UNIT 12: RELATIVITY CONCEPTS AND POSTULATES OF SPECIAL RELATIVITY
Key unit competence: By the end of the unit, I be able to analyse
Relativity Concepts and postulates of special relativity.
Unit Objectives:
By the end of this unit I will be able to;
◊ Explain the concept of general and special relativity.◊ Explain the concept of the frames of reference and apply it in other theories.
Introductory Activity
On the first day of traveling in a car, Shyaka observed trees, stones,
mountains and all stationary saw them moving in the direction where
the car was coming from.
a. Were the trees, stones and mountains actually moving?
b. If No, why did Shakya see them moving?
c. As Shyaka and friends in the same car tried to take over another
speeding vehicle that was travelling in the same direction with
the same speed, Shyaka observed that the car they were trying
to overtake seemed to be stationary. Explain the cause of this
effect.
12.0 INTRODUCTION
The general theory of relativity developed in the early 20th century, originally
attempted to account for certain anomalies in the concept of relative motion.
But it has developed into one of the most important basic concepts in
physical science. The theory of relativity, developed primarily by German
American physicist Albert Einstein, is the basis for later demonstration by
physicists of the essential unity of matter and energy of space and time of
gravity and acceleration.
12.1 DEFINITION OF RELATIVITY
This is a theory developed by Albert Einstein which says that anything
except light moving with respect to the time and space depends on the
position and movement of the observer. Einstein’s special theory of relativity
(special relativity) is all about what’s relative and what’s absolute about
time, space and motion.
The theory states that the laws of motion are the same for all inertial
(non-accelerating) frames of reference and that the speed of light (in a
vacuum) is the same for all inertial reference frames. This leads to the
equivalence of mass and energy, time dilation, and length contraction.
Special relativity requires us to think of space and time as inextricably
linked. All our measurements of distance and time depend on the motion
of the observer. The effects of time dilation and length contraction are only
observed at very high speeds (close to the speed of light).
Thus, in Physics, Relativity refers to Einstein’s theory that time and space
are not absolute. OR, Anything except light moves with respect to time and
space depends on the position and movement of someone who is watching.
12.2 CONCEPT OF SPACE, TIME AND MASS
Time Dilation
Time dilation is the phenomenon where two objects, moving with respect
to each other (or even just a different intensity of gravitational field from
each other) experience different rates of time flow.
Time dilation becomes most apparent when one of the objects is moving at
nearly the speed of light, but it manifests at even slower speeds. Here are
just a few ways we know time dilation actually takes place:
• Clocks in airplanes click at different rates from clocks on the ground.
• Putting a clock on a mountain (thus elevating it, but keeping it
stationary relative to the ground-based clock) results in slightly
different rates.
• The Global Positioning System (GPS) has to adjust for time dilation.
Ground-based devices have to communicate with satellites. To work,
they have to be programmed to compensate for the time differences
based on their speeds and gravitational influences.
Let’s construct a light beam clock. It consists of two mirrors, one at a
distance D above the other. At t = 0, we launch a photon of light upwards
from the bottom of the mirror. It reflects from the top mirror and returns toits starting position, use c as the speed of the photon;
This is the time for one tick of our clock. At least this shows how it seems
to someone at rest with respect to the clock. But how does this appear to an
observer watching us and our clock moves by at constant velocity v? Thisobserver sees the events as pictured below.
Length Contraction
If we turn our light beam clock to face in the direction of motion, time
dilation implies length contraction. If the observer at rest with respect
to the clock (now a ruler) says it has proper length L0
, then an observer
on the earth watching him and his clock/ruler by velocity v sees the ruler
having length L. Objects look shorter (they are contracted) in the directionof motion.
Application Activity 12.1
12.3 CONCEPT OF FRAME OF REFERENCE
Imagine you threw and caught a ball while you were on a train moving at
a constant velocity past a station. To you, the ball appears to simply travel
vertically up and then down under the influence of gravity. However, to an
observer stood on the station platform, the ball would appear to travel in
a parabola, with a constant horizontal component of velocity equal to thevelocity of the train. This is illustrated in Fig.12-4 below.
The different observations occur because the two observers are in different
frames of reference.
This means that when you are standing on the ground, that is your frame
of reference. Anything that you see, watch or measure will be compared to
the reference point of the ground. If a person is standing in the back of a
moving truck, the truck is now the frame of reference and everything will
be measured compared to it.
Types of Frame of Reference
There are two types of frames of reference.
Inertial Frame of Reference: It is a frame of reference in which a body
remains at rest or moves with constant linear velocity unless acted upon
by forces. Any frame of reference that moves with constant velocity with
respect to an inertial system is itself an inertial system. In other words, itis the frame of reference in which Newton’s first law of motion holds good.
Non-inertial Frame of Reference: This is a frame of reference that is
undergoing acceleration with respect to an inertial frame. An accelerometer
at rest in a non-inertial frame will in general detect a non-zero acceleration.In this frame of reference, Newton’s first law of motion does not hold good.
12.4 GALILEAN EQUATION OF TRANSFORMATION
Galilean transformations, also called Newtonian transformations, are set
of equations in classical physics that relate the space and time coordinates
of two systems moving at a constant velocity with respect to each other.
