
where you were at the same point in space where you
were at 12:00. However ,what would a ground-based
person claim?
 If the plane were going 600 mi/hr, that person might say
“ at 12:15 you were at a point in space 150 miles away
from where you were at 12:00”

10. Who is right? According to Aristotle, space and
time are universal and you have moved.
But the Earth is moving around the sun, and the
sun around the Galaxy and the Galaxy is
whizzing through space…….

11. The Relationship between Matter and
Energy
According to Einstein’s formula, in a nuclear
reaction, some mass is converted to energy.
 The c2 factor means that even a tiny amount of
mass is equivalent to a huge amount of energy.

12. Einstein's formula
E = mc2
Mass (kg)
Energy (J) Speed of light
3.0 x108 m/sec
 This equation tells us that matter and energy are
really two forms of the same thing.

13. The speed of light
The speed of light is so important in physics
that it is given its own symbol, a lowercase “c”.
When you see this symbol, remember that “c” is
300 million m/s, or 3 × 108 m/s.

14. The speed of light
Einstein’s theory of
relativity says that
nothing in the
universe can travel
faster than the speed
of light.
If the Sun was to
vanish, we would
still see it in the sky
for 8 minutes and 19
seconds.

15. Special Relativity
The theory of
special relativity
describes what
happens to matter,
energy, time, and
space at speeds close
to the speed of light.

16. Special Relativity
These effects are observed in physics labs:
1. Time moves more slowly for an object in
motion than it does for objects that are not in
motion. This is called time dilation.
2. As objects move faster, their mass increases.
3. The definition of the word “simultaneous”
changes.
4. Space itself gets smaller for an observer
moving near the speed of light.

17. Special Relativity
1. Clocks run slower on moving
vehicles compared with clocks
on the ground. By moving
very fast, it is possible for one
year to pass on a spaceship
while 100 years have passed
on the ground.
2. The closer the speed of an
object gets to the speed of
light, the more of its kinetic
energy becomes mass instead
of motion.
3. The length of an object
measured by one person at rest
will not be the same as the
length measured by another
person who is moving close to
the speed of light.

18. The Motivations of General Relativity
General Relativity, or GR, was created in order
to better understand gravity
It has helped us to answer why gravity exists
General Relativity has many predictions most of
which have been verified by experiment with
amazing accuracy

19. The Motivations of GR
The special theory of relativity encompasses
inertial frames of reference moving at uniform
relative velocities
Einstein asked whether or not systems moving
in non uniform motion with respect to one
another could be relative and came up with the
idea of general relativity

20. The Equivalence Principle
The equivalence principle was Einstein's
`Newton's apple' insight to gravitation. His
thought experiment was the following, imagine
two elevators, one at rest of the Earth's surface,
one accelerating in space. To an observer inside
the elevator (no windows) there is no physical
experiment that he/she could perform to
differentiate between the two scenarios.

21.  The equivalence principle is a fundamental law
of physics that states that gravitational and
inertial forces are of a similar nature and often
indistinguishable.
 In the Newtonian form it asserts, in effect, that,
within a windowless laboratory freely falling in
a uniform gravitational field, experimenters
would be unaware that the laboratory is in a
state of nonuniform motion. All dynamical
experiments yield the same results as obtained
in an inertial state of uniform motion unaffected
by gravity.

23. THE CONSTANCY OF THE SPEED OF
LIGHT
 What is waving?
 A rough analogy is to a sound wave travelling
through the air. The air is the medium and
oscillations of the molecules of the air are what
is "waving."
 Galileo attempted to measure the speed of light
around 1600.

24. The Michelson-Morley Experiment
Before we turn to the experiment itself we will
consider a "race" between two swimmers.
Each swimmer swims the same distance away
from the raft, to the markers, and then swim
back to the raft. Now the raft and markers are
being towed to the left.

26. Einstein "Explains" the Michelson-Morley
Experiment
When Einstein was 16, in 1895, he asked
himself an interesting question
He continued to work on this question for 10
years

27. What is General relativity?
Albert Einstein's general theory of relativity is
one of the towering achievements of 20th-
century physics. Published in 1915, it explains
that what we perceive as the force of gravity in
fact arises from the curvature of space and time.

