1
SPECIAL AND GENERAL
THEORIES OF RELATIVITY
for Physical Science/ Grade 11
Quarter 4/ Week 7
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FOREWORD
This self-learning kit will serve as a guide to understand the
Special Theory of Relativity of the genius, Albert Einstein. This will also
explain how it resolved the conflict between Newtonian mechanics
and Maxwell’s electromagnetic theory.
In this self-learning kit, you will learn how special relativity
eliminates the paradox with respect to Newtonian physics and
electromagnetism of what does a light ray `look like' when the
observer is moving at the speed of light. The solution is that only
massless photons can move at the speed of light, and that matter
must remain below the speed of light regardless of how much
acceleration is applied.
In special relativity, there is a natural upper limit to velocity, the
speed of light. And the speed of light is the same in all directions
with respect to any frame.
This self-learning kit will also serve as a guide to identify the
Special and General Theories of Relativity of Albert Einstein. This will
explain the consequences of the postulates of these two theories.
Hence, you will be able to gain knowledge as to how the theory of
relativity is traditionally broken into two parts, special and general
relativity. Special relativity provides a framework for translating
physical events and laws into forms appropriate for any inertial frame
of reference. General relativity addresses the problem of
accelerated motion and gravity.

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LEARNING COMPETENCIES
• Explain how special relativity resolved the conflict between
Newtonian mechanics and Maxwell’s electromagnetic
theory (S11/12PS-Ivi-j-69)
• Explain the consequences of the postulates of Special and
General Theories of Relativity (S11/12PS-Ivi-j-70 & 71)
OBJECTIVES
At the end of the lesson, the learners will be able to:
K: determine the premise and facts that support the special and
general theories of relativity;
S: describe the consequences of the postulates of the special
and general theories of relativity; and
S: recognize the significant impact of the theory of relativity.

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I. WHAT HAPPENED
PRE-ACTIVITIES/PRE-TEST
Part A: Arrange the scrambled words below. Write your answers in the
notebook.
1. EIMT - the indefinite continued progress of existence and events in
the past, present, and future regarded as a whole.
2. AEPCS - the dimensions of height, depth, and width within which all
things exist and move.
3. THILG - refers to electromagnetic radiation of any wavelength,
whether visible or not.
4. IOTYEVLC - refers to the rate at which an object changes its position.
5. OIOTMN - is the phenomenon in which an object changes its position
over time.
Part B: Storytelling: Let’s take a trip down memory lane!!!
In 1894, a high school teacher suggested to one of his precocious learners
that he should leave because, he was unhappy. The teenager took that advice
and never came back. Later, he tried to apply to a prestigious school university,
but failed the entrance exam. Later in his life, when he tried to get his dream job
as a professor, no university would hire him. He had to settle for a lowly job as a
clerk at a patent office. History does not remember the name of the teacher, or
the names of the universities that rejected him for a job, but it will never forget
that teenager, because he went on to not only revolutionized physics, but
changed the way we view reality itself. In 1999, Time magazine named him
“man of the century.” Today, his name is synonymous with “genius”.
I am talking, of course, about Albert Einstein. Yet this entire revolution in
physics started with a simple thought experiment, conjured up in the prolific
imagination of a teenager before he even graduated from high school.
Einstein’s theory of special relativity is convention today, but to
understand how revolutionary it was for its time, it’s helpful to look at what the

