Post on 02-Jun-2018
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Time Dilation , LengthContraction and Mass Increase
Group 1
Asmah Syafitri
Dian Purnamasari
Yudhistira
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Speed of light is constant
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Our conceptions of space and time has to be
changed.
Facts:
Regardless of speed or direction, observers always
measure the speed of light to be the same value.
Speed of light is maximum possible speed.
Consequences:
The length of an object decreases as its speed
increases
Clocks passing by you run more slowly than do clocks
at rest
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Time dilation
Laser bounces up and down from mirror on train.
Joe on ground measures time interval w/ his clock.
Joe watches Janesclock on train as she measuresthe time interval.
Joe sees that these two time intervals are different.
Reference frame
of Janeon train Reference frameof Joeon ground
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Why is this?
Jane on train: light pulse travels distance 2d.
Joe on ground: light pulse travelsfarther Relativity: both Joe and Jane say light travels at c
Joe measures longer travel time of light pulse
This is time dilation
Reference frame of
Janeon train
Reference frame of
Joeon ground
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Time dilation, continued
ObserverJaneon train: light pulse travels distance 2d. Time = distance divided by velocity = 2d/c
Time in the frame the events occurred at same location
called the proper time tp
Reference frame of Jane
on train
Reference frame of
Joeon ground
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Joe measures a longertime
Time dilation
Time interval in Janes frame
tJane round trip distancespeedof light
2dc
tJoe2 d2 vtJoe /2
2
c
1
1 (v /c)21
tJoe
1
1 (v /c)22d
c
tpd
(vt)/2
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Time Dilation
Events occur in the same location are denoted with the prime frame, S.
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The proper time We are concerned with two time intervals.
Intervals between two events.
A single observer compares time intervals measured in
different reference frames.
If the events are at the same spatial location in
one of the frames
The time interval measured in this frame
is called the proper time.
The time interval measured in a frame moving with
respect to this one will be longer by a factor of tother frametproper, 1
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Length contractionAs measured by anEarthling the Earth-to-star distance is Lo, theproper length as measured by an observer atrest with respect to the ends of the ruler, andthe time to make the trip is t. An Astronautmeasures the distance to be L& the time to.
Voyage to a star!
Lo L
u
u u
to
t
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Length Contraction
The Idea :
If the time intervals are different, and speed isthe same, how can distances be the same?
The distances are not the same!Length contraction
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Length Contraction
Spaceship Moving at the 10 % the Speed of Light
Spaceship Moving at the 86.5 % the Speed of Light
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Length Contraction
Spaceship Moving at the 99 % the Speed of Light
Spaceship Moving at the 99.99 % the Speed of Light
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Length contraction and proper length
Which one is correct?
Just like time intervals,distances are different in different frames.
There is no preferred frame,so one is no more correct than the other.
The proper length Lpis the length measuredin a frame at rest with respect to objects
Here the objects are Earth and star.
LLp
Lp 1
v 2
c 2
Length in moving
frame
Length in objects
rest frame
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