The document presents an overview of special relativity, featuring Maxwell's equations and Lorentz transformations, emphasizing the concept that time and space are interconnected and can be perceived differently by observers in motion. It discusses Minkowski spacetime diagrams and the principles of time dilation and length contraction, along with applications of relativity, such as gravitational effects on light and the nature of black holes. The text highlights how these revolutionary ideas challenge everyday intuitions and the reality of physical observations.

1. SPACETIME
VISHWAS SHUKLA
DAYALBAGH EDUCATIONAL INSTITUTE
JAN, 29 2016

2. OVERVIEW OF PRESENTATION:
MAXWELLS’S EQUATIONS
LORENTZ
TRANSFORMATIONS
MINKOWSKI SPACETIME
DIAGRAM
VISUALIZATION OF SPACE
TIME
APPLICATIONS

3. “
When you are courting a nice girl an hour seems like a second.When you sit on a
red-hot cinder a second seems like an hour. That’s relativity. -Albert Einstein
Relativity challenges your basic intutions that you’ve built up from everyday
experience.It says your experience of time is not what you think it is, that time is
malleable.Your experience of space is not what you think it is: it can stretch and
shrink. -Brian Greene
Einstein,in the special theory of relativity, proved that different obsevers, in
different states of motion, see different realities. -Leonard Susskind
No person can escape Einsteinian relativity, and no soldier or veteran can
escape the trauma of war’s discolation. -Thomas Cochrane
QUOTATIONS

4. MAXWELL’S EQUATIONS:A CONTRADICTION
Old Galilean view of space and time work to explain this?
WAVE EQUATION
• Light is an electromagnetic wave and
travels with speed c=3*10^8m/s
Any such beam of any kind of particles generated at the speed of light by a moving
observer would be received by a stationary observer at that same speed – regardless of
how fast the two observers were moving relative to one another.
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALISATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

5. RESEARCH PAPER ON SPECIAL RELATIVITY BY EINSTEIN

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yy
vtxx
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


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In Galilean relativity In Special relativity
Lorentz
transformations
LORENTZ TRANSFORMATIONS : A SOLUTION
Assumptions:
• Speed of light in vacuum remains same to every inertial observer regardless of the
motion of the source .
• Laws of physics hold in all inertial frames.
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALISATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

7. LORENTZ TRANSFORMATIONS : CONCLUSIONS
1.TIME DILATION
The faster you move ,the slower you would get.
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALISATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

8. LORENTZ TRANSFORMATIONS : CONCLUSIONS
2.LENGTH CONTRACTION
PROPER LENGTH
v = 10% c
v = 80% c
v = 99% c
WARNING : No contraction among perpendicular directions
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALISATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

9. SPACETIME: MINKOWSKI DIAGRAMS
Spacetime diagrams were first used by H. Minkowski in 1908 and are
often called Minkowski diagrams. Paths in Minkowski spacetime are
called worldlines.
If we consider two events, we can determine the quantity Δs2 between the two
events, and we find that it is invariant in any inertial frame. The quantity Δs is
known as the spacetime interval between two events.
Considering space and time together and taking into account that the speed of light must be
constant in any frame, we find that the new line element to satisfy such conditions is
ds2
= −𝑐2
d𝑡2
+ dx2
+ dy2
+ dz2
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALISATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

10. SPACETIME: MINKOWSKI DIAGRAMS
There are three possibilities for the invariant quantity Δs2:
1. Δs2 = 0: Δx2 = c2 Δt2, and the two events can be connected only
by a light signal. The events are said to have a lightlike separation.
2. Δs2 > 0: Δx2 > c2 Δt2, and no signal can travel fast enough to
connect the two events. The events are not causally connected and
are said to have a spacelike separation.
3. Δs2 < 0: Δx2 < c2 Δt2, and the two events can be causally
connected. The interval is said to be timelike.
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALISATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

11. SPACETIME: MINKOWSKI DIAGRAMS
To illustrate observer situated in an inertial frame, it is convenient to overlay spacetime
diagrams as seen by an observer.
x
t
T axis:
when we are not moving, then our path corresponds to the
t axis. Or in general, the t axis is the trajectory of the
observer which perceives himself as stationary.
X axis:
This axis basically shows all events that happen at the same
time
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALIZATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

12. SPACETIME: MINKOWSKI DIAGRAMS
The Sun right now.
It’s 8 light minutes away, what happen
over there right now is not going to
affect us till 8 minutes later.
We are here
right now.
Assume that we
don’t move
about.
The Sun’s future
light cone.
Our trajectory in
spacetime.
Our trajectory intersects with the Sun’s future
light cone – we see the light from the Sun that is
emitted ‘now’ 8 minutes ‘later.’
Trajectory of a spaceship
moving away from Earth in
direction opposite from the Sun.
The light from the Sun
finally catches up with
the spaceship.

13. SPACETIME: MINKOWSKI DIAGRAMS:GEOMETRY
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALIZATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

14. SPACETIME: MINKOWSKI DIAGRAMS:GEOMETRY
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALIZATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

15. SPACETIME: MINKOWSKI DIAGRAMS:GEOMETRY
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALIZATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

16. VISUALIZATION OF SPECIAL RELATIVITY
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALIZATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

17. SPACETIME MAKES SENSE
The views of space and time which I wish to lay before
you have sprung from the soil of experimental physics,
and therein lies their strength. They are radical.
Henceforth space by itself, and time by itself, are
doomed to fade away into mere shadows, and only a
kind of union of the two will preserve an independent
reality. – Hermann Minkowski ,1908
(22 June 1864 – 12 January 1909)

18. APPLICATIONS:
1. Even light is bent by gravity!
The position of a star observed during
an eclipse confirmed Einstein’s theory
2.Black holes
Dying stars can become black holes - gravity to an
extreme! At some point, even light cannot escape!
So named as “black holes” because you cannot see
them … but you can see stuff around them
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALIZATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

19. (Object moving away)
3.Relative motion in the Universe
Red shift
(Object approaching)
Blue shift
APPLICATIONS:
▹ MAXWELLS’
S
EQUATIONS
▹ LORENTZ
TRANSFOR
MATIONS
▹ MINKOWSKI
SPACETIME
DIAGRAM
▹ VISUALIZATI
ON OF
SPACE TIME
▹ APPLICATIO
NS

20. THANK YOU!!!
ANY
QUESTIONS??

21. REFERENCES:
1. NEIL TUROK TALK AT PERIMETER INSTITUTE “ASTONISHING SIMPLICITY OF EVERYTHING”.
2. “A FIRST COURSE IN GENERAL RELATIVITY”-BERNARD SCHUTZ.
3. GOOGLE IMAGES
4. JUAN MALCADENA TALK AT PERIMRTER INSTITUTE
5. BRAINY QUOTES