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conventional understanding of physics was during the time of Einstein’s teenage
years.
First, in 1801 Thomas Young had conducted a simple double slit
experiment that showed that light behaved like a wave. So, the predominant
theory about light at the time was that it was a wave. The problem is that a
wave, it was thought, had to move through some sort of medium. Something
has to be there to make the wave – similar to how waves at an ocean need
water to create a wave. But light was known to travel through outer space,
obvious because you can see star light. Yet, outer space was believed to be
empty, containing nothing. And it could be easily demonstrated the light can
indeed travel in a vacuum. So scientists thought that the only way light waves
could travel through the vacuum was if there was some kind of medium that
pervaded space and the entire cosmos. They called this substance the
“luminiferous ether.” And this theory of ether was the standard theory of physics
for most of the 19th century. Later in that same century in 1887, two scientists by
the name of Albert Michelson and Edward Morley, came up with an idea to test
the existence of ether. The background ether was believed to be unmoving and
static, but because the earth was moving it was thought that it would affect the
speed of particles (or waves), if the wave was traveling in the same direction as
the earth. The speed of the wave should be higher in the direction of the speed
of the earth. This would be similar to how a boat moves faster if it’s moving with
the flow of the current than if it is moving against current. To test this hypothesis,
Michelson and Morley designed a device that split a beam of light and bounce
it off mirrors so that it moved in different directions, and finally hit the same
target. The idea was that if two beams travel the same distance along different
paths through the ether, they should move at different speeds. And therefore,
when they hit the final target screen those light beams would be slightly out of
phase with each other, which would create an interference pattern. The results
of this test were astonishing. They showed that there was no difference in the
speed of light of the two measurements. No matter which path the beam took,
light seemed to be moving at precisely the same speed. This seriously
jeopardized the ether theory at least for light. No one could make sense of this
or come up with an alternate theory to explain it. It was labeled “the greatest
failed experiment of all time.”
This is where Albert Einstein comes in. The term relativity had been around
even before Albert Einstein. But it was thought of in a completely different way.
The term had originated with Galileo Galilei. He and Isaac Newton had
demonstrated relativity. In 1873, it had been recently proposed by James Clerk
Maxwell that light was an electromagnetic wave. And he had calculated its
speed, which was approximately 186,000 miles/second. Einstein knew this. And
he came up with a thought experiment as a sixteen-year-old. His thought was to

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imagine that he was chasing a beam of light while traveling at the speed of
light himself. What would he see? If young Albert could catch up to the beam,
he writes in his notes, “I should observe such a beam of light as an
electromagnetic field at rest, though spatially oscillating.” In other words, Einstein
thought that he should see a stationary wave of light. Yet, that was impossible.
Einstein knew that such stationary fields would violate equations of
electromagnetism developed by James Clerk Maxwell, twenty years earlier.
The laws were quite strict. Any riffles in the electromagnetic field have to
move at the speed of light and cannot stand still. There are no exemptions. In
addition, Einstein reasoned that if someone was traveling on a non-accelerating
train at close to the speed of light, there would be no way for that person to
know how fast he was going, if there were no windows. This had been the
classical view of relativity. Why should the laws of physics be different for a
person traveling at some fixed velocity, versus someone standing still? This
seemed untenable to Einstein. So, he came up with two postulates…
(adapted from https://www.youtube.com/watch?v=ZAf7FXih-Jc)
Questions: (Write your answer in the notebook)
1. Who was named as "man of the century" by the Time magazine and whose
name is synonymous with "genius"?
2. How did Michelson and Morley disprove the presence of ether?
3. What was the simple thought experiment? And how did it lead to probably
the biggest revolution in physics since Isaac Newton?

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II. WHAT I NEED TO KNOW
THE THEORY OF RELATIVITY
Einstein's theory of relativity deals with Newtonian physics when energies or
velocities are near the speed of light. Relativity is usually thought of as modern
physics since it was developed at the start of the 20th century and could only
be tested in the realm available to scientists by high technology. However,
relativity primarily completes the revolution that Newton started and is also
highly deterministic as is much of classical physics.
Source: http://abyss.uoregon.edu/~js/ast122/lectures/lec20.html
In the holistic viewpoint of relativity theory, concepts such as length, mass and
time take on a much more nebulous aspect than they do in the apparently rigid
reality of our everyday world. However, what relativity takes away with one
hand, it gives back in the form of new and truly fundamental constants and
concepts.
The theory of relativity is traditionally broken into two parts, special and general
relativity. Special relativity provides a framework for translating physical events
and laws into forms appropriate for any inertial frame of reference. General
relativity addresses the problem of accelerated motion and gravity.

