The document discusses the concept of time dilation, which arises from changes in frame of reference, as described in the theory of relativity. It outlines the time dilation formula, experimental evidence using cosmic ray particles, and applications in hypothetical time travel scenarios. Additionally, it touches on paradoxes and questions related to time travel and its relation to nature's balance.

1. Presented By :
Mayank Panchal
Abhishek Natani

2. Topic to be covered
1. Terminologies used in time
dilation.
2.What is time dilation .
3.Time dilation formula .
4.Experimental proof of time
dilation.
5.Application of time dilation.
6.Time dilation and nature .

3. Terminologies used in time dilation
Proper time : Time interval between
two events that occur at same place in
observers frame of reference is called
proper time of interval between events .
Lorentz transformation equation :
𝑡′
=
𝑡−
𝑥𝑣
𝐶2
1−
𝑣2
𝐶2

4. Time dilation:
Time dilation is phenomenon which
occurs due to change in frame of
reference.
In the theory of relativity, time dilation
is a difference of elapsed time between
two events as measured by observers
either moving relative to each other or
differently situated from gravitational
masses.

5. X
Y
Z
X’
Y’
Z’
S S’
v
o O’
Time dilation formula:

6. Consider two system s and s’. S’ is moving with
velocity v relative to s along direction of x-axis .
Let clock be situated at x’ in frame s’ and given
signals are interval .
Δ𝑡′
= 𝑡2
′
− 𝑡1
′
…………………(1)
Then interval observed by observer in frame s will
be
Δ𝑡 = 𝑡2 − 𝑡1 …………………..(2)
From Lorentz transformation equation we have

7. 𝒕 𝟐
′
=
𝒕 𝟐−
𝒗𝒙
𝑪 𝟐
𝟏−
𝒗 𝟐
𝑪 𝟐
………..(3)
𝒕 𝟏
′
=
𝒕 𝟏−
𝒗𝒙
𝑪 𝟐
𝟏−
𝒗 𝟐
𝑪 𝟐
…………(4)
By equation (3) and (4)
Δ𝑡′ =
𝑡2 − 𝑡1
1 −
𝑣2
𝐶2
=
Δ𝑡
1 −
𝑣2
𝐶2

8. Because 𝚫𝒕′ ≫ 𝜟𝒕
hence a clock moving with a uniform velocity v
relative to an observer appears to him to go
slow by a factor
1 −
𝑣2
𝐶2
Then when at rest relative to him this
effect is called time dilation.

9. Experimental prof of time dilation :
The confirmation of time dilation is found in a experiment on
cosmic ray
Particle called “meson”.
µ-meson are created at high altitude in earth atmospheric (about
10 km)
By fast cosmic ray photons and are projected towards earth
surface with very high speed about 2.994 x 108 m/sec . Which is
0.998 of speed of light
. µ-meson are unstable and decay into positron and electron with
an average life time of 2 x 10−6
sec therefore in its life time a µ-
meson can travel a distance.
d=vt ≈ 600m
Now, question arises how µ-meson travel a distance 10 km to
reach earth surface. This is because of time dilation effect in fact
µ-meson have an average life time 2 µsec in its own frame of
reference in the observers frame of reference in earth surface life
time is lengthen or diluted due to relativity effect to the value t.

10. 𝒕 =
𝒕 𝟎
𝟏−
𝑽 𝟐
𝒄 𝟐
= 𝟑. 𝟏𝟕 𝐱 𝟏𝟎−𝟓 sec
In this dilated time a µ-meson can travel a
distance
d=vt = 0.998 x 3.17 x 10−5
= 10 km = 103 m
This explains presence of µ-meson on earth
surface despite their brief time life hence this
shows time dilation is real effect.

11. Applications of time dilation:
Imagine that 40 year old men fail in love with a 16
year old girl
They want to marry but age difference . Scientists
plan to marry them by principle of time dilation. He
synchronises his clock men goes to a long space
journey in space ship moving with 0.999C velocity
he return back after 1 year and he finds
Δ𝑡′ =
1
1−
0.999𝐶
𝐶2
2 =22.7 years
Age of girl =16+22.7=38.7 years
age of men = 40+1 =41 years

13. Time travel :
Actually going to future and past.
Time machine is a way to travel in time .
Although it works on time dilation concept but
still it is hypothetical for us because till now we
are unable to make a ideal time machine .
In history we can see the reflection of it .

14. There is no way of knowing what are the
earliest concepts of time travel but there
are many old stories about traveling
forwards in time:
1. 700’s BCE to 300’s CE –Mahabharatha
King Revaita travels to heaven to meet the
creator Brahama, but when he travels back to
Earth, he finds out many years have passed.

15. 2. 720 CE- Urashima Taro – A young
fisherman named Urashima Taro travels to an
undersea palace for three days and finds out
three hundred years have passed on the
surface
3. 1819 Rip Van Winkle – A man named Rip
Van Winkle takes a nap at the top of a
mountain and wakes up twenty years in the
future.
4. 1771 – L’An 2440, reve s’il en fut jamais –
The main character falls asleep and wakes up
in Paris during the year 2440.

17. Time dilation and nature :
Nature is having a tendency of to balance itself
if a part of it get disturb then other part
changes to balance it . some of examples are
give below to prove it .
1. The Grandfather Paradox :
If you could go back in time, you could kill
your grandfather before he could produce any
offspring
But,

18. if you did that, then there would have been no
you to make a time machine and go and kill
him!
Which means that you can’t have killed him…

19. Fathering Yourself is Impossible:
How is it possible for someone to be their
own father??
To father yourself, you would have to
procreate with your mother, but that
probably requires a few shots… and
backwards causation – doesn’t it?
Surely it would be causing a change in the
past, which is impossible!

20. The past has already happened, so how can
we change it?

22. If we require energy to travel through the 3
spatial dimensions ,why don’t we require any
energy to travel through the time dimension
?
So, according to basic lows of the universe
everything that want’s to propagate anywhere
requires energy too to change space time. Let’s
suppose I am standing stationary and opposing wind
force etc…
So I spend zero energy but wait , after an hour the
time on clock has changed and I have an amazing
thought, well why didn’t I required energy to travel
in this dimension. I mean if I require energy for
other dimension why not time .