Galilean transformations formally express the ideas that space and time
are absolute; that length, time, and mass are independent of the relative
motion of the observer; and that the speed of light depends upon the relative
motion of the observer.
Let there be two inertial frames of references S and S′ where S is the
stationary frame of reference and S′ is the moving frame of reference. At
time t = t′ = 0, i.e., in the start, they are at the same position, i.e., observers
O and O′ coincide. After that S′ frame starts moving with a uniform velocity
Let an event happen at position A in
the frame S′. The coordinate of the P will be x′ according to O′, the observer
in S′ and it will be x according to O in S. The frame S′ has moved a distance
The Galilean transformation relates the coordinates of events as measured
in both frames. Given the absolute nature of time, Newtonian physics, it isthe same for both frames. So, this may look over-elaborate if we write.
Activity 12-1: Frames of Reference
Aim: this activity aims at explaining the frames of reference.
a) How many passengers are moving? How many passengers are notmoving? Explain your answer.
b) How many images there on the frame? Explain your answer. (do not
consider the ground and the sky)
12.5 POSTULATES OF SPECIAL THEORY OF
RELATIVITY
With two deceptively simple postulates and a careful consideration of how
measurements are made, Einstein produced the theory of special relativity.
First postulate: The Principle of Relativity
This states that the laws of physics are the same in all inertial frames of
reference.
This postulate relates to reference frames. It says that there is no preferred
frame and, therefore, no absolute motion.
To understand the meaning of this postulate, consider the following
situation.
You are sitting in a train that is stopped at a railway station. Another train
is facing the opposite direction on the track directly beside you. Ten minutes
before your train is due to leave, you look out through the window at the
other train and see that it is slowly starting to move relative to yours. Your
first reaction would probably be one of surprise: your train was leaving
early! After passing the train from your window, you might notice that the
station was still there, and you realize that it was the other train that was
moving.
Second postulate: The Principle of Invariant Light Speed
The speed of light is a constant, independent of the relative motion of the
source and observer.
The speed of light in vacuum (c = 3 × 108 m/s ) is so high that we do not notice
a delay between the transmission and reception of electromagnetic waves
under normal circumstances. The speed of light in vacuum is actually the
only speed that is absolute and the same for all observers as was stated in
the second postulate.
12.6 CONCEPT OF SIMULTANEITY
The concept of simultaneity says that two events that are simultaneous to
one observer are not necessarily simultaneous to a second observer. Both
observers are correct in their observations -- there is no best or preferred
frame of reference.
If the speed of light is the same in all moving coordinate systems, this means
that events that occur simultaneously in one system may not be observed asbeing simultaneous in another coordinate system.
An example is illustrated in the Fig. 12.7 below.
An observer O′ stands in the middle of a moving boxcar and another observer
O stands at rest beside the track. When the positions of the observers
coincide, a lightning bolt strikes at each end of the boxcar, leaving mass on
the ground and at each end of the boxcar. The light from the lightning strikes
at A and B reaches to observer O at the same time, so observer O′ concludes
that the lightning strikes occurred simultaneously. But to observer O′ in
the moving boxcar, the lightning strikes do not appear to occur at the same
time. The light traveling from A′ to O′ travels further than the light from B′
to O′. Because of the motion, O′ moves towards the incoming beam from B′
and away from the incoming beam from A′. So to observer O′ the strike at
B′ appeared to occur before the strike at A′.
END OF UNIT ASSESSMENT
1. If you were on a spaceship travelling at 0.50c away from a star, when
would the starlight pass you?
2. Does time dilation mean that time actually passes more slowly in
moving references frames or that it only seems to pass more slowly?
3. If you were travelling away from the Earth at 0.50c, would you notice
a change in your heartbeat? Would your mass, height, or waistline
change? What would observers on the earth using a telescope to see
you say about you?
4. What happens to the relativistic factor
when objects travel
at normal everyday velocities?
5. A spaceship travels at 0.99c for 3 years ship time. How much time
would pass on the earth?
6. A spaceship is travelling at a speed of 0.94c. It has gone from the earth
for a total of 10 years as measured by the people of the earth. Howmuch time will pass on the spaceship during its travel?
7. A spaceship has gone from the earth for a total time of 5 years ship
time. The people on the earth have measured the time for the ship to
be away to 25 years. How fast was the ship travelling?
8. A 520 m long (measured when the spaceship is stationary) spaceship
passes by the earth. What length would the people on the earth say the
spaceship was as it passed the earth at 0.87c?
9. A 25 m long beam is shot past a stationary space station at 0.99c. What
length does the people on board the space station measure the beam to
be?
10. A 100 m long steel beam is moving past the earth. Observers on the
earth actually measure the steel beam to be only 50 m long. How fastwas the beam travelling?
UNIT SUMMARY
Definition of relativity
Anything except light moves with respect to time and space depends on the
position and movement of someone who is watching.
Concept of space, time and mass
• Time Dilation
Time dilation is the phenomenon where two objects moving relative
to each other (or even just a different intensity of gravitational field
from each other) experience different rates of time flow. The totaltime is given by
Postulates of special theory of relativity
• First postulate
This states that the laws of physics are the same in all inertial frames
of reference.
This postulate relates to reference frames. It says that there is no
preferred frame and, therefore, no absolute motion.
• Second postulate
This states that speed of light, c is a constant, independent of therelative motion of the source and observer.
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