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Special Theory of Relativity
By the late 1800's, it was becoming obvious that there were some serious
problems for Newtonian physics concerning the need for absolute space and
time when referring to events or interactions (frames of reference). In particular,
the newly formulated theory of electromagnetic waves required that light
propagation occur in a medium (the waves had to be waves on something).
In a Newtonian Universe, there should be no difference in space or time
regardless of where you are or how fast you are moving. In all places, a meter is
a meter and a second is a second. And you should be able to travel as fast as
you want, with enough acceleration (i.e. force).
In the 1890's, two physicists (Michelson and Morley) were attempting to measure
the Earth's velocity around the Sun with respect to Newtonian’s absolute space
and time. This would also test how light waves propagated since all waves must
move through a medium. For light, this hypothetical medium was called the
ether.
The results of the Michelson-Morley experiment was that the velocity of light was
constant regardless of how the experiment was tilted with respect to the Earth's
motion. This implied that there was no ether and, thus, no absolute space. Thus,
objects, or coordinate systems, moving with constant velocity (called inertial
frames) were relative only to themselves.
In Newtonian mechanics, quantities such as speed and distance may be
transformed from one frame of reference to another, provided that the frames
are in uniform motion (i.e. not accelerating).
Considering the results of the Michelson-Morley experiment led Einstein to
develop the theory of special relativity. The key premise to special relativity is
that the speed of light (called c = 186,000 miles per sec) is constant in all frames
of reference, regardless of their motion. What this means can be best
demonstrated by the following scenario:

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Figure 1: A photon that propagates electric and magnetic waves
Source: Relativity (uoregon.edu)
The illustration above explains that Einstein noticed a logical flaw with time and
space (frames of reference) and light as electromagnetic waves. A stationary
observer (a person not moving) only sees a photon as a self-propagating
electric and magnetic wave. If the observer is moving at the speed of light
(moving at the same speed as the waves) then the wave motion and the
electric and magnetic fields cannot support themselves.
Source: Relativity (uoregon.edu)
Because of this, Einstein concluded that the speed of light is the upper limit of
motion. Based on this conclusion, he believed that observers must always move
slower than the speed of light and only massless particles like photons can move
at the speed of light. This notion becomes the foundation for the special theory
of relativity. This eliminates the paradox with respect to Newtonian physics and
electromagnetism of what does a light ray `look like' when the observer is
moving at the speed of light.
The change in time is called time dilation, where frames moving near the speed
of light have slow clocks.
Likewise, space is shortened in high velocity frames, which is called Lorentz
contraction.

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Time dilation leads to the famous Twins Paradox, which is not a paradox but
rather a simple fact of special relativity. Since clocks run slower in frames of
reference at high velocity, then one can imagine a scenario were twins age at
different rates when separated at birth due to a trip to the stars.
It is worth noting that direct experiments, largely utilizing subatomic particles in
high-energy accelerators, have proven all of special relativity's predictions,
including length contraction, time dilation, and the twin paradox. The effects of
relativity are dramatic, but only when speeds approach the speed of light. At
normal velocities, the changes to clocks and rulers are too small to be
measured. However, near extreme objects, such as black holes and neutron
stars relativity dominates over Newtonian physics.
Special relativity describes changes in size and time through the use of Lorentz
transformations. For an event that lasts to seconds in your frame, the same event
will appear to last t in a frame that is moving with velocity v such that:
to = t/(1-(v/c)2)1/2
where c is the speed of light.
Spacetime
The theory of special relativity proved that spatial and temporal coordinates
have a connection. Despite the fact that time and three-dimensional space
coordinates are physically distinct, their properties are so closely linked that it
only makes sense to represent them as a four-dimensional continuum.
Spacetime makes sense from special relativity since it was shown that spatial
coordinates (Lorentz contraction) and temporal coordinates (time dilation) vary
between frames of reference. Notice that under spacetime, time does not
`happen' as perceived by humans, but rather all of the time exists, stretched out
like space in its entirety. Time is simply ‘there'.
Theory of General Relativity
Mass-Energy Equivalence
Because special relativity shows that space and time are variable concepts in
different frames of reference, velocity (space divided by time) also becomes a

