Here are the slides of the talk held at NISER's Astronomy club on 18 April, 2015

1. GRAVITATIONAL LENSING AND MASS
DETECTION
-Shubhayan Sarkar
-2nd year SPS

2. OUTLINE:
 Theory of relativity (obviously!!!!)
 What is gravitational lensing ??
 Mass detection using g-lensing

3. THEORY OF RELATIVITY
 There’s nothing so special about theory of relativity.
(Come on we all know it!!!)
 It’s the same old Newtonian mechanics about stuffs moving
w.r.t each other.
 Then why is it so called “THE SPECIAL THEORY OF
RELATIVITY” ??

4.  The specialness in relativity is brought about by a special
property of nature the universal constant c speed of light.
 It was Michelson and Morley who devised a method to
study the speed of light in different directions .
 People believed that light was propagating in a medium
called ether which would lead to change in the speed of
light in different directions.
 But (fortunately!!) they discovered speed of light is
constant in vacuum in any inertial reference frames we
choose. (Later we would see its true for non-inertial too!!)

5. WHAT WILL HAPPEN IF SPEED OF LIGHT IS
CONSTANT IN ALL INERTIAL REFERENCE FRAMES??
Think that a ball is thrown in a vehicle with a velocity u with
respect to a person sitting inside (ALICE)and that the
vehicle is moving at a velocity v with respect to a person
sitting outside (BOB).
Bob will see ball moving at a velocity u+v (quite obvious!!!)

6. LETS REPLACE BALL WITH LIGHT !!
By Newtonian mechanics you find that if light is observed to
move at velocity c by alice, bob will find to be c+v. But we
know that speed of light in different (inertial) reference
frames is c. Then how is bob seeing it at c+v??
Then your intuition would say if bob also sees the velocity
of light as c then might be that the rulers and clocks of alice
and bob are not same, because in that case only its
possible (as velocity is distance by time) that the distance
that bob measures is less than alice (length contraction) or
the time that bob measures is larger than alice (time
dilation).

7. EXAMPLE
With respect to Alice

8. EXAMPLE
With respect to Bob

9. EXAMPLE
This gives you

10. IS THERE A PROBLEM??
So we conclude that the alice sees bob’s clock running
slower and bob sees alice’s clock running slower. But then
who is correct??

11. IS THERE A PROBLEM??
So we conclude that the alice sees bob’s clock running
slower and bob sees alice’s clock running slower. But then
who is correct??
To your surprise both are correct, It’s just that the events
are not same. When alice sees Bob’s clock to know that
he’s clock is running slower than her own, this is a different
event to Bob seeing Alice’s clock.

12. THIS IS PROPER SPACE AND TIME
Same as the previous example the proper (frame) is one in
which the event is relatively at rest.
So the observation of Alice’s clock is a proper event for
Alice but not for Bob. So time would run slower for Alice
according to Bob and vice versa.

13. LOT OF SPECIAL LET’S GO TO GENERAL
Disclaimer: General relativity is subject to brain stressing
risks. Please make sure that you understand special
relativity before investing your mind and time.

14. SO ALL ARE READY WE CAN START!!!
General relativity is one of the greatest achievement of the
human mind(everybody knows!!!)
It replaced the 300 years of Newtonian gravity.
(Everybody knows is but how???)
Let’s see!!!!!!!!!!!!!!!!

15. EQUIVALENCE PRINCIPLE
This is small thought experiment which changed the entire
physics we knew then.
Einstein said “It was the most noble thought which
happened to me”
Okay but what is it???

16. EQUIVALENCE PRINCIPLE
Imagine you are in a rocket closed from sides i.e. you can’t
see outside and your rocket is accelerating at “g” in free
space.

17. EQUIVALENCE PRINCIPLE
Imagine you are in a rocket closed from sides i.e. you can’t
see outside and your rocket is accelerating at “g” in free
space.

18. EQUIVALENCE PRINCIPLE
As you seeing in the picture you can’t differentiate that you
are at rest on earth or you are accelerating at g in the
rocket.

19. EQUIVALENCE PRINCIPLE
Or why not say when you are committing suicide by
jumping from 20 storied building you would discover
beautiful physics (but sorry you won’t be able to share it).
Because a freely falling body doesn’t feel any force
(weightlessness) so he would see the same special
relativistic phenomenon i.e. for him light is moving in a
straight line.

20. WHY EQUIVALENCE PRINCIPLE??
It is quite obvious to ask that why do we need equivalence
principle.

21. WHY EQUIVALENCE PRINCIPLE??
It is quite obvious to ask that why do we need equivalence
principle.
Because Newton laws allows in principle an apple!! falling
towards ground to reach infinite speeds(if there is no ground
and constant acceleration g) which we now know is
ridiculous!!

