The document discusses the concept of time dilation, which refers to the difference in elapsed time measured by two clocks due to relative velocity or gravitational potential. It includes examples such as the μ meson decay experiment, applications in GPS navigation, particle accelerators, and atomic clocks, illustrating the practical effects of time dilation. The document also touches on the philosophical implications of time and relativity, quoting Albert Einstein.

1. T I M E D I L A T I O N
Presented By:
Ranjith.K.S
Sastra Deemed
University

2. Proper Time :
Time interval between two events measured by
a clock that occur at same place in observers
frame of reference is called proper time of
interval between events.
03/10/2024 2

3. 03/10/2024 3
Is Time
Constant
or
Relative ?

4. Is time constant or relative ?
“Put your hand on a hot stove for a minute, and it seems
like an hour. Sit with a pretty girl for an hour, and it seems
like a minute. That's relativity.”
_Albert Einstein
03/10/2024 4

5. What is time dilation?
Time dilation is the difference in
elapsed time as measured by two
clocks, either because of a
relative velocity between them, or a
difference in gravitational potential
between their locations. When
unspecified, "time dilation" usually
refers to the effect due to velocity.
03/10/2024 5

6. Lorentz Inverse Transform Equation:
S S’
Consider two systems S and S’. S’ is moving with velocity V relative
to S. The time interval observed by the observer in S’ frame will be
hen the time interval observed by the observer in S frame will be
Δ 𝑇′
=𝑇1
′
−𝑇 2
′
Δ 𝑇 =𝑇 1−𝑇 2
𝑇
′
=
𝑇 −
𝑥𝑣
𝐶
2
√1 −
𝑣2
𝐶
2
𝑇 1
′
=
𝑇 1 −
𝑥𝑣
𝐶
2
√1 −
𝑣2
𝐶2
𝑇 2
′
=
𝑇 2−
𝑥𝑣
𝐶
2
√1 −
𝑣2
𝐶2
Δ 𝑇′
=
𝑇 1 − 𝑇2
√1 −
𝑣2
𝐶
2
=
Δ 𝑇
√1 −
𝑣2
𝐶
2
⇒
03/10/2024 6
……………………… A
……………………… 1
……………………… 2

7. Time Dilation Verification Experiment – μ meson Decay:
• μ-meson are created at high altitude in the earth's atmosphere (about
10 km).
• By fast cosmic ray photons and are projected towards the earth
surface with very high speed, about 2.994 x 108 m/sec. Which is 0.998
of the speed of light.
• µ-meson are unstable and decay into positrons and electrons with an
average life time of 2 x 10-6 sec; therefore, μ meson can travel a
distance.
d=v*t 600m
≈
• This is because of the time dilation effect; in fact, μ-meson has an
average life time 2μ sec in its own frame of reference, but in the
observers frame of reference, the earth surface life time of μ-meson
is lengthened or diluted due to the relativity effect.
• Hence this experiment shows the time dilation is a real effect.
03/10/2024 7

8. Application of Time Dilation:
Imagine that 40-year-old men fail in love with a 16-year-
old girl. They want to marry but have an age difference.
Scientists plan to marry them by principle of time dilation.
He synchronizes his clock. He goes on a long space
journey in a spaceship moving with 0.999C velocity; he
returns back after 1 year, and he finds
Δ 𝑇′
=
1
√1 −
(0.998 𝐶)
2
𝑐
2
=22 ⋅7 𝑦 ⅇ 𝑎𝑟𝑠
Age of girl =16+22.7=38.7 years
age of men = 40+1=41 years
03/10/2024 8
1. Time Travel

9. 03/10/2024 9
2. GPS Navigation: The clocks used in GPS satellites are adjusted to
account for the time dilation effects of their high altitude and high velocity
orbits. Without this adjustment, GPS signals would become inaccurate and
navigation would be impossible.
3. Particle Accelerators: In particle accelerators, particles are
accelerated to nearly the speed of light, which causes time dilation. This
allows scientists to study particles for longer periods of time and observe
their behavior.
4. Atomic Clocks: Atomic clocks are the most accurate timekeeping
devices available and are used in a variety of scientific and
technological applications. The accuracy of atomic clocks is affected by
time dilation, which must be taken into account when using them for
precise measurements.