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variable. If velocity varies from one reference frame to the next, velocity-related
notions must be relative as well. Momentum, or motion energy, is one such idea.
Under special relativity, momentum, as described by Newtonian mechanics,
cannot be conserved from one frame to the next. A new parameter, relativistic
momentum, has to be defined, which is conserved only when the mass of the
object is added to the momentum equation.
This has a big impact on classical physics because it means there is an
equivalence between mass and energy, summarized by the famous Einstein
equation:
The implications of this were not realized for many years. For example, the
production of energy in nuclear reactions (i.e. fission and fusion) was shown to
be the conversion of a small amount of atomic mass into energy. This led to the
development of nuclear power and weapons.
As an object is accelerated close to the speed of light, relativistic effects begin
to dominate. In particular, adding more energy to an object will not make it go
faster since the speed of light is the limit. The energy has to go somewhere, so it
is added to the mass of the object, as observed from the rest frame. Thus, we
say that the observed mass of the object goes up with increased velocity. So, a
spaceship would appear to gain the mass of a city, then a planet, then a star,
as its velocity is increased.
Figure 2: Object’s mass increases as it approaches the speed of light
Source: Relativity (uoregon.edu)

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Similarly, Einstein was able to anticipate that the photon possesses momentum
despite its mass being zero due to the equivalence of mass and energy. As a
result, light sails and photoelectric detectors can be developed.
Spacetime and Energy
Special relativity and E=mc2 led to the most powerful unification of physical
concepts since the time of Newton. The previously separate ideas of space,
time, energy, and mass were linked by special relativity, although without a
clear understanding of how they were linked.
Figure 3: Unified physical concepts
Source: Relativity (uoregon.edu)
The how and why were left to the area of general relativity, a full theory of
gravity based on spacetime geometry. Einstein's attempt to apply special
relativity in accelerating frames of reference gave rise to general relativity.
Remember that the theories of relativity were developed for inertial frames, or

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those that move at a constant speed. Adding acceleration was a challenge
that Einstein struggled with for ten years.
Equivalence Principle
The equivalence principle was Einstein's `Newton's apple' insight to gravitation.
His thought experiment was the following, imagine two elevators, one at rest of
the Earth's surface, one accelerating in space. To an observer inside the
elevator (no windows) there is no physical experiment that he/she could
perform to differentiate between the two scenarios.
Figure 4: Comparison between two elevators
Source: Relativity (uoregon.edu)
Gravity bends light as an immediate result of the equivalence principle.
Imagine a photon passing the elevator and accelerating into space to
understand why this is true. The floor accelerates upward as the photon
traverses the elevator, and the photon appears to fall below. By the
equivalence principle, the same must be true in a gravitational field.
The principle of equivalence renders the gravitational field fundamentally
different from all other force fields encountered in nature. The new theory of
gravitation, the general theory of relativity, adopts this characteristic of the
gravitational field as its foundation.

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General Relativity
The theory of general relativity, the second component of relativity, is based on
two empirical results that he raised to the rank of fundamental postulates. The
first postulate is the relativity principle, which states that the theory of special
relativity governs local physics. The equivalence principle is the second
postulate: an observer cannot differentiate between gravity and acceleration
locally.
Figure 5: Representation of the 1st and 2nd Postulates of General Relativity
Source: Relativity (uoregon.edu)
Einstein discovered that there is a relationship between mass, gravity and
spacetime. Mass distorts spacetime, causing it to curve.
Figure 6: Relationship between mass, gravity, and space time
Source: Relativity (uoregon.edu)
Gravity can be described as motion caused in curved spacetime .
Thus, the primary result from general relativity is that gravitation is a purely
geometric consequence of the properties of spacetime. Special relativity
destroyed classical physics view of absolute space and time, general relativity
dismantles the idea that spacetime is described by Euclidean or plane
geometry. In this sense, general relativity is a field theory, relating Newton's law
of gravity to the field nature of spacetime, which can be curved.
In general relativity, gravity is described as curved spacetime. The equivalence
principle extends the idea that motion distorts spacetime, as it does in special
relativity, to gravity. Because matter is the source of gravity, the existence of
matter generates distortions or warps in spacetime. Matter tells spacetime how
to curve, and spacetime tells matter how to move (orbits).