22. WHY EQUIVALENCE PRINCIPLE??
It is quite obvious to ask that why do we need
equivalence principle.
Because Newton laws allows in principle an apple!!
falling towards ground to reach infinite speeds(if there is
no ground and constant acceleration g) which we now
know is ridiculous!!
So you want some way to generalize this problem to
some specific one so that speed of light remains
constant.
And that is given by equivalence principle (Your all
problems of gravitation has been shifted to a person
moving in a rocket at g)

23. THAT WAS GOOD BUT BETTER IS YET TO COME!!!
But we don’t know how to handle accelerations!!!!!
I think we know!!!!

24. THAT WAS GOOD BUT BETTER IS YET TO COME!!!
Same old Newton's theory says any accelerated frame can
be thought of as a uniform velocity but for a very small time.

25. THAT WAS GOOD BUT BETTER IS YET TO COME!!!
Same old Newton's theory says any accelerated frame
can be thought of as a uniform velocity but for a very
small time.
So we apply it and find that okkk when light travels in a
accelerated rocket light does look like it travelled in
curved path.

26. THAT WAS GOOD BUT BETTER IS YET TO COME!!!
So by equivalence principle light should behave the same
in an accelerating rocket and on earth. So light is curved by
gravity .
Or when you are freely falling light travels in a straight line
w.r.t . you.

27. BUT WAIT!!!
What was so special here?? It’s just Newton's law!!!(Just
nobody ever thought gravity can be thought like this)
Also when calculations are carried out the value of this
bending is half of what we observe(special case of earth sun
system)

28. BUT WAIT!!!
What was so special here?? It’s just Newton's law!!!(Just
nobody ever thought gravity can be thought like this)
Also when calculations are carried out the value of this
bending is half of what we observe(special case of earth sun
system)
But we are missing an important point. Where is speed of
light always taken to be constant c???

29. CAUTION:
This is the most challenging part of this talk. If you don’t
understand don’t be upset and don’t stress your mind too
much. Enjoy it!!

30. WHAT HAPPENS IF LIGHT SPEED IS ALWAYS C!!
Suppose Alice is in the rocket which is free space initially at
0 velocity. Bob is outside the rocket.
Now a light beam is shot by Bob when v=0, so according to
him light travels always on a straight line.

31. WHAT HAPPENS IF LIGHT SPEED IS ALWAYS C!!
But Alice finds it to be bending (which I said earlier). But the
frame in which the event that light is emitted is in Bob’s
frame. So Alice finds that her ruler is longer as compared to
Bob’s i.e.

32. WHAT HAPPENS IF LIGHT SPEED IS ALWAYS C!!
When bob measures .8m, Alice measures .6m.
So light appears to deviate more because of speed of light
being
c and this compensates for the other half.

33. WHAT HAPPENS IF LIGHT SPEED IS ALWAYS C!!

34. CURVATURE
This is what people mean by curvature.
At different point in space and time you have different
lengths of your ruler and different rates of your running
clock.

35. LETS PROCEED TO GRAVITATIONAL LENSING
So the bending of light because of gravity is gravitational
lensing.
And how it bends by this time you know (I suppose!!)

36. EINSTEIN’S RINGS
A beautiful phenomenon of g-lensing

37. MASS DETECTION
How do we find the mass of a very far away star??

38. MASS DETECTION
How do we find the mass of a very far away star??
One way is to observe the spectrum of the light emitted by
the stars and the intensity of that light, this would tell you the
atoms present and there concentrations.

39. MASS DETECTION
How do we find the mass of a very far away star??
Why not use gravitational lensing??
of course it is a good idea.

40. MASS DETECTION
How do we find the mass of a very far away star??
Why not use gravitational lensing??
of course it is a good idea.
Mass is directly proportional to g and g is directly
proportional to curvature and curvature is related to light
bending.
and yes people have used this technique and this is much
more accurate than conventional methods.

41. MASS DETECTION
Astronomers measure the bending of light and then back-
calculate the mass of the galaxy.
It is not quite advisable to measure mass of a star (though
in principle you can) but because of astronomical
constraints you lose that effect.

42. MASS DETECTION
Even you can measure dark matter!!!
Light coming from a distant galaxy is suddenly bent when it
passes through clusters of dark matter. Since there is no
radiation from dark matter, if you don’t see any radiation but
still light bends means dark matter is present there. And by
the bending of light beam you can calculate the mass.
This is a nice way to measure the dark matter around us!!!

43. SOME MORE PICTURES!!

44. SOME MORE PICTURES!!

45. SOME MORE PICTURES!!

46. THAT WAS GOOD!!!
Such complicated and beautiful astronomical phenomenons
can be understood by such simple physics without any
assumptions .
Nature is simple but not too simple.
-ALBERT EINSTEIN