28. What is General relativity?
 Einstein proposed that objects such as the sun and the
Earth change this geometry. In the presence of matter
and energy it can evolve, stretch and warp, forming
ridges, mountains and valleys that cause bodies moving
through it to zigzag and curve. So although Earth
appears to be pulled towards the sun by gravity, there is
no such force. It is simply the geometry of space-time
around the sun telling Earth how to move.

29.  The general theory of relativity has far-reaching
consequences. It not only explains the motion of the
planets; it can also describe the history and
expansion of the universe, the physics of black
holes and the bending of light from distant stars and
galaxies.

30. According to the General theory
Matter causes space to curve. It is posited that
gravitation is not a force, as understood by
Newtonian physics, but a curved field (an area
of space under the influence of a force) in the
space-time continuum that is actually created by
the presence of mass.

31. How this could be tested?
 By the deflection of starlight traveling near the
sun; he correctly asserted that light deflection
would be twice that expected by Newton's laws.
This theory also explained why the light from
stars in a strong gravitational field was closer to
the red end of the spectrum than those in a
weaker one.

32. The Characteristics of GR
 GR is a theory of gravitation that supersedes
Newton’s Law of Universal Gravitation using
the warping of spacetime by mass to explain
gravitational attraction instead of the idea of
“forces”
 Essentially, massive bodies warp and curve their
local spacetime

33. The 3 “Classic” Tests of General
Relativity
Precession of Mercury’s orbit
Deflection of starlight (gravitational lensing)
Gravitational Red shift

34. An Example of Curved
Spacetime

35. Precession of Mercury’s Orbit
Newtonian General Relativity

36. Mercury Precession
 Known since 1850’s not to match Newtonian theory
 Perihelion precessed by 43 arcseconds per
century Would take 30,000 years to go full-circle
 While putting finishing touches on GR in 1915,
Einstein computed expected perihelion precession
of Mercury
 When he got out 43 arcsec/century, his heart
fluttered
!

37. Deflection of Starlight
Light is deflected by gravitational field called
“gravitational lensing”
Much like ball deflected by divot

38. Think of light as ants trying to go straight
In each case, the ants do their best to pick out
the straightest path they can. Unless space is
flat, they don’t stay on parallel lines forever,
and either converge or diverge.

39. Deflection of Starlight
During an eclipse, the sky around the sun is dark
enough to see distant stars.
Stars close to the sun have their light deflected
and so appear at a shifted position (farther from
sun)
Comparing stellar locations with and without the
presence of the sun along the line of sight allows
for a measurement of the deflection of light
rays.

40. Applications
 Gravitational lensing
 Gravitational waves
 Gravitational Red Shift
 Black Holes

41. Gravitational lensing

42. Gravitational Waves
Fluctuation of spacetime curvature that is
propagated as a wave
Radiates away from accelerating bodies
Carries energy away from source
Predicts that two massive bodies rotating about
their center of mass will loose energy in the
form of gravity waves and the orbit will decay.

43. Gravitational Redshift
 Gravitational redshift occurs when light leaving
a massive body redshifts in order to conserve
energy
 Light can also blueshift if falling into a gravity
well
 The appropriate equation for the red shift is

44. Black Holes
 Black Holes are the most profound prediction of
general relativity
 A black hole is a large body of matter that is so
dense that nothing can escape its gravitational
attraction, at a given distance, known as the
Schwarzschild radius

45. Black Holes
 Black Holes come in two different sizes: Stellar
(5 to 20 solar masses) and super massive
(millions or billions of times the mass of the
sun)
 Black Holes are detected by either their
gravitational influence on nearby bodies or
through electromagnetic radiation

46. Interesting facts about Einstein
 Einstein Failed his University Entrance Exam, and
had to reapply a year later.
 Einstein was famous for having bad memory. He
could not remember names, dates and phone
numbers.
 Einstein, Darwin, Allan Poe & Saddam Hussein,
all married their first cousins.
 Austrian physicist Friedrich Hasenohrl published
the basic equation E = mc2 a year before Einstein
did.

47. Thank you
IMAGINATION IS MOREIMPORTANT THAN KNOWLEDGE