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There were two classical tests of general relativity, the first was that light should
be deflected by passing close to a massive body. The first opportunity occurred
during a total eclipse of the Sun in 1919.
Figure 7: Relationship between matter and spacetime
Source: Relativity (uoregon.edu)
Stellar locations near the darkened solar limb were measured, proving Einstein
correct. The Hubble Space Telescope got direct confirmation of gravitational
lensing.
The second test is that general relativity predicts a time dilation in a gravitational
field, such that clocks (or atomic processes) move slowly in comparison to
someone outside the field. On the mid-1970s, atomic clocks flying in planes
confirmed this.
The general theory of relativity is constructed so that its results are approximately
the same as those of Newton's theories as long as the velocities of all bodies
interacting with each other gravitationally are small compared with the speed
of light--i.e., as long as the gravitational fields involved are weak. The latter
requirement may be stated roughly in terms of the escape velocity. If the
escape velocity approaches the speed of light, the gravitational field is strong; if
it is much smaller, it is feeble. In this sense, all gravitational fields encountered in
the solar system are weak.
Notice that at low speeds and weak gravitational fields, general and special
relativity reduce to Newtonian physics, i.e. everyday experience.

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Summary:
Special Theory of Relativity
Two assumptions underpin Einstein's special theory of relativity. The
consistent law principle, which is founded on the notion that all motions are
relative to the chosen reference frame, is the first principle. This principle can be
stated as follows:
The laws of physics are the same in all frames of reference that are moving at
a constant velocity with respect to one another.
The second principle has something to do with the speed of light. This is
called the constancy of speed principle. It can be stated as follows:
The speed of light in empty space has the same magnitude for all observers
regardless of their velocity.
You have learned that the speed of light in empty space is 3x108 m/s. An
observer traveling toward a light source would perceive light to be traveling at
3x108 m/s. Light would appear to be traveling at 3x108 m/s to an observer who is
not moving in relation to the source. The speed of light would remain constant
regardless of the velocity of the source of light and the velocity of the observer.
Consequences of the Postulates of the Special Theory of Relativity
The special theory of relativity is based solely on the principles of
consistency and the principle of constancy. These principles have very
interesting consequences if you are observing from the ground. While on the
ground, you may compare the measurements of length, time, and mass of a
very fast airplane. While on the ground, you will find that
1. an object’s length shortens while moving (length contraction) –
this means that the observer measures a moving object’s length as smaller
than it would be if it is not moving;
2. clocks run slowly while moving (time dilation) – this means the
slowing of the passage of time experienced by objects in motion relative to an
observer and it is measurable only at relativistic speeds; and
3. the mass of objects increases while moving.

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Therefore, we can conclude that time is relative. It flows at different rates for
different observers. Let us also consider the fact that time and space are not
independent. Special relativity has been verified by countless experiments and
the predicted results always fit Einstein’s equations. This is no fiction at all. This is
how the universe works.
General Theory of Relativity
Einstein’s general theory of relativity has two postulates.
• All laws of nature have the same form for observers in any frame of
reference whether it is accelerated or not.
• In the vicinity of any point, a gravitational field is equivalent to an
accelerated frame of reference in the absence of gravitational effects.
The general theory of relativity predicted the existence of gravitational
waves. Some of the consequences of the theory is that ‘time is altered by
gravity.’
➢ A clock in the presence of gravity runs slower than when there is no
gravity.
➢ Evidence of the theory is the very slight shift in the orbit of Mercury.
➢ The differences between the Newtonian and Einsteinian conceptions
of gravity become significant only in regions where the escape
velocity approaches the speed of light.
➢ The properties of extraordinarily dense collapsed stars can be
explained by the general theory of relativity.
➢ Black holes, as they are called, are very dense that the escape
velocity exceeds that of light
Performance Task
Make a short essay by answering the question below using the concepts and
understanding of the special and general theories of relativity. Do this in your
activity notebook/sheet.
“How did the theory of relativity impact society and change the world?”
Grading criteria: Content---------------------------10 points
Cohesiveness-------------------10 points
Total------------------------------- 20 points

