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1. 1 SPECIAL AND GENERAL THEORIES OF RELATIVITY for Physical Science/ Grade 11 Quarter 4/ Week 7 NegOr_Q4_PhySci11_SLKWeek7_v2
2. NegOr_Q4_PhySci11_SLKWeek7_v2 2 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.
3. NegOr_Q4_PhySci11_SLKWeek7_v2 3 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.
4. NegOr_Q4_PhySci11_SLKWeek7_v2 4 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
5. NegOr_Q4_PhySci11_SLKWeek7_v2 5 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
6. NegOr_Q4_PhySci11_SLKWeek7_v2 6 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?
7. NegOr_Q4_PhySci11_SLKWeek7_v2 7 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.
8. NegOr_Q4_PhySci11_SLKWeek7_v2 8 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:
9. NegOr_Q4_PhySci11_SLKWeek7_v2 9 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.
10. NegOr_Q4_PhySci11_SLKWeek7_v2 10 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
11. NegOr_Q4_PhySci11_SLKWeek7_v2 11 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)
12. NegOr_Q4_PhySci11_SLKWeek7_v2 12 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
13. NegOr_Q4_PhySci11_SLKWeek7_v2 13 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.
14. NegOr_Q4_PhySci11_SLKWeek7_v2 14 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).
15. NegOr_Q4_PhySci11_SLKWeek7_v2 15 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.
16. NegOr_Q4_PhySci11_SLKWeek7_v2 16 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.
17. NegOr_Q4_PhySci11_SLKWeek7_v2 17 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
18. NegOr_Q4_PhySci11_SLKWeek7_v2 18 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
19. NegOr_Q4_PhySci11_SLKWeek7_v2 19 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.
20. NegOr_Q4_PhySci11_SLKWeek7_v2 20 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.
21. NegOr_Q4_PhySci11_SLKWeek7_v2 21 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.