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III. WHAT I HAVE LEARNED
POST-TEST/EVALUATION
A. True or False. Read carefully the statements below. Write T if the statement is
correct and F if it is wrong. Do this in your activity sheet/notebook.
_____ 1. According to Einstein, if an observer moves at the speed of light, there
can be motion of waves and photon can exist.
_____ 2. Einstein concluded that only massless particles like photons can move at
the speed of light.
_____ 3. The key premise to special relativity is that the speed of light changes in
all frames of reference, regardless of their motion.
_____ 4. Time dilation states that frames moving near the speed of light have fast
clocks.
_____ 5. Lorentz contraction determines that an object moving close to the
speed of light appears to be shortened.
B. Essay. Make a brief and concise explanation to the questions below.
1. What is the significant relationship of mass, gravity, and spacetime in general
theory of relativity?
2. What could be the consequences of the postulates of special and general
theories of relativity?
3. In what phenomena can we predict the difference of General relativity and
Newtonian physics?
Criteria for grading
Organization ----------- 5 points
Accuracy----------------5 points
Total-----------------------10 points

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References
Caintic, H. E. Physical science. Quezon City: C & E Publishing, Inc., 2016.
Relativity.Abyss.uoregon.edu.http://abyss.uoregon.edu/~js/ast122/lectures/lec2
0.html. Retrieved June 15, 2021.

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ACKNOWLEDGMENT
DEPARTMENT OF EDUCATION
SCHOOLS DIVISION OF NEGROS ORIENTAL
SENEN PRISCILLO P. PAULIN, CESO V
Schools Division Superintendent
JOELYZA M. ARCILLA EdD
OIC - Assistant Schools Division Superintendent
MARCELO K. PALISPIS EdD
OIC - Assistant Schools Division Superintendent
NILITA L. RAGAY EdD
OIC - Assistant Schools Division Superintendent / CID Chief
ROSELA R. ABIERA
Education Program Supervisor – (LRMS)
ARNOLD R. JUNGCO
PSDS – Division Science Coordinator
MARICEL S. RASID
Librarian II (LRMDS)
ELMAR L. CABRERA
PDO II (LRMDS)
FRUSSELL V. ELTANAL
Writer
Noelyn Siapno
Lay – Out Artists
________________________________
ALPHA QA TEAM
LIEZEL A. AGOR
EUFRATES G. ANSOK
JOAN Y. BUBULI
MA. OFELIA BUSCATO
LIELIN A. DE LA ZERNA
DEXTER D. PAIRA
BETA QA TEAM
LIEZEL A. AGOR - BESAS
JOAN Y. BUBULI - VALENCIA
LIELIN A. DE LA ZERNA
PETER PAUL A. PATRON
THOMAS JOGIE U. TOLEDO
DISCLAIMER
The information, activities and assessments used in this material are designed to provide
accessible learning modality to the teachers and learners of the Division of Negros Oriental. The
contents of this module are carefully researched, chosen, and evaluated to comply with the set
learning competencies. The writers and evaluator were clearly instructed to give credits to
information and illustrations used to substantiate this material. All content is subject to copyright
and may not be reproduced in any form without expressed written consent from the division.

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SYNOPSIS AND ABOUT THE AUTHOR
AUTHOR
Frussell V. Eltanal is a Registered Nurse who graduated in
Silliman University. He took a Crash Program in Education
at LCC-Bais campus. He is a Licensed Professional
Teacher who is currently teaching at Gregorio Elmaga
Memorial High School - Senior High School Department –
in Nasig-id, Zamboanguita, Negros Oriental, Philippines.
He is currently taking up Master of Arts in Science
Teaching at Negros Oriental State University.
This lesson validates and clarifies some
misconceptions about the nature of the
Universe. As it has always been reiterated,
the special and general theories of relativity
by the great Einstein revolutionized the world
of physics.